+++ /dev/null
-/*
- * f25519.c: arithmetic modulo 2^255 - 19
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the 16/32-bit implementation, since C99 always has 64-bit
- * arithmetic.
- *
- * * Remove the test rig code: a replacement is in a separate source file.
- *
- * * Disable some of the operations which aren't needed for X25519.
- * (They're used for Ed25519, which we don't need.)
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * Arithmetic modulo 2^255 - 19
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "f25519.h"
-
-/*----- Basic setup -------------------------------------------------------*/
-
-/* Elements x of GF(2^255 - 19) are represented by ten signed integers x_i: x
- * = SUM_{0<=i<10} x_i 2^ceil(51i/2), mostly following Bernstein's original
- * paper.
- */
-
-typedef int32 piece; typedef int64 dblpiece;
-typedef uint32 upiece; typedef uint64 udblpiece;
-#define P p26
-#define PIECEWD(i) ((i)%2 ? 25 : 26)
-#define NPIECE 10
-
-#define M26 0x03ffffffu
-#define M25 0x01ffffffu
-#define B26 0x04000000u
-#define B25 0x02000000u
-#define B24 0x01000000u
-
-#define PIECES(v) v##0, v##1, v##2, v##3, v##4, v##5, v##6, v##7, v##8, v##9
-#define FETCH(v, w) do { \
- v##0 = (w)->P[0]; v##1 = (w)->P[1]; \
- v##2 = (w)->P[2]; v##3 = (w)->P[3]; \
- v##4 = (w)->P[4]; v##5 = (w)->P[5]; \
- v##6 = (w)->P[6]; v##7 = (w)->P[7]; \
- v##8 = (w)->P[8]; v##9 = (w)->P[9]; \
-} while (0)
-#define STASH(w, v) do { \
- (w)->P[0] = v##0; (w)->P[1] = v##1; \
- (w)->P[2] = v##2; (w)->P[3] = v##3; \
- (w)->P[4] = v##4; (w)->P[5] = v##5; \
- (w)->P[6] = v##6; (w)->P[7] = v##7; \
- (w)->P[8] = v##8; (w)->P[9] = v##9; \
-} while (0)
-
-/*----- Debugging machinery -----------------------------------------------*/
-
-#if defined(F25519_DEBUG)
-
-#include <stdio.h>
-
-#include "mp.h"
-#include "mptext.h"
-
-static mp *get_2p255m91(void)
-{
- mpw w19 = 19;
- mp *p = MP_NEW, m19;
-
- p = mp_setbit(p, MP_ZERO, 255);
- mp_build(&m19, &w19, &w19 + 1);
- p = mp_sub(p, p, &m19);
- return (p);
-}
-
-DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 32, get_2p255m91())
-
-#endif
-
-/*----- Loading and storing -----------------------------------------------*/
-
-/* --- @f25519_load@ --- *
- *
- * Arguments: @f25519 *z@ = where to store the result
- * @const octet xv[32]@ = source to read
- *
- * Returns: ---
- *
- * Use: Reads an element of %$\gf{2^{255} - 19}$% in external
- * representation from @xv@ and stores it in @z@.
- *
- * External representation is little-endian base-256. Some
- * elements have multiple encodings, which are not produced by
- * correct software; use of noncanonical encodings is not an
- * error, and toleration of them is considered a performance
- * feature.
- */
-
-void f25519_load(f25519 *z, const octet xv[32])
-{
- uint32 xw0 = LOAD32_L(xv + 0), xw1 = LOAD32_L(xv + 4),
- xw2 = LOAD32_L(xv + 8), xw3 = LOAD32_L(xv + 12),
- xw4 = LOAD32_L(xv + 16), xw5 = LOAD32_L(xv + 20),
- xw6 = LOAD32_L(xv + 24), xw7 = LOAD32_L(xv + 28);
- piece PIECES(x), b, c;
-
- /* First, split the 32-bit words into the irregularly-sized pieces we need
- * for the field representation. These pieces are all positive. We'll do
- * the sign correction afterwards.
- *
- * It may be that the top bit of the input is set. Avoid trouble by
- * folding that back round into the bottom piece of the representation.
- *
- * Here, we briefly have 0 <= x_0 < 2^26 + 19, but will resolve this later.
- * Otherwise, we have 0 <= x_{2i} < 2^26, and 0 <= x_{2i+1} < 2^25.
- */
- x0 = ((xw0 << 0)&0x03ffffff) + 19*((xw7 >> 31)&0x00000001);
- x1 = ((xw1 << 6)&0x01ffffc0) | ((xw0 >> 26)&0x0000003f);
- x2 = ((xw2 << 13)&0x03ffe000) | ((xw1 >> 19)&0x00001fff);
- x3 = ((xw3 << 19)&0x01f80000) | ((xw2 >> 13)&0x0007ffff);
- x4 = ((xw3 >> 6)&0x03ffffff);
- x5 = (xw4 << 0)&0x01ffffff;
- x6 = ((xw5 << 7)&0x03ffff80) | ((xw4 >> 25)&0x0000007f);
- x7 = ((xw6 << 13)&0x01ffe000) | ((xw5 >> 19)&0x00001fff);
- x8 = ((xw7 << 20)&0x03f00000) | ((xw6 >> 12)&0x000fffff);
- x9 = ((xw7 >> 6)&0x01ffffff);
-
- /* Next, we convert these pieces into a roughly balanced signed
- * representation. For each piece, check to see if its top bit is set. If
- * it is, then lend a bit to the next piece over. For x_9, this needs to
- * be carried around, which is a little fiddly. In particular, we delay
- * the carry until after all of the pieces have been balanced. If we don't
- * do this, then we have to do a more expensive test for nonzeroness to
- * decide whether to lend a bit leftwards rather than just testing a single
- * bit.
- *
- * This fixes up the anomalous size of x_0: the loan of a bit becomes an
- * actual carry if x_0 >= 2^26. By the end, then, we have:
- *
- * { 2^25 if i even
- * |x_i| <= {
- * { 2^24 if i odd
- *
- * Note that we don't try for a canonical representation here: both upper
- * and lower bounds are achievable.
- *
- * All of the x_i at this point are positive, so we don't need to do
- * anything wierd when masking them.
- */
- b = x9&B24; c = 19&((b >> 19) - (b >> 24)); x9 -= b << 1;
- b = x8&B25; x9 += b >> 25; x8 -= b << 1;
- b = x7&B24; x8 += b >> 24; x7 -= b << 1;
- b = x6&B25; x7 += b >> 25; x6 -= b << 1;
- b = x5&B24; x6 += b >> 24; x5 -= b << 1;
- b = x4&B25; x5 += b >> 25; x4 -= b << 1;
- b = x3&B24; x4 += b >> 24; x3 -= b << 1;
- b = x2&B25; x3 += b >> 25; x2 -= b << 1;
- b = x1&B24; x2 += b >> 24; x1 -= b << 1;
- b = x0&B25; x1 += (b >> 25) + (x0 >> 26); x0 = (x0&M26) - (b << 1);
- x0 += c;
-
- /* And with that, we're done. */
- STASH(z, x);
-}
-
-/* --- @f25519_store@ --- *
- *
- * Arguments: @octet zv[32]@ = where to write the result
- * @const f25519 *x@ = the field element to write
- *
- * Returns: ---
- *
- * Use: Stores a field element in the given octet vector in external
- * representation. A canonical encoding is always stored, so,
- * in particular, the top bit of @xv[31]@ is always left clear.
- */
-
-void f25519_store(octet zv[32], const f25519 *x)
-{
- piece PIECES(x), PIECES(y), c, d;
- uint32 zw0, zw1, zw2, zw3, zw4, zw5, zw6, zw7;
- mask32 m;
-
- FETCH(x, x);
-
- /* First, propagate the carries throughout the pieces. By the end of this,
- * we'll have all of the pieces canonically sized and positive, and maybe
- * there'll be (signed) carry out. The carry c is in { -1, 0, +1 }, and
- * the remaining value will be in the half-open interval [0, 2^255). The
- * whole represented value is then x + 2^255 c.
- *
- * It's worth paying careful attention to the bounds. We assume that we
- * start out with |x_i| <= 2^30. We start by cutting off and reducing the
- * carry c_9 from the topmost piece, x_9. This leaves 0 <= x_9 < 2^25; and
- * we'll have |c_9| <= 2^5. We multiply this by 19 and we'll add it onto
- * x_0 and propagate the carries: but what bounds can we calculate on x
- * before this?
- *
- * Let o_i = floor(51 i/2). We have X_i = SUM_{0<=j<i} x_j 2^{o_i}, so
- * x = X_10. We see, inductively, that |X_i| < 2^{31+o_{i-1}}: X_0 = 0;
- * |x_i| <= 2^30; and |X_{i+1}| = |X_i + x_i 2^{o_i}| <= |X_i| + 2^{30+o_i}
- * < 2^{31+o_i}. Then x = X_9 + 2^230 x_9, and we have better bounds for
- * x_9, so
- *
- * -2^235 < x + 19 c_9 < 2^255 + 2^235
- *
- * Here, the x_i are signed, so we must be cautious about bithacking them.
- */
- c = ASR(piece, x9, 25); x9 = (upiece)x9&M25;
- x0 += 19*c; c = ASR(piece, x0, 26); x0 = (upiece)x0&M26;
- x1 += c; c = ASR(piece, x1, 25); x1 = (upiece)x1&M25;
- x2 += c; c = ASR(piece, x2, 26); x2 = (upiece)x2&M26;
- x3 += c; c = ASR(piece, x3, 25); x3 = (upiece)x3&M25;
- x4 += c; c = ASR(piece, x4, 26); x4 = (upiece)x4&M26;
- x5 += c; c = ASR(piece, x5, 25); x5 = (upiece)x5&M25;
- x6 += c; c = ASR(piece, x6, 26); x6 = (upiece)x6&M26;
- x7 += c; c = ASR(piece, x7, 25); x7 = (upiece)x7&M25;
- x8 += c; c = ASR(piece, x8, 26); x8 = (upiece)x8&M26;
- x9 += c; c = ASR(piece, x9, 25); x9 = (upiece)x9&M25;
-
- /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and
- * x >= 2^255 - 19, then we should subtract 2^255 - 19 from the whole
- * value; if c = -1 then we should add 2^255 - 19; and otherwise we should
- * do nothing.
- *
- * But conditional behaviour is bad, m'kay. So here's what we do instead.
- *
- * The first job is to sort out what we wanted to do. If c = -1 then we
- * want to (a) invert the constant addend and (b) feed in a carry-in;
- * otherwise, we don't.
- */
- m = SIGN(c);
- d = m&1;
-
- /* Now do the addition/subtraction. Remember that all of the x_i are
- * nonnegative, so shifting and masking are safe and easy.
- */
- d += x0 + (19 ^ (M26&m)); y0 = d&M26; d >>= 26;
- d += x1 + (M25&m); y1 = d&M25; d >>= 25;
- d += x2 + (M26&m); y2 = d&M26; d >>= 26;
- d += x3 + (M25&m); y3 = d&M25; d >>= 25;
- d += x4 + (M26&m); y4 = d&M26; d >>= 26;
- d += x5 + (M25&m); y5 = d&M25; d >>= 25;
- d += x6 + (M26&m); y6 = d&M26; d >>= 26;
- d += x7 + (M25&m); y7 = d&M25; d >>= 25;
- d += x8 + (M26&m); y8 = d&M26; d >>= 26;
- d += x9 + (M25&m); y9 = d&M25; d >>= 25;
-
- /* The final carry-out is in d; since we only did addition, and the x_i are
- * nonnegative, then d is in { 0, 1 }. We want to keep y, rather than x,
- * if (a) c /= 0 (in which case we know that the old value was
- * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that
- * the subtraction didn't cause a borrow, so we must be in the case where
- * 2^255 - 19 <= x < 2^255).
- */
- m = NONZEROP(c) | ~NONZEROP(d - 1);
- x0 = (y0&m) | (x0&~m); x1 = (y1&m) | (x1&~m);
- x2 = (y2&m) | (x2&~m); x3 = (y3&m) | (x3&~m);
- x4 = (y4&m) | (x4&~m); x5 = (y5&m) | (x5&~m);
- x6 = (y6&m) | (x6&~m); x7 = (y7&m) | (x7&~m);
- x8 = (y8&m) | (x8&~m); x9 = (y9&m) | (x9&~m);
-
- /* Extract 32-bit words from the value. */
- zw0 = ((x0 >> 0)&0x03ffffff) | (((uint32)x1 << 26)&0xfc000000);
- zw1 = ((x1 >> 6)&0x0007ffff) | (((uint32)x2 << 19)&0xfff80000);
- zw2 = ((x2 >> 13)&0x00001fff) | (((uint32)x3 << 13)&0xffffe000);
- zw3 = ((x3 >> 19)&0x0000003f) | (((uint32)x4 << 6)&0xffffffc0);
- zw4 = ((x5 >> 0)&0x01ffffff) | (((uint32)x6 << 25)&0xfe000000);
- zw5 = ((x6 >> 7)&0x0007ffff) | (((uint32)x7 << 19)&0xfff80000);
- zw6 = ((x7 >> 13)&0x00000fff) | (((uint32)x8 << 12)&0xfffff000);
- zw7 = ((x8 >> 20)&0x0000003f) | (((uint32)x9 << 6)&0x7fffffc0);
-
- /* Store the result as an octet string. */
- STORE32_L(zv + 0, zw0); STORE32_L(zv + 4, zw1);
- STORE32_L(zv + 8, zw2); STORE32_L(zv + 12, zw3);
- STORE32_L(zv + 16, zw4); STORE32_L(zv + 20, zw5);
- STORE32_L(zv + 24, zw6); STORE32_L(zv + 28, zw7);
-}
-
-/* --- @f25519_set@ --- *
- *
- * Arguments: @f25519 *z@ = where to write the result
- * @int a@ = a small-ish constant
- *
- * Returns: ---
- *
- * Use: Sets @z@ to equal @a@.
- */
-
-void f25519_set(f25519 *x, int a)
-{
- unsigned i;
-
- x->P[0] = a;
- for (i = 1; i < NPIECE; i++) x->P[i] = 0;
-}
-
-/*----- Basic arithmetic --------------------------------------------------*/
-
-/* --- @f25519_add@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the sum %$x + y$%.
- */
-
-void f25519_add(f25519 *z, const f25519 *x, const f25519 *y)
-{
- z->P[0] = x->P[0] + y->P[0]; z->P[1] = x->P[1] + y->P[1];
- z->P[2] = x->P[2] + y->P[2]; z->P[3] = x->P[3] + y->P[3];
- z->P[4] = x->P[4] + y->P[4]; z->P[5] = x->P[5] + y->P[5];
- z->P[6] = x->P[6] + y->P[6]; z->P[7] = x->P[7] + y->P[7];
- z->P[8] = x->P[8] + y->P[8]; z->P[9] = x->P[9] + y->P[9];
-}
-
-/* --- @f25519_sub@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the difference %$x - y$%.
- */
-
-void f25519_sub(f25519 *z, const f25519 *x, const f25519 *y)
-{
- z->P[0] = x->P[0] - y->P[0]; z->P[1] = x->P[1] - y->P[1];
- z->P[2] = x->P[2] - y->P[2]; z->P[3] = x->P[3] - y->P[3];
- z->P[4] = x->P[4] - y->P[4]; z->P[5] = x->P[5] - y->P[5];
- z->P[6] = x->P[6] - y->P[6]; z->P[7] = x->P[7] - y->P[7];
- z->P[8] = x->P[8] - y->P[8]; z->P[9] = x->P[9] - y->P[9];
-}
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_neg@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z = -x@.
- */
-
-void f25519_neg(f25519 *z, const f25519 *x)
-{
- z->P[0] = -x->P[0]; z->P[1] = -x->P[1];
- z->P[2] = -x->P[2]; z->P[3] = -x->P[3];
- z->P[4] = -x->P[4]; z->P[5] = -x->P[5];
- z->P[6] = -x->P[6]; z->P[7] = -x->P[7];
- z->P[8] = -x->P[8]; z->P[9] = -x->P[9];
-}
-
-#endif
-
-/*----- Constant-time utilities -------------------------------------------*/
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_pick2@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
- * @z = x@. If @m@ has some other value, then scramble @z@ in
- * an unhelpful way.
- */
-
-void f25519_pick2(f25519 *z, const f25519 *x, const f25519 *y, uint32 m)
-{
- mask32 mm = FIX_MASK32(m);
-
- z->P[0] = PICK2(x->P[0], y->P[0], mm);
- z->P[1] = PICK2(x->P[1], y->P[1], mm);
- z->P[2] = PICK2(x->P[2], y->P[2], mm);
- z->P[3] = PICK2(x->P[3], y->P[3], mm);
- z->P[4] = PICK2(x->P[4], y->P[4], mm);
- z->P[5] = PICK2(x->P[5], y->P[5], mm);
- z->P[6] = PICK2(x->P[6], y->P[6], mm);
- z->P[7] = PICK2(x->P[7], y->P[7], mm);
- z->P[8] = PICK2(x->P[8], y->P[8], mm);
- z->P[9] = PICK2(x->P[9], y->P[9], mm);
-}
-
-/* --- @f25519_pickn@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result
- * @const f25519 *v@ = a table of entries
- * @size_t n@ = the number of entries in @v@
- * @size_t i@ = an index
- *
- * Returns: ---
- *
- * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
- * do something unhelpful; otherwise, if @i >= n@ then set @z@
- * to zero.
- */
-
-void f25519_pickn(f25519 *z, const f25519 *v, size_t n, size_t i)
-{
- uint32 b = (uint32)1 << (31 - i);
- mask32 m;
-
- z->P[0] = z->P[1] = z->P[2] = z->P[3] = z->P[4] =
- z->P[5] = z->P[6] = z->P[7] = z->P[8] = z->P[9] = 0;
- while (n--) {
- m = SIGN(b);
- CONDPICK(z->P[0], v->P[0], m);
- CONDPICK(z->P[1], v->P[1], m);
- CONDPICK(z->P[2], v->P[2], m);
- CONDPICK(z->P[3], v->P[3], m);
- CONDPICK(z->P[4], v->P[4], m);
- CONDPICK(z->P[5], v->P[5], m);
- CONDPICK(z->P[6], v->P[6], m);
- CONDPICK(z->P[7], v->P[7], m);
- CONDPICK(z->P[8], v->P[8], m);
- CONDPICK(z->P[9], v->P[9], m);
- v++; b <<= 1;
- }
-}
-
-#endif
-
-/* --- @f25519_condswap@ --- *
- *
- * Arguments: @f25519 *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
- * exchange @x@ and @y@. If @m@ has some other value, then
- * scramble @x@ and @y@ in an unhelpful way.
- */
-
-void f25519_condswap(f25519 *x, f25519 *y, uint32 m)
-{
- mask32 mm = FIX_MASK32(m);
-
- CONDSWAP(x->P[0], y->P[0], mm);
- CONDSWAP(x->P[1], y->P[1], mm);
- CONDSWAP(x->P[2], y->P[2], mm);
- CONDSWAP(x->P[3], y->P[3], mm);
- CONDSWAP(x->P[4], y->P[4], mm);
- CONDSWAP(x->P[5], y->P[5], mm);
- CONDSWAP(x->P[6], y->P[6], mm);
- CONDSWAP(x->P[7], y->P[7], mm);
- CONDSWAP(x->P[8], y->P[8], mm);
- CONDSWAP(x->P[9], y->P[9], mm);
-}
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_condneg@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
- * @z = -x@. If @m@ has some other value then scramble @z@ in
- * an unhelpful way.
- */
-
-void f25519_condneg(f25519 *z, const f25519 *x, uint32 m)
-{
- mask32 m_xor = FIX_MASK32(m);
- piece m_add = m&1;
-# define CONDNEG(x) (((x) ^ m_xor) + m_add)
-
- z->P[0] = CONDNEG(x->P[0]);
- z->P[1] = CONDNEG(x->P[1]);
- z->P[2] = CONDNEG(x->P[2]);
- z->P[3] = CONDNEG(x->P[3]);
- z->P[4] = CONDNEG(x->P[4]);
- z->P[5] = CONDNEG(x->P[5]);
- z->P[6] = CONDNEG(x->P[6]);
- z->P[7] = CONDNEG(x->P[7]);
- z->P[8] = CONDNEG(x->P[8]);
- z->P[9] = CONDNEG(x->P[9]);
-
-#undef CONDNEG
-}
-
-#endif
-
-/*----- Multiplication ----------------------------------------------------*/
-
-/* Let B = 2^63 - 1 be the largest value such that +B and -B can be
- * represented in a double-precision piece. On entry, it must be the case
- * that |X_i| <= M <= B - 2^25 for some M. If this is the case, then, on
- * exit, we will have |Z_i| <= 2^25 + 19 M/2^25.
- */
-#define CARRYSTEP(z, x, m, b, f, xx, n) do { \
- (z) = (dblpiece)((udblpiece)(x)&(m)) - (b) + \
- (f)*ASR(dblpiece, (xx), (n)); \
-} while (0)
-#define CARRY_REDUCE(z, x) do { \
- dblpiece PIECES(_t); \
- \
- /* Bias the input pieces. This keeps the carries and so on centred \
- * around zero rather than biased positive. \
- */ \
- _t0 = (x##0) + B25; _t1 = (x##1) + B24; \
- _t2 = (x##2) + B25; _t3 = (x##3) + B24; \
- _t4 = (x##4) + B25; _t5 = (x##5) + B24; \
- _t6 = (x##6) + B25; _t7 = (x##7) + B24; \
- _t8 = (x##8) + B25; _t9 = (x##9) + B24; \
- \
- /* Calculate the reduced pieces. Careful with the bithacking. */ \
- CARRYSTEP(z##0, _t0, M26, B25, 19, _t9, 25); \
- CARRYSTEP(z##1, _t1, M25, B24, 1, _t0, 26); \
- CARRYSTEP(z##2, _t2, M26, B25, 1, _t1, 25); \
- CARRYSTEP(z##3, _t3, M25, B24, 1, _t2, 26); \
- CARRYSTEP(z##4, _t4, M26, B25, 1, _t3, 25); \
- CARRYSTEP(z##5, _t5, M25, B24, 1, _t4, 26); \
- CARRYSTEP(z##6, _t6, M26, B25, 1, _t5, 25); \
- CARRYSTEP(z##7, _t7, M25, B24, 1, _t6, 26); \
- CARRYSTEP(z##8, _t8, M26, B25, 1, _t7, 25); \
- CARRYSTEP(z##9, _t9, M25, B24, 1, _t8, 26); \
-} while (0)
-
-/* --- @f25519_mulconst@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$a x$%.
- */
-
-void f25519_mulconst(f25519 *z, const f25519 *x, long a)
-{
- piece PIECES(x);
- dblpiece PIECES(z), aa = a;
-
- FETCH(x, x);
-
- /* Suppose that |x_i| <= 2^27, and |a| <= 2^23. Then we'll have
- * |z_i| <= 2^50.
- */
- z0 = aa*x0; z1 = aa*x1; z2 = aa*x2; z3 = aa*x3; z4 = aa*x4;
- z5 = aa*x5; z6 = aa*x6; z7 = aa*x7; z8 = aa*x8; z9 = aa*x9;
-
- /* Following `CARRY_REDUCE', we'll have |z_i| <= 2^26. */
- CARRY_REDUCE(z, z);
- STASH(z, z);
-}
-
-/* --- @f25519_mul@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$x y$%.
- */
-
-void f25519_mul(f25519 *z, const f25519 *x, const f25519 *y)
-{
- piece PIECES(x), PIECES(y);
- dblpiece PIECES(z);
- unsigned i;
-
- FETCH(x, x); FETCH(y, y);
-
- /* Suppose that |x_i|, |y_i| <= 2^27. Then we'll have
- *
- * |z_0| <= 267*2^54
- * |z_1| <= 154*2^54
- * |z_2| <= 213*2^54
- * |z_3| <= 118*2^54
- * |z_4| <= 159*2^54
- * |z_5| <= 82*2^54
- * |z_6| <= 105*2^54
- * |z_7| <= 46*2^54
- * |z_8| <= 51*2^54
- * |z_9| <= 10*2^54
- *
- * all of which are less than 2^63 - 2^25.
- */
-
-#define M(a, b) ((dblpiece)(a)*(b))
- z0 = M(x0, y0) +
- 19*(M(x2, y8) + M(x4, y6) + M(x6, y4) + M(x8, y2)) +
- 38*(M(x1, y9) + M(x3, y7) + M(x5, y5) + M(x7, y3) + M(x9, y1));
- z1 = M(x0, y1) + M(x1, y0) +
- 19*(M(x2, y9) + M(x3, y8) + M(x4, y7) + M(x5, y6) +
- M(x6, y5) + M(x7, y4) + M(x8, y3) + M(x9, y2));
- z2 = M(x0, y2) + M(x2, y0) +
- 2* M(x1, y1) +
- 19*(M(x4, y8) + M(x6, y6) + M(x8, y4)) +
- 38*(M(x3, y9) + M(x5, y7) + M(x7, y5) + M(x9, y3));
- z3 = M(x0, y3) + M(x1, y2) + M(x2, y1) + M(x3, y0) +
- 19*(M(x4, y9) + M(x5, y8) + M(x6, y7) +
- M(x7, y6) + M(x8, y5) + M(x9, y4));
- z4 = M(x0, y4) + M(x2, y2) + M(x4, y0) +
- 2*(M(x1, y3) + M(x3, y1)) +
- 19*(M(x6, y8) + M(x8, y6)) +
- 38*(M(x5, y9) + M(x7, y7) + M(x9, y5));
- z5 = M(x0, y5) + M(x1, y4) + M(x2, y3) +
- M(x3, y2) + M(x4, y1) + M(x5, y0) +
- 19*(M(x6, y9) + M(x7, y8) + M(x8, y7) + M(x9, y6));
- z6 = M(x0, y6) + M(x2, y4) + M(x4, y2) + M(x6, y0) +
- 2*(M(x1, y5) + M(x3, y3) + M(x5, y1)) +
- 19* M(x8, y8) +
- 38*(M(x7, y9) + M(x9, y7));
- z7 = M(x0, y7) + M(x1, y6) + M(x2, y5) + M(x3, y4) +
- M(x4, y3) + M(x5, y2) + M(x6, y1) + M(x7, y0) +
- 19*(M(x8, y9) + M(x9, y8));
- z8 = M(x0, y8) + M(x2, y6) + M(x4, y4) + M(x6, y2) + M(x8, y0) +
- 2*(M(x1, y7) + M(x3, y5) + M(x5, y3) + M(x7, y1)) +
- 38* M(x9, y9);
- z9 = M(x0, y9) + M(x1, y8) + M(x2, y7) + M(x3, y6) + M(x4, y5) +
- M(x5, y4) + M(x6, y3) + M(x7, y2) + M(x8, y1) + M(x9, y0);
-#undef M
-
- /* From above, we have |z_i| <= 2^63 - 2^25. A pass of `CARRY_REDUCE' will
- * leave |z_i| <= 2^38 + 2^25; and a second pass will leave |z_i| <= 2^25 +
- * 2^13, which is comfortable for an addition prior to the next
- * multiplication.
- */
- for (i = 0; i < 2; i++) CARRY_REDUCE(z, z);
- STASH(z, z);
-}
-
-/* --- @f25519_sqr@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z@ to the square %$x^2$%.
- */
-
-void f25519_sqr(f25519 *z, const f25519 *x)
-{
- piece PIECES(x);
- dblpiece PIECES(z);
- unsigned i;
-
- FETCH(x, x);
-
- /* See `f25519_mul' for bounds. */
-
-#define M(a, b) ((dblpiece)(a)*(b))
- z0 = M(x0, x0) +
- 38*(M(x2, x8) + M(x4, x6) + M(x5, x5)) +
- 76*(M(x1, x9) + M(x3, x7));
- z1 = 2* M(x0, x1) +
- 38*(M(x2, x9) + M(x3, x8) + M(x4, x7) + M(x5, x6));
- z2 = 2*(M(x0, x2) + M(x1, x1)) +
- 19* M(x6, x6) +
- 38* M(x4, x8) +
- 76*(M(x3, x9) + M(x5, x7));
- z3 = 2*(M(x0, x3) + M(x1, x2)) +
- 38*(M(x4, x9) + M(x5, x8) + M(x6, x7));
- z4 = M(x2, x2) +
- 2* M(x0, x4) +
- 4* M(x1, x3) +
- 38*(M(x6, x8) + M(x7, x7)) +
- 76* M(x5, x9);
- z5 = 2*(M(x0, x5) + M(x1, x4) + M(x2, x3)) +
- 38*(M(x6, x9) + M(x7, x8));
- z6 = 2*(M(x0, x6) + M(x2, x4) + M(x3, x3)) +
- 4* M(x1, x5) +
- 19* M(x8, x8) +
- 76* M(x7, x9);
- z7 = 2*(M(x0, x7) + M(x1, x6) + M(x2, x5) + M(x3, x4)) +
- 38* M(x8, x9);
- z8 = M(x4, x4) +
- 2*(M(x0, x8) + M(x2, x6)) +
- 4*(M(x1, x7) + M(x3, x5)) +
- 38* M(x9, x9);
- z9 = 2*(M(x0, x9) + M(x1, x8) + M(x2, x7) + M(x3, x6) + M(x4, x5));
-#undef M
-
- /* See `f25519_mul' for details. */
- for (i = 0; i < 2; i++) CARRY_REDUCE(z, z);
- STASH(z, z);
-}
-
-/*----- More complicated things -------------------------------------------*/
-
-/* --- @f25519_inv@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
- * %$x = 0$% then @z@ is set to zero. This is considered a
- * feature.
- */
-
-void f25519_inv(f25519 *z, const f25519 *x)
-{
- f25519 t, u, t2, t11, t2p10m1, t2p50m1;
- unsigned i;
-
-#define SQRN(z, x, n) do { \
- f25519_sqr((z), (x)); \
- for (i = 1; i < (n); i++) f25519_sqr((z), (z)); \
-} while (0)
-
- /* Calculate x^-1 = x^(p - 2) = x^(2^255 - 21), which also handles x = 0 as
- * intended. The addition chain here is from Bernstein's implementation; I
- * couldn't find a better one.
- */ /* step | value */
- f25519_sqr(&t2, x); /* 1 | 2 */
- SQRN(&u, &t2, 2); /* 3 | 8 */
- f25519_mul(&t, &u, x); /* 4 | 9 */
- f25519_mul(&t11, &t, &t2); /* 5 | 11 = 2^5 - 21 */
- f25519_sqr(&u, &t11); /* 6 | 22 */
- f25519_mul(&t, &t, &u); /* 7 | 31 = 2^5 - 1 */
- SQRN(&u, &t, 5); /* 12 | 2^10 - 2^5 */
- f25519_mul(&t2p10m1, &t, &u); /* 13 | 2^10 - 1 */
- SQRN(&u, &t2p10m1, 10); /* 23 | 2^20 - 2^10 */
- f25519_mul(&t, &t2p10m1, &u); /* 24 | 2^20 - 1 */
- SQRN(&u, &t, 20); /* 44 | 2^40 - 2^20 */
- f25519_mul(&t, &t, &u); /* 45 | 2^40 - 1 */
- SQRN(&u, &t, 10); /* 55 | 2^50 - 2^10 */
- f25519_mul(&t2p50m1, &t2p10m1, &u); /* 56 | 2^50 - 1 */
- SQRN(&u, &t2p50m1, 50); /* 106 | 2^100 - 2^50 */
- f25519_mul(&t, &t2p50m1, &u); /* 107 | 2^100 - 1 */
- SQRN(&u, &t, 100); /* 207 | 2^200 - 2^100 */
- f25519_mul(&t, &t, &u); /* 208 | 2^200 - 1 */
- SQRN(&u, &t, 50); /* 258 | 2^250 - 2^50 */
- f25519_mul(&t, &t2p50m1, &u); /* 259 | 2^250 - 1 */
- SQRN(&u, &t, 5); /* 264 | 2^255 - 2^5 */
- f25519_mul(z, &u, &t11); /* 265 | 2^255 - 21 */
-
-#undef SQRN
-}
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_quosqrt@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
- *
- * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
- * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
- * \ne 0$% then the operation fails. If you wanted a specific
- * square root then you'll have to pick it yourself.
- */
-
-static const piece sqrtm1_pieces[NPIECE] = {
-#if F25519_IMPL == 26
- -32595792, -7943725, 9377950, 3500415, 12389472,
- -272473, -25146209, -2005654, 326686, 11406482
-#elif F25519_IMPL == 10
- 176, -88, 161, 157, -485, -196, -231, -220, -416,
- -169, -255, 50, 189, -89, -266, -32, 202, -511,
- 423, 357, 248, -249, 80, 288, 50, 174
-#endif
-};
-#define SQRTM1 ((const f25519 *)sqrtm1_pieces)
-
-int f25519_quosqrt(f25519 *z, const f25519 *x, const f25519 *y)
-{
- f25519 t, u, w, beta, xy3, t2p50m1;
- octet xb[32], b0[32], b1[32];
- int32 rc = -1;
- mask32 m;
- unsigned i;
-
-#define SQRN(z, x, n) do { \
- f25519_sqr((z), (x)); \
- for (i = 1; i < (n); i++) f25519_sqr((z), (z)); \
-} while (0)
-
- /* This is a bit tricky; the algorithm is from Bernstein, Duif, Lange,
- * Schwabe, and Yang, `High-speed high-security signatures', 2011-09-26,
- * https://ed25519.cr.yp.to/ed25519-20110926.pdf.
- *
- * First of all, a complicated exponentation. The addition chain here is
- * mine. We start with some preliminary values.
- */ /* step | value */
- SQRN(&u, y, 1); /* 1 | 0, 2 */
- f25519_mul(&t, &u, y); /* 2 | 0, 3 */
- f25519_mul(&xy3, &t, x); /* 3 | 1, 3 */
- SQRN(&u, &u, 1); /* 4 | 0, 4 */
- f25519_mul(&w, &u, &xy3); /* 5 | 1, 7 */
-
- /* And now we calculate w^((p - 5)/8) = w^(252 - 3). */
- SQRN(&u, &w, 1); /* 6 | 2 */
- f25519_mul(&t, &w, &u); /* 7 | 3 */
- SQRN(&u, &t, 1); /* 8 | 6 */
- f25519_mul(&t, &u, &w); /* 9 | 7 */
- SQRN(&u, &t, 3); /* 12 | 56 */
- f25519_mul(&t, &t, &u); /* 13 | 63 = 2^6 - 1 */
- SQRN(&u, &t, 6); /* 19 | 2^12 - 2^6 */
- f25519_mul(&t, &t, &u); /* 20 | 2^12 - 1 */
- SQRN(&u, &t, 12); /* 32 | 2^24 - 2^12 */
- f25519_mul(&t, &t, &u); /* 33 | 2^24 - 1 */
- SQRN(&u, &t, 1); /* 34 | 2^25 - 2 */
- f25519_mul(&t, &u, &w); /* 35 | 2^25 - 1 */
- SQRN(&u, &t, 25); /* 60 | 2^50 - 2^25 */
- f25519_mul(&t2p50m1, &t, &u); /* 61 | 2^50 - 1 */
- SQRN(&u, &t2p50m1, 50); /* 111 | 2^100 - 2^50 */
- f25519_mul(&t, &t2p50m1, &u); /* 112 | 2^100 - 1 */
- SQRN(&u, &t, 100); /* 212 | 2^200 - 2^100 */
- f25519_mul(&t, &t, &u); /* 213 | 2^200 - 1 */
- SQRN(&u, &t, 50); /* 263 | 2^250 - 2^50 */
- f25519_mul(&t, &t2p50m1, &u); /* 264 | 2^250 - 1 */
- SQRN(&u, &t, 2); /* 266 | 2^252 - 4 */
- f25519_mul(&t, &u, &w); /* 267 | 2^252 - 3 */
-
- /* And finally... */
- f25519_mul(&beta, &t, &xy3); /* 268 | ... */
-
- /* Now we have beta = (x y^3) (x y^7)^((p - 5)/8) = (x/y)^((p + 3)/8), and
- * we're ready to finish the computation. Suppose that alpha^2 = u/w.
- * Then beta^4 = (x/y)^((p + 3)/2) = alpha^(p + 3) = alpha^4 = (x/y)^2, so
- * we have beta^2 = ±x/y. If y beta^2 = x then beta is the one we wanted;
- * if -y beta^2 = x, then we want beta sqrt(-1), which we already know. Of
- * course, it might not match either, in which case we fail.
- *
- * The easiest way to compare is to encode. This isn't as wasteful as it
- * sounds: the hard part is normalizing the representations, which we have
- * to do anyway.
- */
- f25519_sqr(&t, &beta);
- f25519_mul(&t, &t, y);
- f25519_neg(&u, &t);
- f25519_store(xb, x);
- f25519_store(b0, &t);
- f25519_store(b1, &u);
- f25519_mul(&u, &beta, SQRTM1);
-
- m = -ct_memeq(b0, xb, 32);
- rc = PICK2(0, rc, m);
- f25519_pick2(z, &beta, &u, m);
- m = -ct_memeq(b1, xb, 32);
- rc = PICK2(0, rc, m);
-
- /* And we're done. */
- return (rc);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
+++ /dev/null
-/*
- * f25519.h: arithmetic modulo 2^255 - 19
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and lightly modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the 16/32-bit implementation, since C99 always has 64-bit
- * arithmetic.
- *
- * * Disable some of the operations which aren't needed for X25519.
- * (They're used for Ed25519, which we don't need.)
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * Arithmetic modulo 2^255 - 19
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_F25519_H
-#define CATACOMB_F25519_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-#ifndef CATACOMB_QFARITH_H
-# include "qfarith.h"
-#endif
-
-/*----- Data structures ---------------------------------------------------*/
-
-typedef union {
- int32 p26[10];
-} f25519;
-
-/*----- Functions provided ------------------------------------------------*/
-
-#define F25519_TRIM_X25519
-
-/* --- @f25519_set@ --- *
- *
- * Arguments: @f25519 *z@ = where to write the result
- * @int a@ = a small-ish constant
- *
- * Returns: ---
- *
- * Use: Sets @z@ to equal @a@.
- */
-
-extern void f25519_set(f25519 */*x*/, int /*a*/);
-
-/* --- @f25519_load@ --- *
- *
- * Arguments: @f25519 *z@ = where to store the result
- * @const octet xv[32]@ = source to read
- *
- * Returns: ---
- *
- * Use: Reads an element of %$\gf{2^{255} - 19}$% in external
- * representation from @xv@ and stores it in @z@.
- *
- * External representation is little-endian base-256. Elements
- * have multiple encodings, which are not produced by correct
- * software; use of noncanonical encodings is not an error, and
- * toleration of them is considered a performance feature.
- *
- * Some specifications, e.g., RFC7748, require the topmost bit
- * (i.e., bit 7 of @wv[31]@) to be ignored. Callers
- * implementing such specifications should clear the bit
- * explicitly. (It's much easier for a caller who wants the bit
- * to be ignored to clear it than for a caller who wants the bit
- * to be significant to apply the necessary change by hand.)
- */
-
-extern void f25519_load(f25519 */*z*/, const octet /*xv*/[32]);
-
-/* --- @f25519_store@ --- *
- *
- * Arguments: @octet zv[32]@ = where to write the result
- * @const f25519 *x@ = the field element to write
- *
- * Returns: ---
- *
- * Use: Stores a field element in the given octet vector in external
- * representation. A canonical encoding is always stored, so,
- * in particular, the top bit of @xv[31]@ is always left clear.
- */
-
-extern void f25519_store(octet /*zv*/[32], const f25519 */*x*/);
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_pick2@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, set @z = y@; if @m@ is all-bits-set, then set
- * @z = x@. If @m@ has some other value, then scramble @z@ in
- * an unhelpful way.
- */
-
-extern void f25519_pick2(f25519 */*z*/, const f25519 */*x*/,
- const f25519 */*y*/, uint32 /*m*/);
-
-/* --- @f25519_pickn@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result
- * @const f25519 *v@ = a table of entries
- * @size_t n@ = the number of entries in @v@
- * @size_t i@ = an index
- *
- * Returns: ---
- *
- * Use: If @0 <= i < n < 32@ then set @z = v[i]@. If @n >= 32@ then
- * do something unhelpful; otherwise, if @i >= n@ then set @z@
- * to zero.
- */
-
-extern void f25519_pickn(f25519 */*z*/, const f25519 */*v*/, size_t /*n*/,
- size_t /*i*/);
-
-#endif
-
-/* --- @f25519_condswap@ --- *
- *
- * Arguments: @f25519 *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
- * exchange @x@ and @y@. If @m@ has some other value, then
- * scramble @x@ and @y@ in an unhelpful way.
- */
-
-extern void f25519_condswap(f25519 */*x*/, f25519 */*y*/, uint32 /*m*/);
-
-/* --- @f25519_add@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the sum %$x + y$%.
- */
-
-extern void f25519_add(f25519 */*z*/,
- const f25519 */*x*/, const f25519 */*y*/);
-
-/* --- @f25519_sub@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the difference %$x - y$%.
- */
-
-extern void f25519_sub(f25519 */*z*/,
- const f25519 */*x*/, const f25519 */*y*/);
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_neg@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z = -x@.
- */
-
-extern void f25519_neg(f25519 */*z*/, const f25519 */*x*/);
-
-/* --- @f25519_condneg@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, set @z = x@; if @m@ is all-bits-set, then set
- * @z = -x@. If @m@ has some other value then scramble @z@ in
- * an unhelpful way.
- */
-
-extern void f25519_condneg(f25519 */*z*/, const f25519 */*x*/, uint32 /*m*/);
-
-#endif
-
-/* --- @f25519_mulconst@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$a x$%.
- */
-
-extern void f25519_mulconst(f25519 */*z*/, const f25519 */*x*/, long /*a*/);
-
-/* --- @f25519_mul@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$x y$%.
- */
-
-extern void f25519_mul(f25519 */*z*/,
- const f25519 */*x*/, const f25519 */*y*/);
-
-/* --- @f25519_sqr@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z@ to the square %$x^2$%.
- */
-
-extern void f25519_sqr(f25519 */*z*/, const f25519 */*x*/);
-
-/* --- @f25519_inv@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@)
- * @const f25519 *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
- * %$x = 0$% then @z@ is set to zero. This is considered a
- * feature.
- */
-
-extern void f25519_inv(f25519 */*z*/, const f25519 */*x*/);
-
-#ifndef F25519_TRIM_X25519
-
-/* --- @f25519_quosqrt@ --- *
- *
- * Arguments: @f25519 *z@ = where to put the result (may alias @x@ or @y@)
- * @const f25519 *x, *y@ = two operands
- *
- * Returns: Zero if successful, @-1@ if %$x/y$% is not a square.
- *
- * Use: Stores in @z@ the one of the square roots %$\pm\sqrt{x/y}$%.
- * If %$x = y = 0% then the result is zero; if %$y = 0$% but %$x
- * \ne 0$% then the operation fails. If you wanted a specific
- * square root then you'll have to pick it yourself.
- */
-
-extern int f25519_quosqrt(f25519 */*z*/,
- const f25519 */*x*/, const f25519 */*y*/);
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
+++ /dev/null
-/*
- * fgoldi.c: arithmetic modulo 2^448 - 2^224 - 1
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the 16/32-bit implementation, since C99 always has 64-bit
- * arithmetic.
- *
- * * Remove the test rig code: a replacement is in a separate source file.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fgoldi.h"
-
-/*----- Basic setup -------------------------------------------------------*
- *
- * Let φ = 2^224; then p = φ^2 - φ - 1, and, in GF(p), we have φ^2 = φ + 1
- * (hence the name).
- */
-
-/* We represent an element of GF(p) as 16 28-bit signed integer pieces x_i:
- * x = SUM_{0<=i<16} x_i 2^(28i).
- */
-
-typedef int32 piece; typedef int64 dblpiece;
-typedef uint32 upiece; typedef uint64 udblpiece;
-#define PIECEWD(i) 28
-#define NPIECE 16
-#define P p28
-
-#define B28 0x10000000u
-#define B27 0x08000000u
-#define M28 0x0fffffffu
-#define M27 0x07ffffffu
-#define M32 0xffffffffu
-
-/*----- Debugging machinery -----------------------------------------------*/
-
-#if defined(FGOLDI_DEBUG)
-
-#include <stdio.h>
-
-#include "mp.h"
-#include "mptext.h"
-
-static mp *get_pgoldi(void)
-{
- mp *p = MP_NEW, *t = MP_NEW;
-
- p = mp_setbit(p, MP_ZERO, 448);
- t = mp_setbit(t, MP_ZERO, 224);
- p = mp_sub(p, p, t);
- p = mp_sub(p, p, MP_ONE);
- mp_drop(t);
- return (p);
-}
-
-DEF_FDUMP(fdump, piece, PIECEWD, NPIECE, 56, get_pgoldi())
-
-#endif
-
-/*----- Loading and storing -----------------------------------------------*/
-
-/* --- @fgoldi_load@ --- *
- *
- * Arguments: @fgoldi *z@ = where to store the result
- * @const octet xv[56]@ = source to read
- *
- * Returns: ---
- *
- * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
- * external representation from @xv@ and stores it in @z@.
- *
- * External representation is little-endian base-256. Some
- * elements have multiple encodings, which are not produced by
- * correct software; use of noncanonical encodings is not an
- * error, and toleration of them is considered a performance
- * feature.
- */
-
-void fgoldi_load(fgoldi *z, const octet xv[56])
-{
- unsigned i;
- uint32 xw[14];
- piece b, c;
-
- /* First, read the input value as words. */
- for (i = 0; i < 14; i++) xw[i] = LOAD32_L(xv + 4*i);
-
- /* Extract unsigned 28-bit pieces from the words. */
- z->P[ 0] = (xw[ 0] >> 0)&M28;
- z->P[ 7] = (xw[ 6] >> 4)&M28;
- z->P[ 8] = (xw[ 7] >> 0)&M28;
- z->P[15] = (xw[13] >> 4)&M28;
- for (i = 1; i < 7; i++) {
- z->P[i + 0] = ((xw[i + 0] << (4*i)) | (xw[i - 1] >> (32 - 4*i)))&M28;
- z->P[i + 8] = ((xw[i + 7] << (4*i)) | (xw[i + 6] >> (32 - 4*i)))&M28;
- }
-
- /* Convert the nonnegative pieces into a balanced signed representation, so
- * each piece ends up in the interval |z_i| <= 2^27. For each piece, if
- * its top bit is set, lend a bit leftwards; in the case of z_15, reduce
- * this bit by adding it onto z_0 and z_8, since this is the φ^2 bit, and
- * φ^2 = φ + 1. We delay this carry until after all of the pieces have
- * been balanced. If we don't do this, then we have to do a more expensive
- * test for nonzeroness to decide whether to lend a bit leftwards rather
- * than just testing a single bit.
- *
- * Note that we don't try for a canonical representation here: both upper
- * and lower bounds are achievable.
- */
- b = z->P[15]&B27; z->P[15] -= b << 1; c = b >> 27;
- for (i = NPIECE - 1; i--; )
- { b = z->P[i]&B27; z->P[i] -= b << 1; z->P[i + 1] += b >> 27; }
- z->P[0] += c; z->P[8] += c;
-}
-
-/* --- @fgoldi_store@ --- *
- *
- * Arguments: @octet zv[56]@ = where to write the result
- * @const fgoldi *x@ = the field element to write
- *
- * Returns: ---
- *
- * Use: Stores a field element in the given octet vector in external
- * representation. A canonical encoding is always stored.
- */
-
-void fgoldi_store(octet zv[56], const fgoldi *x)
-{
- piece y[NPIECE], yy[NPIECE], c, d;
- uint32 u, v;
- mask32 m;
- unsigned i;
-
- for (i = 0; i < NPIECE; i++) y[i] = x->P[i];
-
- /* First, propagate the carries. By the end of this, we'll have all of the
- * the pieces canonically sized and positive, and maybe there'll be
- * (signed) carry out. The carry c is in { -1, 0, +1 }, and the remaining
- * value will be in the half-open interval [0, φ^2). The whole represented
- * value is then y + φ^2 c.
- *
- * Assume that we start out with |y_i| <= 2^30. We start off by cutting
- * off and reducing the carry c_15 from the topmost piece, y_15. This
- * leaves 0 <= y_15 < 2^28; and we'll have |c_15| <= 4. We'll add this
- * onto y_0 and y_8, and propagate the carries. It's very clear that we'll
- * end up with |y + (φ + 1) c_15 - φ^2/2| << φ^2.
- *
- * Here, the y_i are signed, so we must be cautious about bithacking them.
- */
- c = ASR(piece, y[15], 28); y[15] = (upiece)y[15]&M28; y[8] += c;
- for (i = 0; i < NPIECE; i++)
- { y[i] += c; c = ASR(piece, y[i], 28); y[i] = (upiece)y[i]&M28; }
-
- /* Now we have a slightly fiddly job to do. If c = +1, or if c = 0 and
- * y >= p, then we should subtract p from the whole value; if c = -1 then
- * we should add p; and otherwise we should do nothing.
- *
- * But conditional behaviour is bad, m'kay. So here's what we do instead.
- *
- * The first job is to sort out what we wanted to do. If c = -1 then we
- * want to (a) invert the constant addend and (b) feed in a carry-in;
- * otherwise, we don't.
- */
- m = SIGN(c)&M28;
- d = m&1;
-
- /* Now do the addition/subtraction. Remember that all of the y_i are
- * nonnegative, so shifting and masking are safe and easy.
- */
- d += y[0] + (1 ^ m); yy[0] = d&M28; d >>= 28;
- for (i = 1; i < 8; i++)
- { d += y[i] + m; yy[i] = d&M28; d >>= 28; }
- d += y[8] + (1 ^ m); yy[8] = d&M28; d >>= 28;
- for (i = 9; i < 16; i++)
- { d += y[i] + m; yy[i] = d&M28; d >>= 28; }
-
- /* The final carry-out is in d; since we only did addition, and the y_i are
- * nonnegative, then d is in { 0, 1 }. We want to keep y', rather than y,
- * if (a) c /= 0 (in which case we know that the old value was
- * unsatisfactory), or (b) if d = 1 (in which case, if c = 0, we know that
- * the subtraction didn't cause a borrow, so we must be in the case where
- * p <= y < φ^2.
- */
- m = NONZEROP(c) | ~NONZEROP(d - 1);
- for (i = 0; i < NPIECE; i++) y[i] = (yy[i]&m) | (y[i]&~m);
-
- /* Extract 32-bit words from the value. */
- for (i = 0; i < 7; i++) {
- u = ((y[i + 0] >> (4*i)) | ((uint32)y[i + 1] << (28 - 4*i)))&M32;
- v = ((y[i + 8] >> (4*i)) | ((uint32)y[i + 9] << (28 - 4*i)))&M32;
- STORE32_L(zv + 4*i, u);
- STORE32_L(zv + 4*i + 28, v);
- }
-}
-
-/* --- @fgoldi_set@ --- *
- *
- * Arguments: @fgoldi *z@ = where to write the result
- * @int a@ = a small-ish constant
- *
- * Returns: ---
- *
- * Use: Sets @z@ to equal @a@.
- */
-
-void fgoldi_set(fgoldi *x, int a)
-{
- unsigned i;
-
- x->P[0] = a;
- for (i = 1; i < NPIECE; i++) x->P[i] = 0;
-}
-
-/*----- Basic arithmetic --------------------------------------------------*/
-
-/* --- @fgoldi_add@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the sum %$x + y$%.
- */
-
-void fgoldi_add(fgoldi *z, const fgoldi *x, const fgoldi *y)
-{
- unsigned i;
- for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] + y->P[i];
-}
-
-/* --- @fgoldi_sub@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the difference %$x - y$%.
- */
-
-void fgoldi_sub(fgoldi *z, const fgoldi *x, const fgoldi *y)
-{
- unsigned i;
- for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i];
-}
-
-/*----- Constant-time utilities -------------------------------------------*/
-
-/* --- @fgoldi_condswap@ --- *
- *
- * Arguments: @fgoldi *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
- * exchange @x@ and @y@. If @m@ has some other value, then
- * scramble @x@ and @y@ in an unhelpful way.
- */
-
-void fgoldi_condswap(fgoldi *x, fgoldi *y, uint32 m)
-{
- unsigned i;
- mask32 mm = FIX_MASK32(m);
-
- for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm);
-}
-
-/*----- Multiplication ----------------------------------------------------*/
-
-/* Let B = 2^63 - 1 be the largest value such that +B and -B can be
- * represented in a double-precision piece. On entry, it must be the case
- * that |X_i| <= M <= B - 2^27 for some M. If this is the case, then, on
- * exit, we will have |Z_i| <= 2^27 + M/2^27.
- */
-#define CARRY_REDUCE(z, x) do { \
- dblpiece _t[NPIECE], _c; \
- unsigned _i; \
- \
- /* Bias the input pieces. This keeps the carries and so on centred \
- * around zero rather than biased positive. \
- */ \
- for (_i = 0; _i < NPIECE; _i++) _t[_i] = (x)[_i] + B27; \
- \
- /* Calculate the reduced pieces. Careful with the bithacking. */ \
- _c = ASR(dblpiece, _t[15], 28); \
- (z)[0] = (dblpiece)((udblpiece)_t[0]&M28) - B27 + _c; \
- for (_i = 1; _i < NPIECE; _i++) { \
- (z)[_i] = (dblpiece)((udblpiece)_t[_i]&M28) - B27 + \
- ASR(dblpiece, _t[_i - 1], 28); \
- } \
- (z)[8] += _c; \
-} while (0)
-
-/* --- @fgoldi_mulconst@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
- * @const fgoldi *x@ = an operand
- * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$a x$%.
- */
-
-void fgoldi_mulconst(fgoldi *z, const fgoldi *x, long a)
-{
- unsigned i;
- dblpiece zz[NPIECE], aa = a;
-
- for (i = 0; i < NPIECE; i++) zz[i] = aa*x->P[i];
- CARRY_REDUCE(z->P, zz);
-}
-
-/* --- @fgoldi_mul@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$x y$%.
- */
-
-void fgoldi_mul(fgoldi *z, const fgoldi *x, const fgoldi *y)
-{
- dblpiece zz[NPIECE], u[NPIECE];
- piece ab[NPIECE/2], cd[NPIECE/2];
- const piece
- *a = x->P + NPIECE/2, *b = x->P,
- *c = y->P + NPIECE/2, *d = y->P;
- unsigned i, j;
-
-# define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j])
-
- /* Behold the magic.
- *
- * Write x = a φ + b, and y = c φ + d. Then x y = a c φ^2 +
- * (a d + b c) φ + b d. Karatsuba and Ofman observed that a d + b c =
- * (a + b) (c + d) - a c - b d, saving a multiplication, and Hamburg chose
- * the prime p so that φ^2 = φ + 1. So
- *
- * x y = ((a + b) (c + d) - b d) φ + a c + b d
- */
-
- for (i = 0; i < NPIECE; i++) zz[i] = 0;
-
- /* Our first job will be to calculate (1 - φ) b d, and write the result
- * into z. As we do this, an interesting thing will happen. Write
- * b d = u φ + v; then (1 - φ) b d = u φ + v - u φ^2 - v φ = (1 - φ) v - u.
- * So, what we do is to write the product end-swapped and negated, and then
- * we'll subtract the (negated, remember) high half from the low half.
- */
- for (i = 0; i < NPIECE/2; i++) {
- for (j = 0; j < NPIECE/2 - i; j++)
- zz[i + j + NPIECE/2] -= M(b,i, d,j);
- for (; j < NPIECE/2; j++)
- zz[i + j - NPIECE/2] -= M(b,i, d,j);
- }
- for (i = 0; i < NPIECE/2; i++)
- zz[i] -= zz[i + NPIECE/2];
-
- /* Next, we add on a c. There are no surprises here. */
- for (i = 0; i < NPIECE/2; i++)
- for (j = 0; j < NPIECE/2; j++)
- zz[i + j] += M(a,i, c,j);
-
- /* Now, calculate a + b and c + d. */
- for (i = 0; i < NPIECE/2; i++)
- { ab[i] = a[i] + b[i]; cd[i] = c[i] + d[i]; }
-
- /* Finally (for the multiplication) we must add on (a + b) (c + d) φ.
- * Write (a + b) (c + d) as u φ + v; then we actually want u φ^2 + v φ =
- * v φ + (1 + φ) u. We'll store u in a temporary place and add it on
- * twice.
- */
- for (i = 0; i < NPIECE; i++) u[i] = 0;
- for (i = 0; i < NPIECE/2; i++) {
- for (j = 0; j < NPIECE/2 - i; j++)
- zz[i + j + NPIECE/2] += M(ab,i, cd,j);
- for (; j < NPIECE/2; j++)
- u[i + j - NPIECE/2] += M(ab,i, cd,j);
- }
- for (i = 0; i < NPIECE/2; i++)
- { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; }
-
-#undef M
-
- /* That wraps it up for the multiplication. Let's figure out some bounds.
- * Fortunately, Karatsuba is a polynomial identity, so all of the pieces
- * end up the way they'd be if we'd done the thing the easy way, which
- * simplifies the analysis. Suppose we started with |x_i|, |y_i| <= 9/5
- * 2^28. The overheads in the result are given by the coefficients of
- *
- * ((u^16 - 1)/(u - 1))^2 mod u^16 - u^8 - 1
- *
- * the greatest of which is 38. So |z_i| <= 38*81/25*2^56 < 2^63.
- *
- * Anyway, a round of `CARRY_REDUCE' will leave us with |z_i| < 2^27 +
- * 2^36; and a second round will leave us with |z_i| < 2^27 + 512.
- */
- for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
- for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-}
-
-/* --- @fgoldi_sqr@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z@ to the square %$x^2$%.
- */
-
-void fgoldi_sqr(fgoldi *z, const fgoldi *x)
-{
- dblpiece zz[NPIECE], u[NPIECE];
- piece ab[NPIECE];
- const piece *a = x->P + NPIECE/2, *b = x->P;
- unsigned i, j;
-
-# define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j])
-
- /* The magic is basically the same as `fgoldi_mul' above. We write
- * x = a φ + b and use Karatsuba and the special prime shape. This time,
- * we have
- *
- * x^2 = ((a + b)^2 - b^2) φ + a^2 + b^2
- */
-
- for (i = 0; i < NPIECE; i++) zz[i] = 0;
-
- /* Our first job will be to calculate (1 - φ) b^2, and write the result
- * into z. Again, this interacts pleasantly with the prime shape.
- */
- for (i = 0; i < NPIECE/4; i++) {
- zz[2*i + NPIECE/2] -= M(b,i, b,i);
- for (j = i + 1; j < NPIECE/2 - i; j++)
- zz[i + j + NPIECE/2] -= 2*M(b,i, b,j);
- for (; j < NPIECE/2; j++)
- zz[i + j - NPIECE/2] -= 2*M(b,i, b,j);
- }
- for (; i < NPIECE/2; i++) {
- zz[2*i - NPIECE/2] -= M(b,i, b,i);
- for (j = i + 1; j < NPIECE/2; j++)
- zz[i + j - NPIECE/2] -= 2*M(b,i, b,j);
- }
- for (i = 0; i < NPIECE/2; i++)
- zz[i] -= zz[i + NPIECE/2];
-
- /* Next, we add on a^2. There are no surprises here. */
- for (i = 0; i < NPIECE/2; i++) {
- zz[2*i] += M(a,i, a,i);
- for (j = i + 1; j < NPIECE/2; j++)
- zz[i + j] += 2*M(a,i, a,j);
- }
-
- /* Now, calculate a + b. */
- for (i = 0; i < NPIECE/2; i++)
- ab[i] = a[i] + b[i];
-
- /* Finally (for the multiplication) we must add on (a + b)^2 φ.
- * Write (a + b)^2 as u φ + v; then we actually want (u + v) φ + u. We'll
- * store u in a temporary place and add it on twice.
- */
- for (i = 0; i < NPIECE; i++) u[i] = 0;
- for (i = 0; i < NPIECE/4; i++) {
- zz[2*i + NPIECE/2] += M(ab,i, ab,i);
- for (j = i + 1; j < NPIECE/2 - i; j++)
- zz[i + j + NPIECE/2] += 2*M(ab,i, ab,j);
- for (; j < NPIECE/2; j++)
- u[i + j - NPIECE/2] += 2*M(ab,i, ab,j);
- }
- for (; i < NPIECE/2; i++) {
- u[2*i - NPIECE/2] += M(ab,i, ab,i);
- for (j = i + 1; j < NPIECE/2; j++)
- u[i + j - NPIECE/2] += 2*M(ab,i, ab,j);
- }
- for (i = 0; i < NPIECE/2; i++)
- { zz[i] += u[i]; zz[i + NPIECE/2] += u[i]; }
-
-#undef M
-
- /* Finally, carrying. */
- for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
- for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-
-}
-
-/*----- More advanced operations ------------------------------------------*/
-
-/* --- @fgoldi_inv@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
- * @const fgoldi *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
- * %$x = 0$% then @z@ is set to zero. This is considered a
- * feature.
- */
-
-void fgoldi_inv(fgoldi *z, const fgoldi *x)
-{
- fgoldi t, u;
- unsigned i;
-
-#define SQRN(z, x, n) do { \
- fgoldi_sqr((z), (x)); \
- for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \
-} while (0)
-
- /* Calculate x^-1 = x^(p - 2) = x^(2^448 - 2^224 - 3), which also handles
- * x = 0 as intended. The addition chain is home-made.
- */ /* step | value */
- fgoldi_sqr(&u, x); /* 1 | 2 */
- fgoldi_mul(&t, &u, x); /* 2 | 3 */
- SQRN(&u, &t, 2); /* 4 | 12 */
- fgoldi_mul(&t, &u, &t); /* 5 | 15 */
- SQRN(&u, &t, 4); /* 9 | 240 */
- fgoldi_mul(&u, &u, &t); /* 10 | 255 = 2^8 - 1 */
- SQRN(&u, &u, 4); /* 14 | 2^12 - 16 */
- fgoldi_mul(&t, &u, &t); /* 15 | 2^12 - 1 */
- SQRN(&u, &t, 12); /* 27 | 2^24 - 2^12 */
- fgoldi_mul(&u, &u, &t); /* 28 | 2^24 - 1 */
- SQRN(&u, &u, 12); /* 40 | 2^36 - 2^12 */
- fgoldi_mul(&t, &u, &t); /* 41 | 2^36 - 1 */
- fgoldi_sqr(&t, &t); /* 42 | 2^37 - 2 */
- fgoldi_mul(&t, &t, x); /* 43 | 2^37 - 1 */
- SQRN(&u, &t, 37); /* 80 | 2^74 - 2^37 */
- fgoldi_mul(&u, &u, &t); /* 81 | 2^74 - 1 */
- SQRN(&u, &u, 37); /* 118 | 2^111 - 2^37 */
- fgoldi_mul(&t, &u, &t); /* 119 | 2^111 - 1 */
- SQRN(&u, &t, 111); /* 230 | 2^222 - 2^111 */
- fgoldi_mul(&t, &u, &t); /* 231 | 2^222 - 1 */
- fgoldi_sqr(&u, &t); /* 232 | 2^223 - 2 */
- fgoldi_mul(&u, &u, x); /* 233 | 2^223 - 1 */
- SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */
- fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */
- SQRN(&t, &t, 2); /* 459 | 2^448 - 2^224 - 4 */
- fgoldi_mul(z, &t, x); /* 460 | 2^448 - 2^224 - 3 */
-
-#undef SQRN
-}
-
-/*----- That's all, folks -------------------------------------------------*/
+++ /dev/null
-/*
- * fgoldi.h: arithmetic modulo 2^448 - 2^224 - 1
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and lightly modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the 16/32-bit implementation, since C99 always has 64-bit
- * arithmetic.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * Arithmetic in the Goldilocks field GF(2^448 - 2^224 - 1)
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_FGOLDI_H
-#define CATACOMB_FGOLDI_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-#ifndef CATACOMB_QFARITH_H
-# include "qfarith.h"
-#endif
-
-/*----- Data structures ---------------------------------------------------*/
-
-typedef union {
- int32 p28[16];
-} fgoldi;
-
-#if !defined(FGOLDI_IMPL) && defined(HAVE_INT64)
-# define FGOLDI_IMPL 28
-#endif
-
-#ifndef FGOLDI_IMPL
-# define FGOLDI_IMPL 12
-#endif
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @fgoldi_load@ --- *
- *
- * Arguments: @fgoldi *z@ = where to store the result
- * @const octet xv[56]@ = source to read
- *
- * Returns: ---
- *
- * Use: Reads an element of %$\gf{2^{448} - 2^{224} - 19}$% in
- * external representation from @xv@ and stores it in @z@.
- *
- * External representation is little-endian base-256. Some
- * elements have multiple encodings, which are not produced by
- * correct software; use of noncanonical encodings is not an
- * error, and toleration of them is considered a performance
- * feature.
- */
-
-extern void fgoldi_load(fgoldi */*z*/, const octet /*xv*/[56]);
-
-/* --- @fgoldi_store@ --- *
- *
- * Arguments: @octet zv[56]@ = where to write the result
- * @const fgoldi *x@ = the field element to write
- *
- * Returns: ---
- *
- * Use: Stores a field element in the given octet vector in external
- * representation. A canonical encoding is always stored.
- */
-
-extern void fgoldi_store(octet /*zv*/[56], const fgoldi */*x*/);
-
-/* --- @fgoldi_set@ --- *
- *
- * Arguments: @fgoldi *z@ = where to write the result
- * @int a@ = a small-ish constant
- *
- * Returns: ---
- *
- * Use: Sets @z@ to equal @a@.
- */
-
-extern void fgoldi_set(fgoldi */*x*/, int /*a*/);
-
-/* --- @fgoldi_add@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the sum %$x + y$%.
- */
-
-extern void fgoldi_add(fgoldi */*z*/,
- const fgoldi */*x*/, const fgoldi */*y*/);
-
-/* --- @fgoldi_sub@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the difference %$x - y$%.
- */
-
-extern void fgoldi_sub(fgoldi */*z*/,
- const fgoldi */*x*/, const fgoldi */*y*/);
-
-/* --- @fgoldi_condswap@ --- *
- *
- * Arguments: @fgoldi *x, *y@ = two operands
- * @uint32 m@ = a mask
- *
- * Returns: ---
- *
- * Use: If @m@ is zero, do nothing; if @m@ is all-bits-set, then
- * exchange @x@ and @y@. If @m@ has some other value, then
- * scramble @x@ and @y@ in an unhelpful way.
- */
-
-extern void fgoldi_condswap(fgoldi */*x*/, fgoldi */*y*/, uint32 /*m*/);
-
-/* --- @fgoldi_mulconst@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
- * @const fgoldi *x@ = an operand
- * @long a@ = a small-ish constant; %$|a| < 2^{20}$%.
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$a x$%.
- */
-
-extern void fgoldi_mulconst(fgoldi */*z*/, const fgoldi */*x*/, long /*a*/);
-
-/* --- @fgoldi_mul@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x, *y@ = two operands
- *
- * Returns: ---
- *
- * Use: Set @z@ to the product %$x y$%.
- */
-
-extern void fgoldi_mul(fgoldi */*z*/,
- const fgoldi */*x*/, const fgoldi */*y*/);
-
-/* --- @fgoldi_sqr@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
- * @const fgoldi *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Set @z@ to the square %$x^2$%.
- */
-
-extern void fgoldi_sqr(fgoldi */*z*/, const fgoldi */*x*/);
-
-/* --- @fgoldi_inv@ --- *
- *
- * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
- * @const fgoldi *x@ = an operand
- *
- * Returns: ---
- *
- * Use: Stores in @z@ the multiplicative inverse %$x^{-1}$%. If
- * %$x = 0$% then @z@ is set to zero. This is considered a
- * feature.
- */
-
-extern void fgoldi_inv(fgoldi */*z*/, const fgoldi */*x*/);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
+++ /dev/null
-/*
- * montladder.h: Montgomery's ladder
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb (2017-04-30). The file's original comment headers
- * are preserved below.
- */
-/* -*-c-*-
- *
- * Definitions for Montgomery's ladder
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_MONTLADDER_H
-#define CATACOMB_MONTLADDER_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Notes on the Montgomery ladder ------------------------------------*
- *
- * The algorithm here is Montgomery's famous binary ladder for calculating
- * x-coordinates of scalar products on a particular shape of elliptic curve,
- * as elucidated by Daniel Bernstein.
- *
- * Let Q = (x_1, y_1) be the base point, for some unknown y_1 (which will
- * turn out to be unimportant). Define x_n, z_n by x(n Q) = (x_n : z_n).
- * Given x_n, z_n, x_{n+1}, z_{n+1}, Montgomery's differential addition
- * formulae calculate x_{2i}, z_{2i}, x_{2i+1}, z_{2i+1}. Furthermore,
- * calculating x_{2i}, z_{2i} requires only x_n, z_n, and the calculation of
- * x_{2i+1}, z_{2i+1} is symmetrical.
- */
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* F designates a field, both naming the type of its elements and acting as a
- * prefix for the standard field operations `F_add', `F_sub', `F_mul',
- * `F_sqr', and `F_inv' (the last of which should return zero its own
- * inverse); and the constant-time utility `F_condswap'.
- *
- * The macro calculates the x-coordinate of the product k Q, where Q is a
- * point on the elliptic curve B y^2 = x^3 + A x^2 + x or its quadratic
- * twist, for some irrelevant B. The x-coordinate of Q is given as X1 (a
- * pointer to a field element). The scalar k is given as a vector of NK
- * unsigned integers KW, each containing NBITS significant bits, with the
- * least-significant element first. The result is written to the field
- * element pointed to by Z.
- *
- * The curve coefficient A is given indirectly, as the name of a macro MULA0
- * such that
- *
- * MULA0(z, x)
- *
- * will store in z the value (A - 2)/4 x.
- */
-#define MONT_LADDER(f, mula0, kw, nk, nbits, z, x1) do { \
- f _x, _z, _u, _w; \
- f _t0, _t1, _t2, _t3, _t4; \
- uint32 _m = 0, _mm = 0, _k; \
- unsigned _i, _j; \
- \
- /* Initialize the main variables. We'll have, (x, z) and (u, w) \
- * holding (x_n, z_n) and (x_{n+1}, z_{n+1}) in some order, but \
- * there's some weirdness: if m = 0 then (x, z) = (x_n, z_n) and \
- * (u, v) = (x_{n+1}, z_{n+1}); if m /= 0, then the pairs are \
- * swapped over. \
- * \
- * Initially, we have (x_0, z_0) = (1, 0), representing the identity \
- * at projective-infinity, which works fine; and we have z_1 = 1. \
- */ \
- _u = *(x1); f##_set(&_w, 1); f##_set(&_x, 1); f##_set(&_z, 0); \
- \
- /* The main ladder loop. Work through each bit of the clamped key. */ \
- for (_i = (nk); _i--; ) { \
- _k = (kw)[_i]; \
- for (_j = 0; _j < (nbits); _j++) { \
- /* We're at bit i of the scalar key (represented by 32 (7 - i) + \
- * (31 - j) in our loop variables -- don't worry about that). \
- * Let k = 2^i k_i + k'_i, with 0 <= k'_i < 2^i. In particular, \
- * then, k_0 = k. Write Q(i) = (x_i, z_i). \
- * \
- * We currently have, in (x, z) and (u, w), Q(k_i) and Q(k_i + \
- * 1), in some order. The ladder step will double the point in \
- * (x, z), and leave the sum of (x : z) and (u : w) in (u, w). \
- */ \
- \
- _mm = -((_k >> ((nbits) - 1))&1u); _k <<= 1; \
- f##_condswap(&_x, &_u, _m ^ _mm); \
- f##_condswap(&_z, &_w, _m ^ _mm); \
- _m = _mm; \
- \
- f##_add(&_t0, &_x, &_z); /* x + z */ \
- f##_sub(&_t1, &_x, &_z); /* x - z */ \
- f##_add(&_t2, &_u, &_w); /* u + w */ \
- f##_sub(&_t3, &_u, &_w); /* u - w */ \
- f##_mul(&_t2, &_t2, &_t1); /* (x - z) (u + w) */ \
- f##_mul(&_t3, &_t3, &_t0); /* (x + z) (u - w) */ \
- f##_sqr(&_t0, &_t0); /* (x + z)^2 */ \
- f##_sqr(&_t1, &_t1); /* (x - z)^2 */ \
- f##_mul(&_x, &_t0, &_t1); /* (x + z)^2 (x - z)^2 */ \
- f##_sub(&_t1, &_t0, &_t1); /* (x + z)^2 - (x - z)^2 */ \
- mula0(&_t4, &_t1); /* A_0 ((x + z)^2 - (x - z)^2) */ \
- f##_add(&_t0, &_t0, &_t4); /* A_0 ... + (x + z)^2 */ \
- f##_mul(&_z, &_t0, &_t1); /* (...^2 - ...^2) (A_0 ... + ...) */ \
- f##_add(&_t0, &_t2, &_t3); /* (x - z) (u + w) + (x + z) (u - w) */ \
- f##_sub(&_t1, &_t2, &_t3); /* (x - z) (u + w) - (x + z) (u - w) */ \
- f##_sqr(&_u, &_t0); /* (... + ...)^2 */ \
- f##_sqr(&_t1, &_t1); /* (... - ...)^2 */ \
- f##_mul(&_w, &_t1, (x1)); /* x_1 (... - ...)^2 */ \
- } \
- } \
- \
- /* Almost done. Undo the swap, if any. */ \
- f##_condswap(&_x, &_u, _m); \
- f##_condswap(&_z, &_w, _m); \
- \
- /* And convert to affine. */ \
- f##_inv(&_t0, &_z); \
- f##_mul((z), &_x, &_t0); \
-} while (0)
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
+++ /dev/null
-/*
- * qfarith.h: utilities for quick field arithmetic
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Use C99 signed integer types instead of our own local probing.
- *
- * * Remove the support for non-two's-complement targets.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * Utilities for quick field arithmetic
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_QFARITH_H
-#define CATACOMB_QFARITH_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <limits.h>
-#include <stdint.h>
-
-#include "fake-mLib-bits.h"
-
-/*----- Signed integer types ----------------------------------------------*/
-
-typedef int_fast32_t int32;
-typedef int_fast64_t int64;
-#define HAVE_INT64 1
-
-/*----- General bit-hacking utilities -------------------------------------*/
-
-/* Individual bits, and masks for low bits. */
-#define BIT(n) (1ul << (n))
-#define MASK(n) (BIT(n) - 1)
-
-/* Arithmetic right shift. If X is a value of type TY, and N is a
- * nonnegative integer, then return the value of X shifted right by N bits;
- * alternatively, this is floor(X/2^N).
- *
- * GCC manages to compile this into a simple shift operation if one is
- * available, but it's correct for all C targets.
- */
-#define ASR(ty, x, n) (((x) - (ty)((u##ty)(x)&MASK(n)))/(ty)BIT(n))
-
-/*----- Constant-time utilities -------------------------------------------*/
-
-/* The following have better implementations on a two's complement target. */
-#ifdef NEG_TWOC
-
- /* If we have two's complement arithmetic then masks are signed; this
- * avoids a switch to unsigned representation, with the consequent problem
- * of overflow when we convert back.
- */
- typedef int32 mask32;
-
- /* Convert an unsigned mask M into a `mask32'. This is a hairy-looking
- * no-op on many targets, but, given that we have two's complement
- * integers, it is free of arithmetic overflow.
- */
-# define FIX_MASK32(m) \
- ((mask32)((m)&0x7fffffffu) + (-(mask32)0x7fffffff - 1)*(((m) >> 31)&1u))
-
- /* If Z is zero and M has its low 32 bits set, then copy (at least) the low
- * 32 bits of X to Z; if M is zero, do nothing. Otherwise, scramble Z
- * unhelpfully.
- */
-# define CONDPICK(z, x, m) do { (z) |= (x)&(m); } while (0)
-
- /* If M has its low 32 bits set, then return (at least) the low 32 bits of
- * X in Z; if M is zero, then return (at least) the low 32 bits of Y in Z.
- * Otherwise, return an unhelful result.
- */
-# define PICK2(x, y, m) (((x)&(m)) | ((y)&~(m)))
-
- /* If M has its low 32 bits set then swap (at least) the low 32 bits of X
- * and Y; if M is zero, then do nothing. Otherwise, scramble X and Y
- * unhelpfully.
- */
-# define CONDSWAP(x, y, m) \
- do { mask32 t_ = ((x) ^ (y))&(m); (x) ^= t_; (y) ^= t_; } while (0)
-#else
-# error "Targets without two's complement arithmetic aren't supported"
-#endif
-
-/* Return zero if bit 31 of X is clear, or a mask with (at least) the low 32
- * bits set if bit 31 of X is set.
- */
-#define SIGN(x) (-(mask32)(((uint32)(x) >> 31)&1))
-
-/* Return zero if X is zero, or a mask with (at least) the low 32 bits set if
- * X is nonzero.
- */
-#define NONZEROP(x) SIGN((U32(x) >> 1) - U32(x))
-
-/*----- Debugging utilities -----------------------------------------------*/
-
-/* Define a debugging function DUMPFN, which will dump an integer represented
- * modulo M. The integer is represented as a vector of NPIECE pieces of type
- * PIECETY. The pieces are assembled at possibly irregular offsets: piece i
- * logically has width PIECEWD(i), but may overhang the next piece. The
- * pieces may be signed. GETMOD is an expression which calculates and
- * returns the value of M, as an `mp *'.
- *
- * The generated function writes the value of such an integer X to the stream
- * FP, labelled with the string WHAT.
- *
- * The definition assumes that <stdio.h>, <catacomb/mp.h>, and
- * <catacomb/mptext.h> have been included.
- */
-#define DEF_FDUMP(dumpfn, piecety, piecewd, npiece, noctet, getmod) \
- static void dumpfn(FILE *fp, const char *what, const piecety *x) \
- { \
- mpw w; \
- mp m, *y = MP_ZERO, *t = MP_NEW, *p; \
- octet b[noctet]; \
- unsigned i, o; \
- \
- p = getmod; \
- mp_build(&m, &w, &w + 1); \
- for (i = o = 0; i < npiece; i++) { \
- if (x[i] >= 0) { w = x[i]; m.f &= ~MP_NEG; } \
- else { w = -x[i]; m.f |= MP_NEG; } \
- t = mp_lsl(t, &m, o); \
- y = mp_add(y, y, t); \
- o += piecewd(i); \
- } \
- \
- fprintf(fp, "%s = <", what); \
- for (i = 0; i < npiece; i++) { \
- if (i) fputs(", ", fp); \
- fprintf(fp, "%ld", (long)x[i]); \
- } \
- fputs(">\n\t= ", fp); \
- mp_writefile(y, fp, 10); \
- fputs("\n\t== ", fp); \
- mp_div(0, &y, y, p); \
- mp_writefile(y, fp, 10); \
- fputs("\n\t= 0x", fp); \
- mp_writefile(y, fp, 16); \
- fputs(" (mod 2^255 - 19)\n\t= [", fp); \
- mp_storel(y, b, sizeof(b)); \
- for (i = 0; i < 32; i++) { \
- if (i && !(i%4)) fputc(':', fp); \
- fprintf(fp, "%02x", b[i]); \
- } \
- fputs("]\n", fp); \
- mp_drop(y); mp_drop(p); mp_drop(t); \
- }
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
+++ /dev/null
-### Test cases for arithmetic mod 2^255 - 19. -*-conf-*-
-
-###--------------------------------------------------------------------------
-test add
-
-## Some easy things, mostly to test loading and storing.
-x 0102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f20
-y 0000000000000000000000000000000000000000000000000000000000000000
-z 0102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f20
-
-x ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
-y 0000000000000000000000000000000000000000000000000000000000000000
-z ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
-
-x edffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff7f
-y 0000000000000000000000000000000000000000000000000000000000000000
-z 0000000000000000000000000000000000000000000000000000000000000000
-
-## Random tests.
-x bb8cd45b6185ee8ca34c4d7560425fd5c2fc22871113c6427198e8f9439a8523
-y 98f16cc5e44b7228b7f3b6ed91930d68bba5071157d19259c48034d2817e30d5
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-
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-
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-
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-
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-
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-
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-
-x 1637e3eb4c5d173b8cba29bdb13b930f48ae0599e354819f8ae0cf70f0f7b61b
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-
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-
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-
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-
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-
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-
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-
-x bc3422b79e01234fefd3637a19bfb2dd0a83bf2071b27bf5389918a50e579294
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-
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-
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-z f16b5f4146d9641935ee65236a0fc343a70dbf91ae0545ce75ea5aff08a8a450
-
-###--------------------------------------------------------------------------
-test sub
-
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-
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-
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-
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-x b66b49190a99456aaac5c33beaec423a3fa79a84df0f00122aed29151185ceef
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-z 52cf4f0f5bd7531fdaea122feb9b4841ce5359db85258408db7a0d863e9ab22a
-
-x ef0f6c7f56ff22260c66d583f79c7f581181d3a0f3167c93786bb6c89de4372c
-y be934afeffaf5e6755a92e6606ffd054627dbe1b18ad6ae543363a01da605512
-z 317c2181564fc4beb6bca61df19dae03af031585db6911ae34357cc7c383e219
-
-x 773e0db8f86c5182b5f51d10376f42cde275dac6a646ab1cab065760e045107e
-y 3f92ddafdfe67d357b4f9b61807bcb8b0f1f6c2dacba27902f48fc15a31db606
-z 38ac2f081986d34c3aa682aeb6f37641d3566e99fa8b838c7bbe5a4a3d285a77
-
-x 34860a848d0afb20e43f4a36b3c8941f5821864216da9cb3ce1a11f056565a3d
-y 9dfed86048acd45ec0009c1ba3b20a1ba645ec141070fd8ae41d25e159bbce9f
-z 84873123455e26c2233fae1a10168a04b2db992d066a9f28eafceb0efd9a8b1d
-
-x 854ba91672ae1b8f6c29395dcfa4f3514ed97dc2c9e1e419f926825619fac55b
-y 7a700653ad355caf17f89045ecfb3ee821194b54048e55d8eed41fea2b0a22ab
-z f8daa2c3c478bfdf5431a817e3a8b4692cc0326ec5538f410a52626cedefa330
-
-x 0c66b3d8c3916940b70d381d232ba8aecfe27e3ae63fa6cbb287216708f224f0
-y 477186656245c4083dff93a95c6e5deb707916e52cd74abbd522743c24c53088
-z c5f42c73614ca5377a0ea473c6bc4ac35e696855b9685b10dd64ad2ae42cf467
-
-###--------------------------------------------------------------------------
-test condswap
-
-x 14e55571df646a69a8280bf8dbf8e9afc15bf5558bb8b8236ebcaa19a96053bd
-y 8bef5021598a8175565e1f2b522ed1c4306fef4e0e973b50d3a03db1fcf11a43
-m 0xffffffff
-xx 8bef5021598a8175565e1f2b522ed1c4306fef4e0e973b50d3a03db1fcf11a43
-yy 27e55571df646a69a8280bf8dbf8e9afc15bf5558bb8b8236ebcaa19a960533d
-
-x 53d8c54864e18f8fc742b2cb996f1d7595122ca9c90de9f49485cf5a5ef05058
-y 9aa95be655b6704a3dd482e8424f82d17443ae26ab41092fad95df9cac678787
-m 0x00000000
-xx 53d8c54864e18f8fc742b2cb996f1d7595122ca9c90de9f49485cf5a5ef05058
-yy ada95be655b6704a3dd482e8424f82d17443ae26ab41092fad95df9cac678707
-
-x 8c7b4ffbf50edf7edcf8d69b67796de38b56a5d4e3a9fb2201354cca0b1b7c57
-y 856e707988c37e59fc6689d024b98bc01b71034484ba194ec7f45106267cb7f6
-m 0xffffffff
-xx 986e707988c37e59fc6689d024b98bc01b71034484ba194ec7f45106267cb776
-yy 8c7b4ffbf50edf7edcf8d69b67796de38b56a5d4e3a9fb2201354cca0b1b7c57
-
-x c8cb24a636f6d8f2c045c8441b21314884a71d55c73d4ef7ad65620ac0d86616
-y 02b47be53df7c8521d57589256e69b8bbeb1e838d84c090287c04a25d5c08e1a
-m 0x00000000
-xx c8cb24a636f6d8f2c045c8441b21314884a71d55c73d4ef7ad65620ac0d86616
-yy 02b47be53df7c8521d57589256e69b8bbeb1e838d84c090287c04a25d5c08e1a
-
-x 7d96f47612fb7135edfa71dd4526d8b4c944d74ddf004e1653d3af52485168b4
-y a4e83162602d20cf71a279c1071038ecf94f38be11ad1191927b3f480d393e1d
-m 0x00000000
-xx 9096f47612fb7135edfa71dd4526d8b4c944d74ddf004e1653d3af5248516834
-yy a4e83162602d20cf71a279c1071038ecf94f38be11ad1191927b3f480d393e1d
-
-x c3a3d4462091b36bd6fd494e70c3166478be0a65bca7f7361246c52dda402981
-y 62d0ae1abbe5cb909328f59e71330269e4f2b1d3c664e7f1f0780e0a4774c262
-m 0xffffffff
-xx 62d0ae1abbe5cb909328f59e71330269e4f2b1d3c664e7f1f0780e0a4774c262
-yy d6a3d4462091b36bd6fd494e70c3166478be0a65bca7f7361246c52dda402901
-
-x 38c9b0d92be50270e29cc3181952e745cbf21c8d145ae0c0a6e59f25394ea59c
-y caf4896a2d3666200741d817ee1dac661652b9a1741ea966d5ed7cbc4c76217a
-m 0x00000000
-xx 4bc9b0d92be50270e29cc3181952e745cbf21c8d145ae0c0a6e59f25394ea51c
-yy caf4896a2d3666200741d817ee1dac661652b9a1741ea966d5ed7cbc4c76217a
-
-x d637a72affa4112bbccd2878208ce34fae442e97175e1b39f43c00b14d312a2b
-y 76209f8b1f152ba7e1e6294f707831021eb2ac03872ed3774ab8fc5e6a0e864f
-m 0x00000000
-xx d637a72affa4112bbccd2878208ce34fae442e97175e1b39f43c00b14d312a2b
-yy 76209f8b1f152ba7e1e6294f707831021eb2ac03872ed3774ab8fc5e6a0e864f
-
-x 12f3bd417fb3860b2a4fd04eb1c51c558a4c5a3dcc1ac457654a45a3cd45b0d4
-y 46f802836c7bde099775f3fb4f5f6345364a7e158bae9e16c4c99aee0cfa5e42
-m 0xffffffff
-xx 46f802836c7bde099775f3fb4f5f6345364a7e158bae9e16c4c99aee0cfa5e42
-yy 25f3bd417fb3860b2a4fd04eb1c51c558a4c5a3dcc1ac457654a45a3cd45b054
-
-x bf1809201f83a34cb07aa2e2372516631ba0513e600956e6702903e9084770c4
-y 414bbc77d13d7b4e706acc07406e8d624f2485463f9948d81b72268c1e086a14
-m 0xffffffff
-xx 414bbc77d13d7b4e706acc07406e8d624f2485463f9948d81b72268c1e086a14
-yy d21809201f83a34cb07aa2e2372516631ba0513e600956e6702903e908477044
-
-x bb8703f2ddaaaaa6ad19219684b1bde576b38bbe9065178b24c1bc55563fe525
-y 1cb3ca7846a3c584b1bc05b25ee91d4779ab9ac64ecef0fcbaea8d311b55d618
-m 0xffffffff
-xx 1cb3ca7846a3c584b1bc05b25ee91d4779ab9ac64ecef0fcbaea8d311b55d618
-yy bb8703f2ddaaaaa6ad19219684b1bde576b38bbe9065178b24c1bc55563fe525
-
-x a07c7110c32e362864a42cd2f371ff420bfd442d291cc15ec079d642b5c85bdf
-y 497fa7867fcd0617c4cd765aa6f46b89390744b5b57d11ab732153e075fcb607
-m 0xffffffff
-xx 497fa7867fcd0617c4cd765aa6f46b89390744b5b57d11ab732153e075fcb607
-yy b37c7110c32e362864a42cd2f371ff420bfd442d291cc15ec079d642b5c85b5f
-
-x 10fddb7f48015b394512257da026938b67f65dd0a84dace51417d68da003a913
-y ebd6706b7cd2ee2d97848ee1adaa990d8ddbfad48e43f51d7ef843fa7597410c
-m 0xffffffff
-xx ebd6706b7cd2ee2d97848ee1adaa990d8ddbfad48e43f51d7ef843fa7597410c
-yy 10fddb7f48015b394512257da026938b67f65dd0a84dace51417d68da003a913
-
-x 1dd835e2173b936a91da37b3aa11e848e4497964a9a78ea929a19105eb981a24
-y 3e6f1ab7d5c460dfb7ad1926c60b64a8dd48ed0115b0655a6d8619666b8c8dde
-m 0xffffffff
-xx 516f1ab7d5c460dfb7ad1926c60b64a8dd48ed0115b0655a6d8619666b8c8d5e
-yy 1dd835e2173b936a91da37b3aa11e848e4497964a9a78ea929a19105eb981a24
-
-x c4541b1380e796a333d88affdccb4d2bc68bc5a1b3890ef2fc1a2c38dbcac725
-y 6f6338ad8dc0562bc02e307743b81013ffff6c135fdf8603f9956b7f94eb55fa
-m 0xffffffff
-xx 826338ad8dc0562bc02e307743b81013ffff6c135fdf8603f9956b7f94eb557a
-yy c4541b1380e796a333d88affdccb4d2bc68bc5a1b3890ef2fc1a2c38dbcac725
-
-x d71f16494f041d1547e5dd9ed539e6b9c1506cebb66f6424e6c7aaf6d0ace080
-y 78c1e6cc0b6f64e161def3b2ede7465f21f6afe61299e9a3c52b1a7a080b9b26
-m 0x00000000
-xx ea1f16494f041d1547e5dd9ed539e6b9c1506cebb66f6424e6c7aaf6d0ace000
-yy 78c1e6cc0b6f64e161def3b2ede7465f21f6afe61299e9a3c52b1a7a080b9b26
-
-x 4d90838ab9cc0a79f4e2aa6a860bf8cfbce5f834aab428d4a06f8ef4a2da582a
-y 53124b302e7675ea5784e2e7d9fdecb38d9c8be158312dd81c51757bafb79b42
-m 0x00000000
-xx 4d90838ab9cc0a79f4e2aa6a860bf8cfbce5f834aab428d4a06f8ef4a2da582a
-yy 53124b302e7675ea5784e2e7d9fdecb38d9c8be158312dd81c51757bafb79b42
-
-x c8e764092ea695b0dd8f0ecbca5a4e02096c821b0f5cd57de8e3e50d8b2a40db
-y db7fb38dfede5259a584dbcc697f259ce380110636e301acb308bf687449110e
-m 0x00000000
-xx dbe764092ea695b0dd8f0ecbca5a4e02096c821b0f5cd57de8e3e50d8b2a405b
-yy db7fb38dfede5259a584dbcc697f259ce380110636e301acb308bf687449110e
-
-x 34cf8e55b3d2494362a87a24907fbdab61cb4f452ef5a889a1aa40a22be6d976
-y 679c6d6f6dca1b71bb098e3854c63ffb8ddb76f1a1cb246ce956fd71d6477c20
-m 0x00000000
-xx 34cf8e55b3d2494362a87a24907fbdab61cb4f452ef5a889a1aa40a22be6d976
-yy 679c6d6f6dca1b71bb098e3854c63ffb8ddb76f1a1cb246ce956fd71d6477c20
-
-x 9638ab322ced065068f98597cc61fc2bd846b5849dc39a881209b8efcbc95eec
-y 32922ff2b62e968417225b765f2787387c8a42fcab1dbec3815298f53813a8cd
-m 0xffffffff
-xx 45922ff2b62e968417225b765f2787387c8a42fcab1dbec3815298f53813a84d
-yy a938ab322ced065068f98597cc61fc2bd846b5849dc39a881209b8efcbc95e6c
-
-###--------------------------------------------------------------------------
-test mulconst
-
-x 8d517a8804d934ae93388e1d59748c3c22866d7be6cec58a357ec43f6dd029db
-a -319312
-z 3f2fea85c9195f2246f4f6fd2e8d5de95c5065edbea45a174bc0d1ef3db4aa54
-
-x 1b5d6a6c9cdd0dabd126e5f5ee2513f3d27c56dd3aad89c882fe9fd2d38a93b9
-a 499342
-z dd310555966ebe7f409dcce2933f91af8e14c8909f78e4f113606789dd7f504b
-
-x 9e03b44e93743e0cf5768f65bd3c0f255e001de330d5e1a863d6e4dbb11748a9
-a -284189
-z 6e8c7f8d0f1476cf2603f5702fe8e8bba5c01e86b6e008ac72987fdd6721183c
-
-x 9cc65e302736aab9bf02dd451c216ac3dd2066af299d7f6bb361eb3b36777f74
-a -15738
-z 8c067e5dccdafaf56301050be17b8895c07e7f13572bbc5ce1af8b5be043d91b
-
-x 7f36ff91ed165c6ee44aca261dc09e3e124c2ed8167064c20d9b84fa226e2555
-a 423857
-z dc7415db1ab5e5a5658d089ced49bf97718bccc55e2f15b83a28157cbe47e559
-
-x e8852c80db69c7e55d476ed00ca7c0735052f7f72f81198a57236feb89a5903c
-a -140934
-z 4923ee40bb01314c2fe9f2f87d0743823311b2d9265219eb7a6de5fdfd09a308
-
-x 505ef65d294b77e260757bc867199c4b0922b5022dfd6a1fe7478ea27ec102c5
-a -307893
-z b14d72c991a0bfc22b1b95934bbe589b6a4a1f9c76a89d7012f8cb03379a8844
-
-x e410c260dc8c1838f3e9658ae586425039b373ee2ab88c750a51853b012af0af
-a 471420
-z 42ae337a920ee1b83768cbf0750f524cf1f9e98b99f195e869785f90a2356756
-
-x e2d181914b54175190462d11402717f42efa37967b2fe0bc4433fd4c862fd646
-a 492178
-z 4c6e1ba6896d2d661fbf99b77f63e3095d3341f04bf258dc3e4f51e39c68f576
-
-x 9cdda0d7da106ef5cfb34774f48308b64953e92869dab0ba804927080509d8a2
-a -312149
-z 4e75e56793563268480efaf6232ad702bc5aef6246bd44e3499ff437810b523b
-
-x 9dac4442858b8dcc324464911e6f23ed046e42612e8105dc3aa2b9eccea15dc8
-a -88818
-z ce52a0897600a05383df0a0b99a451f0d5568146b4323392fc164153715ecb0a
-
-x c9f92ceffa7027ffa71e64b714c36b28a6a18c3608f8170d11d51acbee3c62ba
-a -259755
-z 89582517069925572219b2eec2a25029e8e1c78772ca8c50bf23220d02740763
-
-x 8f8bcf28f4920465680c8e15befba4ebd23c1e27b71c224c98461f69caf76eb1
-a -430350
-z e96b93f0aab6ca70f7d2c1121110efc320aff34e1ec693d7bf17bce1a756d622
-
-x 6f4d413a27388fe84a2585e809927bd470ba1b0dc749ae6e2dfa100617a5a7db
-a 11486
-z 1cf1f5bd0770d949ee36df858e5842805d121722de30d2ef6bc2b82d021fc14b
-
-x e1d05a072d1ab70d895969271f44b7c9d1654171836cf234724d2f90434c04e6
-a 8057
-z e32b3c792cd3b6a770eaa2627ff8de8895873d73d734b961646fbce0643a443d
-
-x d8564ee3ff02c80f0bf3e9cdfce42cd8ac1012ad8ea74f8c0f5754b5775a8de5
-a -304373
-z 884266ea43a6a9b72d113b437dae63c664ef53884c893212fd864412f4e5e457
-
-x bf66769ee0cf873764524e760ee654e8d5090aa774f2e96144d945f8da37af19
-a -159091
-z d7438999b3bdb99a46e2f3dc8492cbaf52b0a19c651cc382c384940861bccb6b
-
-x 72b7d02b1fe23adea87696864c0a9f0466db85e39db397f0eb428a50e277aa2a
-a -521654
-z a611bd153336e178a7f3d912adc2fb39b342132458faeedbdb0a35973efae23e
-
-x ff5c39d4b7fff86810a7a3b14a58bc01e6ecf062116adaa78dac0d1bd3f6039b
-a -140759
-z eb9e32bf7d027cda198048da50aa79a11bc99f3b37a219a2104c78f4affb584f
-
-x a6f1f7f30e3f9e5467f180f92d2c94165fd9427d0c7d383b9077ca9a7e50dac5
-a -317637
-z 56a32847c50bc9609db9796e1650fbe97524aacea746d3cf285f0f2fced01a49
-
-###--------------------------------------------------------------------------
-test mul
-
-## Easy multiplication.
-x 0500000c00003800006000004000000009000006000048000090000040000000
-y 070000180000200000e00000800200000400000c000030000090000080020000
-z de200094610090df0020fe0180270700650d00dc2a00f84100e0340040570000
-
-## Random tests.
-x adcc6f10734dae2273304a6aa493ee8f96e05f2402341c0d997dce58ea57ff6f
-y df3c8d5bb6380fa278d4ff2994c7865bcc146596d3c3126242f0dc3509b57449
-z 5ee2615b75a40367ced4ed4bf1578d13e7afa4d415f38f802b7e7b374365b627
-
-x 054bc4d5e9b78b068fd20645eeb1f03aef2e89a1f56cb50e5f1170a86529526a
-y f976ffa1d1b4a33d0fd866528897cea3eaffdc75e31aa65450a62ff765fe7985
-z 0210280745f6c29a04433f07f880bfd2eddd758d82996e79c65de817c30e7309
-
-x e361c6fedbbe081b7cd683d23a2bf0ac889806be7230b56d9398959713a300ec
-y c8121e53d78c2e9ba2ba7f51b7cb15cec970a63b4a642ac470aa1f2145f07bd0
-z b48bb1c7ddd26cd9e5a2cb73bb3885dbe4a47e03886d4dfd59e5729d544d566a
-
-x 463158a2077f931567d45e19deb4454a2ae77045db70a2c078e160ebdb74fd94
-y 3f311e3f8d225016448fbce3fbfbe84002736e3b0d5a90f57d705ede8706008f
-z 44cd97e25c20ae2fe2ef4f2630981a1fe54c79ebd904bc40e39d9fa615ffa76c
-
-x 1c73fca52556e01204d4b957a01d1049f2247c8666d90c1d3703cff16a38c8bf
-y e9afa0cc85577ec7eb1ac66d87260d5f3659936ff88cde8bd1c3fa1d499e8bcb
-z 0979a8baf734c86a4f57ae400b7790c4985fba3088cb1b265dfc7a66c794121b
-
-x 6e2bab74e427b1a44f0cb181f9dedd6fed43cfd395d3708c4ae8fd2137215eb6
-y ef400834f2dad8763a1a5a58a37d1b36a78873860e4dac808d3166f13724942c
-z 0d481adbce7bd82ebc5a3e5ed7a492e78a032ebf211a5bd2371c528c77954936
-
-x cb3575b41d9521da5c85c6438af14903a8d6d9c3857aa8e101e5295fb277de7b
-y 9f76715d2ae3c8ca182406553d3481fc36d67727ca2d51f5db37940aa3208d8d
-z 0b2fa619265bd424b9e20d38bf4552ad63de8ab552166080d099edea5fbadf7f
-
-x abd66cf3b20dc4c5a866f1a3b965f794a726f96dd00f576d16ead66eea3a1177
-y 97f70fc92e0cda0e010f2a9d7608c33db954af18bc18ad55bf66e7d91ae31abd
-z dcbb2cf34274971ef030827865b093a00761de3da90e46f00e18d0fd934a2b7f
-
-x 3b3c96ff9be8e17e0a0d3979ea5e5623fff5fa18914151abf79fe66639beef06
-y 1d29c361677805f1dd2b839e025e56208a10c0b8d9f2a8c490b0a892c0e27080
-z 0050873016bc67023d0c479fffa56a5a70512f9864d00b0a3e951f1e85c8b412
-
-x b263d4a71b6d963e0a972819e5e5805b9522f142d3c0ff2738c51cce31e9f0d5
-y 64f3fbcff2195c297292df3e1cf900aae457e09864c5a6248ea21ef8efd557d9
-z 7e6f6f511cbf2743c0fc1c6431243908606cb257d20f8a8a0885e6ecd000e811
-
-x 0df0497e1e01dbcc4a48d4865127d9cc31a9a0a56e90cc31619e65c1521b2369
-y 9277f0c6a5bcd7c7ed8dcf7182795f67a12e856b126d09966689834c43aada47
-z 798d270ae34aa2452694b4ff74049a6a5169d71c85bd1a9ac59625e9298cdf1b
-
-x 1dc64bef2189eb5349f5a8983c1854a40141a5390ea4bf8535a15aa71d0289b7
-y fb59dc9b08f9163881b10020ce040da296ed8c1a9a935c27ca0047a4d7f6342b
-z 9fc23104cefd3014a469e6d3a0631338eaf91e24994ecd50bfc0b4547317317e
-
-x 975b108909e87803af98af9425d2a982865b6cc9c144985b32fe5bb842702e24
-y a69e9130dc40be50e827dc50dac05bf900946cf67ec35f1bb1705001314e4fcb
-z 12d042e50d0cff7b43a5ede61ce827a99619bf84995d488fe9eb56a8de769164
-
-x 39c0db5a4b161c368b0f71c7e8ef97dddc444e4a33181e0743519f2a879ae04f
-y d3cc45ff509ed45998bd5f218408ad51f7457b35e8ad69d5431f174047d7c6e5
-z 96b877604f52782ff2a5b1a12d7db642371ca993b648c4971cbf593213503219
-
-x f8c6715e4a327cbbdbb08d74121619abc73dc421d7267029e39b50c1510d2045
-y 63870a83cad4c1c64195ae7b92f3b19c830f35f1a3186815565d846c787c7ffc
-z 286a0b8c6681a7b79a5f85426fb60819b7bd349e93c1e11943c41c8dfd57d00f
-
-x 49c9bcaf5434b8205a348df290a96da27df084f34047efbf91cf544057a50bde
-y 54269f8b23c05b94c9c1cd74eae88d9227af12a6fb337548eb93c2a88a75a8a5
-z 1e3dcab5d7361f00e70198b52e8fb6d1fba74abd79d99480527f6711b21b833b
-
-x c7212b43ff0d10fc52d3a2a7e15bb9cf53856f7ce33b79df89e1d13f95a94511
-y 5213ec20bd054491a5485f665075835da609ad4f3dc005744f061480862ee602
-z e136339fa01067c6c0823a7ebe2f84d917600e244a9883191900bb95a3b59764
-
-x a15d62c6308448f1f70602f43be1825696d228eb170bed55322a21d2b1afa915
-y 58afe65bc8adbe22807026aa1b0d68af330bca268fdc054406aa41c820960e71
-z 996c597e0a024c2ff0ffe289d8c7270e4ea1d38e294d7210eddeb2c0725a1305
-
-x ea233ae033ca93034bc8fd8ea3c0625bbb15b00265264fdd61f62cc808b505fe
-y 09e12ef9b3426991f7119c2e8349278342ed0072317c4ec7ab24561b61396b39
-z 1fd72191fe9f00b0cca6a635d14904bd0c1e0ccd1275e84ad0b7bde134866e2a
-
-x fe1fd3da05524af4ccd538f1d2ede09582101fc2a47c2e63758a546bed6cc5ec
-y 523346406ef3df6ac9a455d0d2e7f732ad01c88245b07a888cc21c40fce11a76
-z de6cac8fdc878d9c4eda6b78f8b629ecf776980e49fed56bab936fc03924f44e
-
-###--------------------------------------------------------------------------
-test sqr
-
-x 4dc87ad85abe8938634492ce2ea10bf48dc4aa2fa37a6a0fde3e5a01e90dde2b
-z 346297c756d77b8ea312ddc455223f4577aea2a2e8d944cb24adb487de143b46
-
-x a33aed91165d7fd13a543760d3915c1b5d411a21895cde81b2f3640b87550cc9
-z f923e49da9d5f45e23a782f911fac1a6c2e67cbbc7b03ee4675a0c5fbec03641
-
-x a1406e453db6c92ef808295d1919c5bb2491c0ce6d5326d276c57e57943e0acc
-z 18425bbd92149991c4545e65495af0e6372289e9a32649c127122243204bdd73
-
-x 70a56b8484234ed002a68c8d535a4e527a61c360f7d4ee5b4970c8ace1e12de0
-z bed1c435139f151d0650577e03c32428f63cdb7bc1920110b5fdbb27f08cb200
-
-x 86c3236a6194f1585b4dbeb09d0247fb7d3ae08063ccf9fc4fde70fc23735710
-z 9b6509acadd5d31c4c843e91cec78be00aec4fdf7d86132965bd6f62f078f711
-
-x 0e5e83c51a8c091673425c38785e0aa1d74c7261a035a891bf734cca8c8a3db3
-z 4efe5029e99438835a8a45d0180b8de357eac82ba9dd8e127baac0d758dfca1d
-
-x 31c39a5afc33f8a8d3c570b9dc5389bea6fdaaeeb44cd7524f6c445b9583a34c
-z 359b7c8791cc87aa8b3c799c9d4d7e1f4062a4f64436d8c01071597e8c262127
-
-x 5a06203c15d6c1db6ea0fcf468a1e3f09d68c4a0f64c3d7e30e70290545e708e
-z 07f8b435ea322bedf613458b1eb420f1d6bc96741d69695899bd40f7eca6f72a
-
-x b1973433646474167b791b326827641260fb33d6a2c96d4e963a6b091f824505
-z 52a62396dbbceead62912f8adfed2707fc25edb51aac19b2a274c246f1209f26
-
-x 96b157d71e107168fac206dd63007f10f4ae1225b0761c470ee18ecdb4fff20b
-z 84ba2a84b156437cdcc39ecc8b1ad01bba934d8dfb7d504b9f2442db0ad01167
-
-x 6167d77675e19785960c28df551b458e41dfd0dfe5e56e785b7367997d5eb0a6
-z 79a558436af4310d3eaee93f9a7cab72bd817fdf59d267e2c530ba8d667a005c
-
-x fb4b2ab08db932ce10dd62639aabbb266f9ce775fb5a5e0875864f18a3ee506c
-z a6013661f2f0ab875739836039bff6bff4c993aefdda43dccecf4c404b9a612a
-
-x ea26bcf0bfc3e15d4df7ddbcac8b5b9e9a7215d74196d77c9e0524e861c6aeb4
-z 113e06861e3d338618695f4713464cea536c8019da77ff0dd9946f3b860df062
-
-x b67b1ffffec757ef147e86cf60898c5dac515f080f43f4e120017caab4eee5ee
-z 7d9748a1ff6ca9cdebeb3dd6668522767afb9ebf1c680fe7fb3f5848f7222036
-
-x c122016f17f12e53f9ac031719fe428c826217b2b757ae44f2f33d1b8b1bb553
-z dc068d032b97c98eea6dd6c8bc42e9a0a6250c81a36a8f64615489e191287c72
-
-x 1266ff0654c08e6183cd6c3cc760cc5c88d1f49b918f2f8f587b3edd4adea513
-z f07f17fadb2e2dbd282d296fe5a15cc5c2baf6b45f5fd5dc4692f252039bc862
-
-x 4c4dd9c6e46fb2c096388583f2a0c969245452b23f16ea43e15064c45357ccef
-z 5127fd4415a84115997b8b3ebe88a590efde9f8b53a43e86b1a4d60782c91025
-
-x 095d149c2616212e5f770f133e719d285a8bc888414271296684e732feb5473f
-z d8038bee551cac14d1c610bbc0960d943b01526072c589bc913ab51fd47bc848
-
-x ad55f9f916d62bb13ceb1461b99e82d76b860c084ca408dd4a18f154b907754a
-z e5c86ee6350c9ab736229f3f53e2ab852641bb8a62fdda609444df377e9ca04a
-
-x 2e4976f45acc671e38add93aa6a89669cdc9874975879b3134dd37c633c9eb14
-z c6513f1a11346d33b05ad65eca13f11125cf70bdcdd6e666a8a7b9c5b6098429
-
-###--------------------------------------------------------------------------
-test inv
-
-x 344ff33a2bc801f861bd13575797da35352c8164808d27f51ea7ca46931b2b1f
-z 07f678dfeef071b038d692bf825cb4e75bc1934bd3a6e3dfea99e78bdaeecf3a
-
-x 670097e2fbbecf6516e949d98f6d722d3f732c33bfb4e62512f9d28d94546b64
-z b2f5cbcd7d8c996ed33a813b1aa39c36f5826b436867bd89b4ce43a156c1e96b
-
-x 234f3bd8760cdc8ae7fac9457da418cd082e42906ffe59a13e52185a7845e61c
-z 7488ff9231e4819684148e16ebc25440732ffe7d211eb3d3263db1af9f1d0513
-
-x 22a39a35b1cabc6dfecd1b898593070f0c81bbd04b4b20f43a9c7c14b5dfe967
-z 892024fdbc8937b9b3aef794f57b8ed8517510b6de3f6088987b1310c1dc7932
-
-x d850c118c69198268826d05650958c6bed55b181090cf1c96493ecc4635a913f
-z 7aeae1b0dc5211f374872e78da8f225325f3f33f9c42bfdeff25d425dff7710f
-
-x 33ccdc0e39f7cd0a61782c87ac089eb7bbcabce4dd222f05088d3d6332efe959
-z 668f87e23239e965c80740d4daa9c913609388f291c11f950684f45e689a061d
-
-x 7c06f93b2f66001c74073b8ba7536049738e89b0a0d859a8a73710de3fadcf79
-z 52df0aa24bb4a7474e6ed9852ba542c1f4c5219372a7b5d60988890e2955491e
-
-x 9a0ce9ff4026bd58abcf8a128dbc55a19c446005834a143634452821d5f9f0ee
-z 79eaa93b6287705c0ba564c31bab1854c7f4354845be065c4bf94d38a7a8b421
-
-x a13a127490bd3443fdba99baf61d113f3aadd6966c9732cd16348f9fbed32e0e
-z 67290b25e6bd7328dd804309a6203c02a75657f593c7e66e48c9192524e5b87b
-
-x 35f7ac3eaa36c4ed338388fe7eda61cf237eff6ddc0847cb0c95255bbaef8ddc
-z 4950601d2cfe75eb9c4524e2f40f404fe82d0014c916dc43d9416cd2e274992d
-
-x 8a058593035986da3a19e63dacaf40fb3db4cf382205fc4e4802e0ff0c61c8d6
-z 6a23b743dc2fa4a4132780cf6edfed4c219760f3b31343b08710ea18d2c0fc43
-
-x a10d03234e700ec92270b6105fdb787d8edd3f960fdd78ea2e169f49dc708d45
-z 101dad1720604d0b093831baaa97fd0701ce773b9c1be1db0403533ad4376c0a
-
-x 52d3b9e030a5ed574f7f9489c47e73f78ef88a39b570045f9ef73c9a3e65f425
-z 83da3e088dbc9a3cbe06496c5a52edc8d7abcbb8a0f839361762137b119d961a
-
-x 9928b5f14ec80a036479d7b08c128e601db880daebef36adde6fbd1f50f82629
-z 8dcaa9a2439b77cbe44928ac2877e09755c505f58df4d0ffb9b23fc256b12779
-
-x 5a956523956f8ace6166ea6cb3c7421f8d1142d26084a81d615f00d578e03448
-z 658a3ee24ec5b5f1d2d12614e535247c9f2f259131b00f654e09b4517c63ea09
-
-x 157492cd38a07802351ca0d1a5615d5c5f254692acce930fb6be351e9a52f088
-z 32fec1eab85ddf8d27a437876e7f5a07f012b02e7971869811c3c31230204164
-
-x 2d07c109c332847567621ef4338e149b99c5bc3bf6e50943695da7fed5d8141e
-z a81472d28a8235bff43ad5cc012d52e95ece3dbc5ba2962dc54cf9e7f81bee04
-
-x 7e172f6c03415e83d4671e0191151d49e5257651ba73848254e68fad0a095c50
-z 1a8efdc57ae9d39ffa64afbc5d2dc1f25a29d365ac3dee0d8529977c14aa4415
-
-x 1934546e37b0bac80319fa7f2f86c18e83de8da830b9d0b5019c26768974eda4
-z ffe55479771f20518d8fc6491055368b5dcce9b4e193d19897f1e116b9cdf946
-
-x 90324ccfe0e34e9b08db1862be3bc17798a8581ee097be76545e3bf9d586a2e6
-z 0f5ccf4920d617c9b4f7fe6e2c9e95e89b5516555d5e3f5f9900485451d7425f
-
-###--------------------------------------------------------------------------
-test xdh
-
-## These are from Daniel J. Bernstein, `Cryptography in NaCl', 2009-03-10,
-## https://cr.yp.to/highspeed/naclcrypto-20090310.pdf
-
-k 77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a
-X 0900000000000000000000000000000000000000000000000000000000000000
-Z 8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a
-
-k 5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb
-X 0900000000000000000000000000000000000000000000000000000000000000
-Z de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f
-
-k 77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a
-X de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f
-Z 4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742
-
-k 5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb
-X 8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a
-Z 4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742
-
-## These tests are from RFC7748.
-
-k a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4
-X e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c
-Z c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552
-
-k 4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d
-X e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493
-Z 95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957
-
-###--------------------------------------------------------------------------
-test xdh-mct
-
-## These tests are from RFC7748.
-
-k 0900000000000000000000000000000000000000000000000000000000000000
-X 0900000000000000000000000000000000000000000000000000000000000000
-n 1
-Z 422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079
-
-k 0900000000000000000000000000000000000000000000000000000000000000
-X 0900000000000000000000000000000000000000000000000000000000000000
-n 1000
-Z 684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51
-
-## This one takes aaaaages.
-##k 0900000000000000000000000000000000000000000000000000000000000000
-##X 0900000000000000000000000000000000000000000000000000000000000000
-##n 1000000
-##Z 7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424
+++ /dev/null
-/*
- * x25519.c: Bernstein's X25519 key-exchange function
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the test rig code: a replacement is in a separate source file.
- *
- * * Ignore the top bit of the input public key: in Secnet, conformance
- * with RFC7748 is more valuable than flexibility.
- *
- * * Strip out the key-management definitions.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * The X25519 key-agreement algorithm
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-#include "montladder.h"
-#include "f25519.h"
-#include "x25519.h"
-
-/*----- Important constants -----------------------------------------------*/
-
-const octet x25519_base[32] = { 9, 0, /* ... */ };
-
-#define A0 121665
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @x25519@ --- *
- *
- * Arguments: @octet zz[X25519_OUTSZ]@ = where to put the result
- * @const octet k[X25519_KEYSZ]@ = pointer to private key
- * @const octet qx[X25519_PUBSZ]@ = pointer to public value
- *
- * Returns: ---
- *
- * Use: Calculates X25519 of @k@ and @qx@.
- *
- * Note that there is disagreement over whether the most
- * significant bit of @qx@ (i.e., the value @qx[31]&0x80@)
- * should be ignored or counted towards the represented value.
- * Historically implementations respected the bit; later
- * convention seems to be to ignore it. This implementation
- * honours the bit: a caller who wants to ignore the bit can
- * easily clear it, while caller who wants to respect it has a
- * difficult job if this function ignores it.
- */
-
-void x25519(octet zz[X25519_OUTSZ],
- const octet k[X25519_KEYSZ],
- const octet qx[X25519_PUBSZ])
-{
- uint32 kw[8];
- uint8_t b[X25519_PUBSZ];
- f25519 x1;
-
- /* Load and clamp the key. The low bits are cleared to kill the small
- * subgroups on the curve and its twist, and a high bit is set to guard
- * against careless implementations, though this isn't one of those.
- */
- kw[0] = LOAD32_L(k + 0); kw[1] = LOAD32_L(k + 4);
- kw[2] = LOAD32_L(k + 8); kw[3] = LOAD32_L(k + 12);
- kw[4] = LOAD32_L(k + 16); kw[5] = LOAD32_L(k + 20);
- kw[6] = LOAD32_L(k + 24); kw[7] = LOAD32_L(k + 28);
- kw[0] &= 0xfffffff8; kw[7] = (kw[7]&0x3fffffff) | 0x40000000;
-
- /* Copy the input point and clamp the top bit. */
- memcpy(b, qx, sizeof(b)); b[31] &= 0x7f;
- f25519_load(&x1, b);
-
- /* And run the ladder. */
-#define MULA0(z, x) do { f25519_mulconst((z), (x), A0); } while (0)
- MONT_LADDER(f25519, MULA0, kw, 8, 32, &x1, &x1);
-#undef MULA0
- f25519_store(zz, &x1);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#include <stdio.h>
-#include <string.h>
-
-#include <mLib/report.h>
-#include <mLib/testrig.h>
-
-static int vrf_x25519(dstr dv[])
-{
- dstr dz = DSTR_INIT;
- int ok = 1;
-
- if (dv[0].len != 32) die(1, "bad key length");
- if (dv[1].len != 32) die(1, "bad public length");
- if (dv[2].len != 32) die(1, "bad result length");
-
- dstr_ensure(&dz, 32); dz.len = 32;
- x25519((octet *)dz.buf,
- (const octet *)dv[0].buf,
- (const octet *)dv[1].buf);
- if (memcmp(dz.buf, dv[2].buf, 32) != 0) {
- ok = 0;
- fprintf(stderr, "failed!");
- fprintf(stderr, "\n\t k = "); type_hex.dump(&dv[0], stderr);
- fprintf(stderr, "\n\t p = "); type_hex.dump(&dv[1], stderr);
- fprintf(stderr, "\n\twant = "); type_hex.dump(&dv[2], stderr);
- fprintf(stderr, "\n\tcalc = "); type_hex.dump(&dz, stderr);
- fprintf(stderr, "\n");
- }
-
- dstr_destroy(&dz);
- return (ok);
-}
-
-static int vrf_mct(dstr dv[])
-{
- octet b0[32], b1[32], *k = b0, *x = b1, *t;
- unsigned long i, niter;
- dstr d = DSTR_INIT;
- int ok = 1;
-
- if (dv[0].len != sizeof(b0)) { fprintf(stderr, "k len\n"); exit(2); }
- if (dv[1].len != sizeof(b1)) { fprintf(stderr, "x len\n"); exit(2); }
- if (dv[3].len != sizeof(b0)) { fprintf(stderr, "result len\n"); exit(2); }
- memcpy(b0, dv[0].buf, sizeof(b0));
- memcpy(b1, dv[1].buf, sizeof(b1));
- niter = *(unsigned long *)dv[2].buf;
- dstr_ensure(&d, 32); d.len = 32; t = (octet *)d.buf;
-
- for (i = 0; i < niter; i++) {
- x[31] &= 0x7f;
- x25519(x, k, x);
- t = x; x = k; k = t;
- }
- memcpy(d.buf, k, d.len);
-
- if (memcmp(d.buf, dv[3].buf, d.len) != 0) {
- ok = 0;
- fprintf(stderr, "failed...");
- fprintf(stderr, "\n\tinitial k = "); type_hex.dump(&dv[0], stderr);
- fprintf(stderr, "\n\tinitial x = "); type_hex.dump(&dv[1], stderr);
- fprintf(stderr, "\n\titerations = %lu", niter);
- fprintf(stderr, "\n\texpected = "); type_hex.dump(&dv[3], stderr);
- fprintf(stderr, "\n\tcalculated = "); type_hex.dump(&d, stderr);
- fputc('\n', stderr);
- }
-
- dstr_destroy(&d);
- return (ok);
-}
-
-static test_chunk tests[] = {
- { "x25519", vrf_x25519, { &type_hex, &type_hex, &type_hex } },
- { "x25519-mct", vrf_mct,
- { &type_hex, &type_hex, &type_ulong, &type_hex } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, tests, SRCDIR "/t/x25519");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
+++ /dev/null
-/*
- * x25519.h: Bernstein's X25519 key-exchange function
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Strip out the key-management definitions.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * The X25519 key-agreement algorithm
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_X25519_H
-#define CATACOMB_X25519_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Notes on the X25519 key-agreement algorithm -----------------------*
- *
- * This is X25519, as described in Daniel J. Bernstein, `Curve25519: new
- * Diffie--Hellman speed records', PKC 2006,
- * https://cr.yp.to/ecdh/curve25519-20060209.pdf
- *
- * Since then, the name `Curve25519' has shifted somewhat, to refer to the
- * specific elliptic curve used, and the x-coordinate Diffie--Hellman
- * operation is now named `X25519'.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-/*----- Important constants -----------------------------------------------*/
-
-#define X25519_KEYSZ 32u
-#define X25519_PUBSZ 32u
-#define X25519_OUTSZ 32u
-
-extern const octet x25519_base[32];
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @x25519@ --- *
- *
- * Arguments: @octet zz[X25519_OUTSZ]@ = where to put the result
- * @const octet k[X25519_KEYSZ]@ = pointer to private key
- * @const octet qx[X25519_PUBSZ]@ = pointer to public value
- *
- * Returns: ---
- *
- * Use: Calculates X25519 of @k@ and @qx@.
- *
- * Note that there is disagreement over whether the most
- * significant bit of @qx@ (i.e., the value @qx[31]&0x80@)
- * should be ignored or counted towards the represented value.
- * Historically implementations respected the bit; later
- * convention seems to be to ignore it. This implementation
- * honours the bit: a caller who wants to ignore the bit can
- * easily clear it, while caller who wants to respect it has a
- * difficult job if this function ignores it.
- */
-
-extern void x25519(octet /*zz*/[X25519_OUTSZ],
- const octet /*k*/[X25519_KEYSZ],
- const octet /*qx*/[X25519_PUBSZ]);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
+++ /dev/null
-### Test cases for arithmetic mod 2^448 - 2^224 - 1. -*-conf-*-
-
-###--------------------------------------------------------------------------
-test add
-
-## Some easy ones.
-x ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
-y 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-z ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
-
-x fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
-y 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-z fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
-
-x fefffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffffffffffffffffffffffffffffffffffffffffffffffffff
-y 0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-z 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-
-## Random tests.
-x 6b3944398448a0a5f6c4e1be9abfcbb082b8f68f1c831d51ef2244f6e1a4c4baaf0ada769c1261b8e14b4856de381d69961078ea1949d39c
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-
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-
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-
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-
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-
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-
-###--------------------------------------------------------------------------
-test sub
-
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-z 6e1136912135ab628146ae4b7567e6e5b79e1829bfc3d638a39499b0545adb0660c4bbeffe2c8abb7ed2e79df8e2e809d043941fcf4614a7
-
-x 25ce194230be078d7f35b85d68706d768fec7994654fcd3f63f3d32eaf59f17bc87a617d41f76b7d0c78b63377a203e43194f0b056d26b0b
-y 76266bea72a15cdc355867a490e775c909b7b6cfc833107e7c6b7dbaed2c8491c6d000b2d7d2beb72d72937285aa1bceff18aa35d0c52158
-z aea7ae57bd1cabb049dd50b9d788f7ac8535c3c49c1bbdc1e6875674c02c6dea01aa60cb6924adc5de0523c1f1f7e715327b467b860c4ab3
-
-x c010bfa3d130f868f2b975318139c2a847c69014b76164192b437fd7e26b892a5a2425670fe3e8fd9efdfa250f57579d1af2d24f8eb6ce92
-y bfe65616e278b6ce46b295600131bf5ea092451a87f6bc3adf1c86f2fe717351b073062ced1394a14051bb33f3874cca569aae8ba97605f9
-z 002a688defb7419aab07e0d07f08034aa7334bfa2f6ba7de4b26f9e4e2f915d9a9b01e3b22cf545c5eac3ff21bcf0ad3c35724c4e43fc999
-
-x b2f21992b1f2155b7afc3a1d731b52c03cf14208e634b7da123888d652afcd919e9f5f0bea8b9986c71a7ba08fefe58ee0402d9a23b95f2c
-y ae241fa6292c63f3c09301255a866825b39c9645512ea123486f9a873cacab567cd169c463fb1cf0417633a7055d831d23fd1d58dd42e726
-z 04cefaeb87c6b267b96839f81895e99a8954acc2940616b7cac8ed4e1603223b22cef54686907c9685a447f989926271bd430f4246767805
-
-x b714b60b2614ab6ce63bf8eae621357f2e921f79de94982fcd5f524015db3faa52b15ff042733958fa202786f61bfed0b9fb5d5873619aec
-y 0c99e1da4c747ad1a625321cf9359b1d823544d1eacfddc38e4bfd729ed2f9fb37760242340f7986843fb8fa0435bcb5cffdf11453caebcf
-z ab7bd430d99f309b3f16c6ceedeb9961ac5cdba7f3c4ba6b3e1455cd760846ae1a3b5dae0e64c0d175e16e8bf1e6411beafd6b432097ae1c
-
-x c5425daf8f7089def2ff910e256d9496fc109d2698cf15dec1ce3f8116231969c5ed327626362b0658c60e74023a3cae5ef128fb5d27cad7
-y bc4e49fbf095f73894c4d623a210475cb7ba78ebbcbee8ab55a851162f789fb21e72de95afe4ddd45b90289f94f6d02b5f5a4b90c603ea31
-z 09f413b49eda91a55e3bbbea825c4d3a4556243bdb102d326c26ee6ae7aa79b6a67b54e076514d31fc35e6d46d436b82ff96dd6a9723e0a5
-
-x 9aa20b4259efd3a701a63347181fa63f56f42a97ef836bf3aab88d30bbf28a91bbf713a0170024e6057e2281ac113f9b58cb13d63e850ea7
-y 09e7104367d8c0441d811ecc619af04def9236752c2d47bc508b0de3c3b29c74533d8eb9fee13279aed8d58247e4010206c697d9b72bab43
-z 91bbfafef1161363e424157bb684b5f16661f421c35624375a2d804df73fee1c68ba85e6181ef16c57a54cfe642d3d9952057cfc86596363
-
-x e8ead9316aeb8f56d43418cd3bb1a71234c9e20b4a6dc1604ffdfdbcaacebe73b71d18c2c167544304d895d67e2daa2538a4ad0708cd9acf
-y ff3603f0960bb7a92f2b7fbfe242b467164e0ca72e89bcab6c467b5391166d05c601b38de40643f04d5b50ff8ec62b18c69e9df74f01babe
-z e9b3d641d3dfd8aca409990d596ef3aa1d7bd6641be404b5e2b6826919b8516ef11b6534dd601153b67c45d7ef667e0d72051010b8cbe010
-
-x f37b41d9950036d560f02b8befd6f5c73096b8995850b9fc563291fba59fd994916744fbd4c1dd5d17a9e5ecd4ec4a658dfdae1ba7024bc6
-y eeda58ba400f16a946381fb11f0ac0db895957236bcc629ce9d1ea425eef8412ea73af488b97f1afa950736f26c3cace887417b699cc3410
-z 05a1e81e55f11f2c1ab80cdacfcc35eca63c6176ed8356606d60a6b847b05482a7f394b2492aecad6d58727dae298096048997650d3616b6
-
-x 2bdb71a053047c4173718ce104e5b8671fbd61c59bfe8b20b890ceda15a69d24eec3775f4ce8a9c16d36e50626bc334e0fc1be492d800c06
-y b1ccd0dac33ac46b2709f9626ed70136f98dfbc705ad93ea8f1b325d644daf2c0180cb83bfdbb7398d3f58c0f6600056a174850b9db91ed4
-z 790ea1c58fc9b7d54b68937e960db731262f66fd9551f83528759c7db058eef7ec43acdb8c0cf287e0f68c462f5b33f86d4c393e90c6ed31
-
-x 8f3fd6346c7f2dacf0d7cdb88a5bca3b222a895a07b169d0bcd0af0a9aa634876ae1a939262dd75bd12b5a97127155a015e00acac7d5cbc8
-y 0e9c03c5a06accdddd0d8613e41a00f2b586e297e366987e02e7536e0ca1b4c2c75fed619655acddffe8585c7a828432d90575731a4c8519
-z 81a3d26fcb1461ce12ca47a5a640ca496ca3a6c2234ad151bae95b9c8d0580c4a281bcd78fd72a7ed142013b98eed06d3cda9556ad8946af
-
-###--------------------------------------------------------------------------
-test condswap
-
-x db0be3ccfda1e2f8492bffb5d3344f1856ff1896b6a067d2fa064423ac5b05b669db1c9b51899c44a7f470be4173856d9aa3d1cd10cb8c9b
-y 3005560f89232a97cebf6808e7493dd0f17e572556b53723b57faee51d8a0a45c7fb51aeb916f59c74ea6041494483b2fdce72189d1bd031
-m 0xffffffff
-xx 3005560f89232a97cebf6808e7493dd0f17e572556b53723b57faee51d8a0a45c7fb51aeb916f59c74ea6041494483b2fdce72189d1bd031
-yy db0be3ccfda1e2f8492bffb5d3344f1856ff1896b6a067d2fa064423ac5b05b669db1c9b51899c44a7f470be4173856d9aa3d1cd10cb8c9b
-
-x ea009751f6a7045ec7d6d46b16cbe663f5a78fca3835626c79864bec4030443bb9349654d52b2edab92b8f4aa876a97e868aa6267a54e6b1
-y 8c6f864ef7f664f4985ed8c1ea0c63bd7ab355b5321c2712791b610a2dadddc90a65ca8d5c25ff199b011193796b08f96420934615103b7b
-m 0x00000000
-xx ea009751f6a7045ec7d6d46b16cbe663f5a78fca3835626c79864bec4030443bb9349654d52b2edab92b8f4aa876a97e868aa6267a54e6b1
-yy 8c6f864ef7f664f4985ed8c1ea0c63bd7ab355b5321c2712791b610a2dadddc90a65ca8d5c25ff199b011193796b08f96420934615103b7b
-
-x dc3aa7d363058993cbdc54e95f3c972a2cea17cdf9370fccdfedfa1ba939ca35f762c5c6283f84348282fd56d83539804427eabe3bd6170d
-y 8c47a0990eccf7300986232dbc8ee26e8996c3bb4b73663ec5525312bea8975221c9f49039840c181d042654a8c1806bb86702ac7d0b80f4
-m 0x00000000
-xx dc3aa7d363058993cbdc54e95f3c972a2cea17cdf9370fccdfedfa1ba939ca35f762c5c6283f84348282fd56d83539804427eabe3bd6170d
-yy 8c47a0990eccf7300986232dbc8ee26e8996c3bb4b73663ec5525312bea8975221c9f49039840c181d042654a8c1806bb86702ac7d0b80f4
-
-x 69b45538513af2148e0a2903539bc5e20fca4da447278bf5967091d2e781121080c14a41989f9ee5218c444d3a42989ba890c7be7faae5d3
-y 935eadbde0c571c29deb4d8404dd39a8cca177ced36c359abfa7a6cafe6075422e1d79cba8d81cdbdfa4a5144faf37b19ca22b2b40fe1a0b
-m 0x00000000
-xx 69b45538513af2148e0a2903539bc5e20fca4da447278bf5967091d2e781121080c14a41989f9ee5218c444d3a42989ba890c7be7faae5d3
-yy 935eadbde0c571c29deb4d8404dd39a8cca177ced36c359abfa7a6cafe6075422e1d79cba8d81cdbdfa4a5144faf37b19ca22b2b40fe1a0b
-
-x de30072f175127ad4200a08099f4d0df0edfa40eb02e21a03c5628dcb2f70da8bce9ebbb1ebed2aca391e73a4114c06bcdbf762bf28777cf
-y 5eaf3aecf1f7d1fd3b43be8fa450163c79f162b0c6eaa4b1ad39baaf3a4c36564e001c935fdce38e90789151beff0f3cc4fdfc2d86dcb587
-m 0x00000000
-xx de30072f175127ad4200a08099f4d0df0edfa40eb02e21a03c5628dcb2f70da8bce9ebbb1ebed2aca391e73a4114c06bcdbf762bf28777cf
-yy 5eaf3aecf1f7d1fd3b43be8fa450163c79f162b0c6eaa4b1ad39baaf3a4c36564e001c935fdce38e90789151beff0f3cc4fdfc2d86dcb587
-
-x 1bb20a5a05b190737ad6b2bc5bc2b9259fa7e36eac8f3032a7c56ed59c1510baaea32bba898b329b0c64fadbe454095b9f82b366bfae3d8b
-y cf0a87c8befed020caf82f37b4c5f17d2aa9ff8ab75baa156cfe2716ac1eaabf9bc760c2ddcd66a9d02a8384ad1db9e8f857b151d126e0ef
-m 0x00000000
-xx 1bb20a5a05b190737ad6b2bc5bc2b9259fa7e36eac8f3032a7c56ed59c1510baaea32bba898b329b0c64fadbe454095b9f82b366bfae3d8b
-yy cf0a87c8befed020caf82f37b4c5f17d2aa9ff8ab75baa156cfe2716ac1eaabf9bc760c2ddcd66a9d02a8384ad1db9e8f857b151d126e0ef
-
-x c186531a219344dc485cd5dad6500616ac8e0653693168573cb9be590b02dfb1ddc5d87d27f2d9fa46ffeda955a6285b7ef2b9bf84825d06
-y 91f3be7eb2e0be38d92974d81be5126ef40d358f242d23aa4863fb16ba3e8844e02edc87c0206e211587886ed532da0ab148cfcf64e9b58d
-m 0x00000000
-xx c186531a219344dc485cd5dad6500616ac8e0653693168573cb9be590b02dfb1ddc5d87d27f2d9fa46ffeda955a6285b7ef2b9bf84825d06
-yy 91f3be7eb2e0be38d92974d81be5126ef40d358f242d23aa4863fb16ba3e8844e02edc87c0206e211587886ed532da0ab148cfcf64e9b58d
-
-x 9f2476d6db424d19ee0cba4ed091da5b44ca63caf2f711eaeb7edcc75f49e0d0c367c1f2817b6bb39460f897432901064cabed7f6a03b1f0
-y 66e7dcd34d76a19e3285685112b7619f9a3557764a918922faf1370bb97c2b2fa845dd34662cfe7299ab702c68fd43b5f6f15a0af6625f2e
-m 0xffffffff
-xx 66e7dcd34d76a19e3285685112b7619f9a3557764a918922faf1370bb97c2b2fa845dd34662cfe7299ab702c68fd43b5f6f15a0af6625f2e
-yy 9f2476d6db424d19ee0cba4ed091da5b44ca63caf2f711eaeb7edcc75f49e0d0c367c1f2817b6bb39460f897432901064cabed7f6a03b1f0
-
-x f124ac31d304a29cdd94bdc0611c61064a7c5f09cf6847bccd52fc7a7b77ede73b42b1ef75f000de4361028e0fb63896f4ef5ad3bc1b9c90
-y 6629084a230c793086e469b9a01e052ad7a5680d6955667e0dfb19a250f447d9e238695400dc4ecaeefcebed44d374e57ec4e414f5629e63
-m 0x00000000
-xx f124ac31d304a29cdd94bdc0611c61064a7c5f09cf6847bccd52fc7a7b77ede73b42b1ef75f000de4361028e0fb63896f4ef5ad3bc1b9c90
-yy 6629084a230c793086e469b9a01e052ad7a5680d6955667e0dfb19a250f447d9e238695400dc4ecaeefcebed44d374e57ec4e414f5629e63
-
-x b64f2952510827bef3d32ef6347251274c7241d9913268a7a6a5c360a4b29e7ed04d09a9ee5aa83235eaf8c0582b076b21d78b7062952773
-y 77897028a9a81fd54362a6085aa2c2fd6fdd44589f447c7310b9b3b5a29b54ed15c57e2c9fbff16f20129a4dbd43640a0d1037e277ca5c93
-m 0xffffffff
-xx 77897028a9a81fd54362a6085aa2c2fd6fdd44589f447c7310b9b3b5a29b54ed15c57e2c9fbff16f20129a4dbd43640a0d1037e277ca5c93
-yy b64f2952510827bef3d32ef6347251274c7241d9913268a7a6a5c360a4b29e7ed04d09a9ee5aa83235eaf8c0582b076b21d78b7062952773
-
-x 4d75efd204a66aed323456e6f55cb891ee7a31d739ae89726e0ea84532f9c740d1b647b117094fb85da2c62da04f3b9cb13db6b840046b7c
-y 0afd07bb073a150e7b82711e1f42f7b0789af8192ea6b4e1b24a3d48de7f8b802875aca5a02a9d24deca0b58c895992a449d01026495b96c
-m 0x00000000
-xx 4d75efd204a66aed323456e6f55cb891ee7a31d739ae89726e0ea84532f9c740d1b647b117094fb85da2c62da04f3b9cb13db6b840046b7c
-yy 0afd07bb073a150e7b82711e1f42f7b0789af8192ea6b4e1b24a3d48de7f8b802875aca5a02a9d24deca0b58c895992a449d01026495b96c
-
-x 1ff4eb5f0280744f0c909cede8be29cccb8ae43e4626018a9a1d352a97d987678863ba34bdeb183bb5e9347e96760665f5881570778a2e19
-y 49cd390a9edc7fad6c84c2e44ce09e490161094d2dc6cad30759fbef10aa30e5aa6474bc46571188418f3e4a2b19ecfc379a1f94e3a44e48
-m 0x00000000
-xx 1ff4eb5f0280744f0c909cede8be29cccb8ae43e4626018a9a1d352a97d987678863ba34bdeb183bb5e9347e96760665f5881570778a2e19
-yy 49cd390a9edc7fad6c84c2e44ce09e490161094d2dc6cad30759fbef10aa30e5aa6474bc46571188418f3e4a2b19ecfc379a1f94e3a44e48
-
-x e96c0316baf01c25ef8a41c02e99aa84c82f8eecd3249be268834afb5f7e95f0ad10bfad4160bb335c30ffd6a1090c91c57eb6ac7a7a5e66
-y 115e6f115bc4e19af60710f3dd821fb58cb680a32d6973eae9ea3e48f1928dc1d9f684a8c8de80affc59bc0fb342bb040f89d2d46b8ff8fc
-m 0x00000000
-xx e96c0316baf01c25ef8a41c02e99aa84c82f8eecd3249be268834afb5f7e95f0ad10bfad4160bb335c30ffd6a1090c91c57eb6ac7a7a5e66
-yy 115e6f115bc4e19af60710f3dd821fb58cb680a32d6973eae9ea3e48f1928dc1d9f684a8c8de80affc59bc0fb342bb040f89d2d46b8ff8fc
-
-x 71bd8f5036da4c33f6940348ea448c2f9bccb152dab40b410bd695923a9e255b33aaf361055be4bb9a570e201dce784cc1ccb0f89faca85f
-y 971b2f6569ddd9099a87ec4086d8218abcfbe81579f25f03634e471170a5088f48a6cfd09ed9e389ca37b780165c00b206304229135b6044
-m 0xffffffff
-xx 971b2f6569ddd9099a87ec4086d8218abcfbe81579f25f03634e471170a5088f48a6cfd09ed9e389ca37b780165c00b206304229135b6044
-yy 71bd8f5036da4c33f6940348ea448c2f9bccb152dab40b410bd695923a9e255b33aaf361055be4bb9a570e201dce784cc1ccb0f89faca85f
-
-x 0f1165e19968f3e6159e9f7f843c1b849e5c3917af4e2798869112c6efca9993ed339c8495eec8c54b286820bf7befdc8ae344e4d309c077
-y 7ce5a2ae66b9bddd30c98d9aa9fcdd6ef90d244d10115d15cf5d81e9e389f6852b153a42c642447043fcfd278166b92c624508973449b0e8
-m 0xffffffff
-xx 7ce5a2ae66b9bddd30c98d9aa9fcdd6ef90d244d10115d15cf5d81e9e389f6852b153a42c642447043fcfd278166b92c624508973449b0e8
-yy 0f1165e19968f3e6159e9f7f843c1b849e5c3917af4e2798869112c6efca9993ed339c8495eec8c54b286820bf7befdc8ae344e4d309c077
-
-x 6dd07b4891d8f45ad1ee64da38383ec50d6f29634767607eca19a547cadc3c157ebe7d86a28d4d2fa2d40f2c5402d8b338cfd8d30aeadb6a
-y 63da9a5a0cd51e58168ddb305c0e70a2f898279dae6394e1b3e1ef3a0763847d5d2f15be493114360204d037d7d3c3a9e746d27dcb544ded
-m 0xffffffff
-xx 63da9a5a0cd51e58168ddb305c0e70a2f898279dae6394e1b3e1ef3a0763847d5d2f15be493114360204d037d7d3c3a9e746d27dcb544ded
-yy 6dd07b4891d8f45ad1ee64da38383ec50d6f29634767607eca19a547cadc3c157ebe7d86a28d4d2fa2d40f2c5402d8b338cfd8d30aeadb6a
-
-x d91228b648f75350d775432af35be9aa283e9729fcd3b689f0c7ee02ea67efd33493980ae5eec92ad6ab42ccd253a7aab5a62c26be275278
-y 07c5d1b4f9b8db88cd4187b1ae5e175bf703af12b26d066c1d55dd367569d3e23e3d0470f3c47e6761746ce7de39cf563500d026a6791980
-m 0xffffffff
-xx 07c5d1b4f9b8db88cd4187b1ae5e175bf703af12b26d066c1d55dd367569d3e23e3d0470f3c47e6761746ce7de39cf563500d026a6791980
-yy d91228b648f75350d775432af35be9aa283e9729fcd3b689f0c7ee02ea67efd33493980ae5eec92ad6ab42ccd253a7aab5a62c26be275278
-
-x f9e764e20657319802b53ee29df43b0d83d994d9049b9820fc0c31b631265c49f6613923a042eadce5902fb81753784ff5a9c0de2c4f6b12
-y 6ab2f8279e82aa65e8326e5c60bfa067e4967b3ea67d0369853282e5429736529a43eeee3fdf24ebbe5ca85b59647994fc99c90da83c6229
-m 0xffffffff
-xx 6ab2f8279e82aa65e8326e5c60bfa067e4967b3ea67d0369853282e5429736529a43eeee3fdf24ebbe5ca85b59647994fc99c90da83c6229
-yy f9e764e20657319802b53ee29df43b0d83d994d9049b9820fc0c31b631265c49f6613923a042eadce5902fb81753784ff5a9c0de2c4f6b12
-
-x 772289865ac905fac203e4654b258890ddb91cac71c6d2af3826e3acfebfa222c937b40069ce3a757e2ffd960b5821ed1ad54e4ad2e3c6fd
-y 58dbf838ab81a754533c7f80fea48cbc981f724e4c150ddbb0afb5c711a8e21079446f77c427f7eb1892c096fa3eae5e2b070413611cd184
-m 0xffffffff
-xx 58dbf838ab81a754533c7f80fea48cbc981f724e4c150ddbb0afb5c711a8e21079446f77c427f7eb1892c096fa3eae5e2b070413611cd184
-yy 772289865ac905fac203e4654b258890ddb91cac71c6d2af3826e3acfebfa222c937b40069ce3a757e2ffd960b5821ed1ad54e4ad2e3c6fd
-
-x 0bd6656d68c41bfc5389db274367f69191754919435ba58d2256017b5bc595d102c6f4f745b3ceb0c32bd0a6cdadded3a3dc925ef2b5c73c
-y 1d903009c74d3d135a192bd42466cd28303f482626a7d10832f1f6eae72c3b051b0373e62300a71226011475034f0bfc6c9a65601bb83993
-m 0xffffffff
-xx 1d903009c74d3d135a192bd42466cd28303f482626a7d10832f1f6eae72c3b051b0373e62300a71226011475034f0bfc6c9a65601bb83993
-yy 0bd6656d68c41bfc5389db274367f69191754919435ba58d2256017b5bc595d102c6f4f745b3ceb0c32bd0a6cdadded3a3dc925ef2b5c73c
-
-###--------------------------------------------------------------------------
-test mulconst
-
-x cb908747a1af81f52715ef8440aed06aaacbcd7903c99cdecef5ec54e7845bedaad6475028b0cbdb0d53b6eeb71843f900fefd398a083d5a
-a -417895
-z e95e64fd1b2e2e79d1bfef5c96942eaf7ca5d40b1af774ed9c4ea2351c8ae81013f896bafd1f0b0e3a3c2ca3347c6cf88f988877af5e009b
-
-x 46b23d83c0848e79af947191cb76b087483beec6224af749e59c0c5ae27ff8abada31da895f8132aae0457f5ddc30d18a8d52046fbe6ef55
-a 384370
-z 31c9bf2f3bdfd3c1dc115db96d7a1c15e2a9ae67dfebccddc9408a0dcd147d9aa62ce4a55a2d6ad54542317756a08d6be3b959bf132624e2
-
-x 53e19751de62909506bebf74411d359014ec4b6afbb8ce14eeed8a3938013f0fee6897e3cc3adcbc90d7df321c4caa1941d0e5909551335d
-a -49682
-z 82fb902a8992ec1032a6837cec56189c45d1c1fdc47748e17dd9ecabc807a52eb537d6411f99f4d3b328e7ca76475924f90506a8adeb908e
-
-x 7ff3b9b3d8ee248a48d0c8d308d8c3658374acc92303143061a46656ae2b35094ed7b5b27d23366c0e42ee0a9471a4355d81cda0e4390348
-a 131908
-z adbb3dd21e634dfe2c41593c65249f03a048338037d4a107892df36f10e3ff68402d6f48e74bc7a7858f2c3650fd2a10acdfd4213850529e
-
-x f532f4f5ab5447b083ee4225246aaa4448696e4fc8bcf5b0ec1b52df88354e5327d7a3cf6e15db9945205968c275755ea3906a27437d29ed
-a 383911
-z 1f42b3585a2553ab19b14639c3e3aca636d88053c70fb758962713783bcd824b729fb4d01dd56a344d991bf2d32a2967acf470b39bee88a6
-
-x ef0e2a829097e50575eae6b1ad3fa10b8e417b0363654e0cb07a563a905c02e367c6f1ad7be1469b9f5295e3db0726853adffb820715f7d1
-a -226220
-z a7c5387af1b9f61f09d628feac1a050173021386775c9f534557b8841b812155325e3632eee7a2302ef8af0b4746575d6c2bcf3b29f674b0
-
-x 3b4655b1c22542ca413f76bc24751a01cdab6b385b50301d67fd62ba31ad132150e38e12a849405112c4742e93b92849bd8b872c29edb2f9
-a -89924
-z b51c0dfa2407a89435fedbcfd7835b6e0849d8626995fd00974f44c49d794d3c5dc16028e9fdee45bbcd269035e8bdba695a6653028d4d59
-
-x 48bdc2073bff25ae9bf7fcc368d65602a71e48c343bc7181c361331f108867d56c588f698aa5b91222f5dbbc859bce656f2607b053222fc7
-a 66432
-z e845dfe65d563884074ffeecaa325706df4a129b73b056cab6ad999588216d72525222ce00ce4d2ffb09fcf6f010a6eeb2eb753fefd44b47
-
-x 98a26f23f83673a480076b2fc7ccfef07fbbe70c4160d5af638c345f7d17b00931efff543fd47b7b8b362a70657a458566ada4aefd1c5eaf
-a 492192
-z 0ef483482255b5ca0f8338317f6eaf9c4fbf8bde8b8b04e26d2cdc0632186f1e62a9c3a1be23e8dc444ce50783135aeca614c884bdb77a30
-
-x 6ebf7c4e06837120cc852a077945656046e64c2d88ce440bdfc8d38736a4d510a722bc8b0d225f11df0e704e4b04c48bf481da68fd1e150e
-a -7098
-z 8d4e2cd12323b5744442fe4e4fc21748b344d7f94794398ec187f0f986ee743cd733a7a16bd4495818ab033103f020c794c988c5d2c1628a
-
-x 94e49f2bb473a7273abed94363c4dc3d13db159e3c3698a62ce5f321252aa03c7f63dd6eff9529c985f43abc7283d11140cb44ff6fd0f3d3
-a -392951
-z 58a606cdc1bf1d5646fc08c7a6b3336fbe532c823c70242ea7536cc6dcdde7c4f492306e39ac0fb88367e41d63a8305d69fab57a52c8c284
-
-x cd262298ce3b73294bfb523c30206fc3771144890a0ebcef19e02e5085973a6aeefabdf8cb7186d57be38ee84b114b9a7a22556c0cf88df1
-a -237681
-z 7553420c53b255fb909d6e9008f043e7af25a2a9c29b177b830ff1ae6f6fdcb6aefb8386465f24634fb04c6078322ac691586f91cf7928bd
-
-x cc9bd2e72ce15dd50877f95812b65c65cf09b14e2817784a5b296c123e498c532362180a932a455b2ddb75e26335dbcb21eb94a90ebb6940
-a 246794
-z 8838e720b6e497d9cde9fbddc2333c13cb5bdbbbe5afe41ffd61f5035c8c4987fddb8036c25b0505765bf1a5aa369c6bf7723c65278584a8
-
-x d8ab6b8f3523e98f49140e051c0b744bb0068d20f499c0763aa28ec1d1dd7e86356f357149c317376be96cd520b3ae04a2c4d468d74745e8
-a -360296
-z 4c0bc5f6fc52c6302b74c790d57ccc8fae59f2aeebb59c3393c56e70060f4d170ea41354f5040804a6e8dcb4a7c585ee71a6d90454e701de
-
-x 6036fbfb9fcc223a1776ec67c9424788aabe553a7d6a0472159edc747ebaf97e99f7263ece635ef0b702a3610aef32e17f59fae503e18d74
-a -5433
-z f6fa9a49b55077330fcda976a19ba7cfd98e44fa54044840df0ae9e19710193e684703f7fadbcbbc534e7be3adec0cae0d95ea414494f368
-
-x a3433dfc89ec4d6d858bb5b018e2d474b7de7604ed4491957fe16453d3793740ef88136814f59b19ed3610252e74cbc3a36571d02e57913b
-a 237641
-z 7a01a802b7a5aca44675887d9cf94d04d4893e2dc5d7474090cb32798fa370690255f57d18dce2a57126bb5883672b5a74a1c780f48f7bd8
-
-x c17ecc6099e9630a4ec20f4199abe1c10d414f6d734014ada1e6f097090a2bb4e638fb52d9bf56080d77c2b535f52cb091cbaad3c65072e8
-a 517226
-z 708adeac4ff99cac4c3eb649d55276f58a7d21a0507af176a53893c567050d352af501a9c242baf53121e8b56f5679b175dc01538350b644
-
-x 134263fd765e5f1da64900df5643c5241d4fa8a9e96ee59f01667b64f9122e85e995b90d4bf5d5fe9f68825dfa6edd19d8ce009270ae2984
-a 390674
-z 2ffbda7ccbeecd8dc4600965679146753c496d35bfa546e13edbbaa259065b024c8aaa3a17a3384f4f14d5ee01371ac55fb50a153b4ac1c0
-
-x 54326fffef9f0fe1207a07c8ac063d64b3fe81528e005f857319a74da2c3423a552b05f8c465908b028a2dcf15cb7158c99a1d2bdfd890da
-a -255467
-z e554e875e480c68c4fd780425ff8fb50f18bbafd0536a09489bc7cf197fdcb80dd4c7e31447a1a862066b6761ea39ea3b8c3002039c86b40
-
-x 5c30f73ec3addb2d27e0e79579063f2d30fa9fb47c2b6a3a32553120a047cad83abc901e5a5b4a65f8e51144f7eb0abec9a4d105236b2618
-a -466309
-z 5ec894f6abe2d88971da11b982c3322d1f533a326057816f6273585bfa186a7f569ddf93c27e8e74719ddb515689d5935c56e6b86936f22b
-
-###--------------------------------------------------------------------------
-test mul
-
-## Easy tests.
-x 0300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-y 0200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-z 0600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-
-x f7ffffdfffffff00000050000000000000a0ffffff03000090fffffffbffffafffffff00000020000000fdffff9ffffffff9ffff7fffffff
-y ffffffffffffff01000030000000ffffff2f00000002000030000000ffffff5f000000fbfffffffffffffcffff4f000000ffffffefffffff
-z bfffff6f02000083ffff5f010000a1ffff9ffcffffc0ffff6ffdffffc4ffffff02000082ffff8f03000089ffff6ffaffff7cffffff000000
-
-x f8ff7ffeff5f00001000000800000300000100a0ffffafffff130000fbffff0100000000e0ffffebffffffff7ffffffffeff1f0000080000
-y f7ff7f0200e0ffffefffff070000faff7ffefffffefffffffff7ffff040080ffff1fffff8ffffff7ffff0500800200000000f0fffffbffff
-z 0a0100240020f5ff7ffdff4fffff4100003a00201400400300a8feff030180e6fffff9ff8f02003001002c0000f0ff9f0600d0f8ff670200
-
-## Random tests.
-x 94aa99eaba90c5eb2efd7101c8efeffc1e44c8fcd84ccb8ef27b9792ae12534c0a250e5400407177bd655e51c343f776a3fd26474da4dc74
-y 284a0f7df2d7d7c760cc57b1606625884c1643020230a9eecca7de6098f5338ddf9297daecae8a07e199494cb6db91c2c683566bf79545d2
-z 213a31ed7e494f470736ded872f2c4f3675562a7b42bf01ea246be0ecaae2a61ae500690df9f99ea9fa8e5e1b9ccf3614bc34148b7693c91
-
-x a434abefb0de3c7f5e33f9230ead871bb3f06888c0d568b9a74fa32b676dc600fed2d54a042e1b97340852c4d6ef796a18561884d760d4ad
-y 99d4c85f047d3dd8e530c50ae7d80815a30ec6ba820316f5da922cfa7a51ab45290ac2ab8a53082716a6d7f77ac5a285fac298eca4fd9c52
-z 97b2991fcc858d5667d3674484db9435ba71ab0c836c534efb823c123f9e94d0d3445257c55c73e8bd62f1d7acf1d75fea5eea669bfb9912
-
-x fe9911abbe57f1ddd61acd062d59637b129a1571af65fb70169db0d8b12b498a66d1eefcf9c8cbea01179f113afef0ae192550828885689c
-y e371e9a11f662e38caff28cf4cf5ca8cdfe4a8b99fa12a33765a22ae25506874fdcd85388ed406a955d293320e01957f119027ec4803c2a9
-z 171b49441f9891d927d2f6436eee1dc59e7872730be496638017b42151cdf00e9abb212bafc47c05a4e185bf7cf21ccd97b0c8ea426e4381
-
-x 1c300df44d28406d070b10c1920e01ea8b9056d9e1d6f9704dbda3f6328c26a28e9e4aa07dc79e03c09c5639cf8b8c783c8b430b9d8c21a8
-y c565b0357a1e8aff3b3a6164ff34c9598a1c15a1551224fb38d25dfa3b0627c9d992dbd215910236aeeed23f4efd99640054b6648946346c
-z f7871e06efb6f737cb4e04f708827092e94e3c70faee57f70096b9d674d0ac5b228824924bb705de49de9f9c0e834462093a9a5551fc7d5d
-
-x 9014dd22854f1f21fa1475d74eba669101c871c2a21ffd5d10f0792e3cc5d34f15b4735759575dda169e2dd868a5ae64dbeaa2a654cfde5c
-y c6f59ecf6add5ff92813cd6f37de9c6f8d3ae9cd33e4f3236ff43127f463f297c3067493868adf7823bc285a3d609a57d9b0b841a9b628a1
-z cbebe67e30ed82acb0de699a5d874121257b78c2b0642583713b58fdcd089a6277a5c5e571538e4af9025dfc63cd78931be51780055dfb2f
-
-x c8fc23a431d744e45e8bcd2dd2ca612db40b26287970aa878a5cf6283c51b2bd4edb76f705f29bc3911a9aee8fb7272009520f3590ac4c4a
-y c1015900ea58d6305b8b558c992bff50a8614843cd3d11274830dff6e1db405f8b268100fbc5e44c477cc2a9e83f825c7840e560fc2b2920
-z 6ecf49d92efb60a15a9de38ff37d3b23b339d889ad8b11cb332df260b9c49fd28b287a559fa5a5edf732b3bd1014711fb7d088a37cf6ef72
-
-x daaea5c9549776d866be36a032027a65eb8325b1684d3c37cba068e69aad7d4f104ff47c14f669883cdef5dae9a0c7840379631ef97e6bc3
-y f8dc00891a9c55481a224309a8024ea257850b2bc62ab10bb5ea5b836776cd46994900d6656b7f7e0d9092fd824b16d20ea14528a0de7729
-z 83d3eb62429c2ece396cd7069dfa2985630da2fb0949b52f1df9231c82f32022543d4a2302241d0146b4db97f44ec5342b6444f463ad056f
-
-x 786f4ebb20161c96f93ffe3ee2b0cae50fc454d910b3fae4fbd8454b8ab7975c6cab8f6a1b593996b24b22603137a52ee732f9d19f9a6e43
-y d78d3df4f455c8f5d98baaa17200d4c94056e21768c4ca783188bf15c28dc86c581fd9c150f923f905becba19361ca94f7434d8a74744669
-z e857a2020e1877b50151772bcf06763285c1d8b2b5ffdb63e13ef4985ccc3b965fdb053305f16feea4a3ac0edad21423c80ef847181bdff7
-
-x 6b48bf18ec4557e745cad3e106511bd5a9bbe136c77cf639745f891f54bb16c11e19770eb5112df8bb6755b97cb1e23c9c7efe589693764e
-y 95c2a38f889c451f792c3d5d8b3237eed3f99e2b4857bfc48f75d7c0de3f293d2cfa7f97d65d75e0e3df633d84931973ac542ce07ba974b1
-z 2fdfb1146b569ac98b0811e600e2d8e578023024ed704f97c7f7d56a2b4a33ac6ec68d14f0789441a904d175fbf8b91603c532ecdffd27e4
-
-x 1fbba059c333843e3cf0cff19bec99bd0cfc89c3b390200165680b742fe540b32042959022e7393c9e13ef7fa3f1dd5ac46595803210c536
-y c723bb3649b1d95647636abffd325e363931782f02002ad6d75d2082c980a7a2c5e1d51045880b36d4f62c16250faffcb2acb824d8d3d5d4
-z 97041eef8892ecaaa97c4effb8c69160b3878fd302bc5f0862bfe4894bf23193738d8dd95c9eee9539e23fff67243372b97f02c3a3934555
-
-x 26f5bc0c2c49899690fa423478ab1cf7000be27609bf683896a6ce3f619510b061ca04debb6c64540e724d113cd4b8ff3485337851367700
-y b8540188b9ca77a82899c7fd26412dcbd6a3c9b45be595f63bce7426d7c16eb20c3a2dc86afe9064edc19840f75f05de828c276e98451ee5
-z d973580e88abb6c83defc009607082ffbdcae6ce9d577218580459711682f8708a15de9c62e3ca3b50e91a7bf5781deee152ac801a64fe81
-
-x 6c044d6556abb8efdf5b180695293464a8bc4b9cab201822053c7295973ea0a8866425629cfff1d372a48f51dbc6a7f828691194c32c2c5c
-y da28b84dfd48f206972fe282449991597bc7f0734916b6f7a253897fca2ccd6b80aa477cfd08549b6d25bd18932128e59889e2dcfaf76157
-z a599fabf997468487b9376500b58a51e0e00c86d9eac6f50157aa1017d99ac8b95e7842b36071a192784ef72433c06a1dd042990b71ffe8f
-
-x 50378c6ac56816962d428ea523a0cf87121fb3c53b37bac6d3a05fcbdfb8a5fb20aa014f1e1b01a3963534d403baeb7c436f72cf3cc5db58
-y 78901fa015c6f0d3e1072aa87d865579fa405615691a3f27945f9b1431ee8bce8ac9965a1f9b0f42ff10bc77c43cc93566eee9a9b79866ed
-z 00127644003ed4b518f04abbd058a46015fb328883b92070bc5cf0fd98d7307dfabbc65f3e8551c622792efabe55f03953e498e360410790
-
-x 5db2f6db35af2e1c84ab6832b967bf987cd03adea7113fb8806ce8fb3ffa426dc10997e13afcd39cf5cd65f65f8a09e650fad8e5f6ef2648
-y b063695bc97a18d6ccb0785ee4588951dcbee420ce8e37b25cce325352968015c94f9bb784f3a2bfa34c6a1edf710b63f139fff6d4f7b2f3
-z 999284a309482f67ab6460e73ad1ad267052b59fe50cd58a245e22079e2b50b119e312ff60a65037cf9faeaa259d22f689eaedd7924f1093
-
-x d5baefaae7fc9000e0d55f287f740dfb1899ba6e9e36338959a16ac5e5f45442a37086b5519a0b439f38b129328aebf468dec4b59c89a249
-y 4febc8666dcf2b150faec9902a5f57e97275e7b122724c2b77d9b78655b455d424db93f859b8de6b09c4bad6d5ba68349c65c41caca67f8b
-z 19e6ed86dc819e6b4368d196679328710f63bf1fcba6652265508b509ecd0e3e8b8bf17f8f1eeb361af107ef684a729a3635cb55de3f8605
-
-x 9974be322a0f471cfe0855456104219d8037ca1cb5aacb9ff5da86a047ce159430cfd92f67e764244996668ac44d8d9787dc1b5754d215c1
-y 78c00f878fb41fdb0cd22c026881d5022fc470755e6261945b9bfcc3868f591f08288e4d64a65c9f3d0b05d3ab7f27d801aef29e5e98caf8
-z fd51b84f21b06377054dc879b8a176a7799951d5669486b210e4528b9f52bd60f88c2a068f722d85fa12761a4caf2f05bcdeecb7ed62646e
-
-x f4048d4a1602eeec43cdf20c3ac9f7b359935bae3648070276faf07a5c58fdf79771ba6c077ddeae47617971e2145f4960587637e7028822
-y 32635c7425108f5d19e35e4d91a4bdf3310bc884c9061d0697556ae25e17cd611e090c1179ca9a68225b283c8ab98a7b1e97508592c60c66
-z 8d6a91d016aaa7a0da03b06f5876ce8e8a71d1e5e5eb430d6c5ae16e1d6d9b61e77179b4f6fe43ce37cae27689983d41923f3b30e9d9f930
-
-x 9023c019bf7ef6df45e0e44111903c622220bd3dde046679540302451d001e47a153b0ac7dcfb9831e2d262d8e27002197d9640900e4c1cc
-y 1f5e2ca612ec6f14df4b528cc35001e763b9414a81381a1a3c7008c0cc525bdb00aea94ce2348f380dda43b5edf4fec7c8cf5ea2f5fec4b8
-z bf2c241efc180988232b83cda91e12dd0aec0d22ab68353c9841c4ea0547fd1b377fbca125f8cf92c426f8eb859f85a3853516ec104d9b6e
-
-x bbdecfafa9284e3067081b7d1bd7ce0e488829859628a8f6a38bc1a3ca6ec3130dbc1345b69abb7224b047fd3f2dadcf9cc11a8ec46a6436
-y 49a956ee69cdfecf29440d60fde9db1edd94619af97f625d45dc83c64994fe6c1ac858150cb526ca3c58a9fdc09d409ee3ed0b0cbcdb711c
-z 7abfd47fdfcceb278c917afd059e335110bec63fea48dedf7f8275da8922201ea06be39e3d1bccea2d38f5eb7d7aa5ef4e6fe6792a9f0ce0
-
-x a9483d4f0c94eac273adc392c3f425be610206683cbb6806dca47be3b54ad142fa2c54a7a473675556bcc8cfd50649af3c58d7a91e84b428
-y b986365aa08f088fe04aaaf2e00468af3fb41cda961b56ece5bedfd83cf9a0fb959ae70c23d9b27cd1eaf8b611d9e578aa0b9d899b81d5f1
-z 4af529627637ad3f3f1269319f4fd426d31e276287ee525d0c64974e55fca1cd58694eadf47e44dc3e843e01c36b22f9717067a907840ca1
-
-###--------------------------------------------------------------------------
-test sqr
-
-## Easy tests.
-x 0300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-z 0900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-
-x f7ffffdfffffff00000050000000000000a0ffffff03000090fffffffbffffafffffff00000020000000fdffff9ffffffff9ffff7fffffff
-z 8c000040010000f3ffffff040000f4000040120000ff0000800a000099000060060000030000000a0000e7010000180000290200800b0000
-
-## Random tests.
-x 776cf7ee39df23538f76e6be87ecbb1ed78477b858e3520f24b2b36f09a7dd61daf7bd5990af13c11b1419d8215eb69c30efc3917097797b
-z 870001f8ff173e02ce682526a513ff99c6e9688cbec13839ecbf0fbc11d8f84f6cf53041b5bdcbc624f9787db9babe61cd477cb9395590d1
-
-x 1e5ef8dd68207b3c3d3c670acee7ecb277ee6bc10be9fa3f3d800e1414bf402298ca443de6fd57ca899188c884a93d4b9c9d1b00a7c9ce44
-z 4a6d6da8002b6a0f3f5c3a9631254ccc62cf66c93279c4b77dda55d32514c8b388b543002f8055321c7195ce1fd26f51f48732e664cdc62f
-
-x e02eba6cd5ec1cc39ab92db439896520e50a5f9e9ed6d31ad37d00ebb2a54cb68f1c0ae537006ec2ffb14aaad2de16ff06194929b702b95a
-z 95632fd74045a49782f6f9d0c86d554cf6efd07f9eef57d669828c77537d4c3a69138d755855640064f5e9bc8fbe0eca96fb04053f565431
-
-x bad2a1348fc0b54791f9f2875009c8be2d30f14526fbbc22c439c1ae2b865436cd74f428766e4e676b795fe9333312f6334d4e4ec2378e26
-z d87a8f7ca45620b4646fad2c22792538bd16f37879dbc4d87c21cafa60c282f6415fde2fb6293a8b8a6e5b3901f88d75f9243023b68f41d3
-
-x d6d221f2bf71eba62e49db570e13ca69f4a8a33543298619cda7c8d2524c9446b11ae7b7d301579f047565b7044b5286c2478896800ad992
-z fdb163312b884bc6d74c4c269011311388ead9c069884f48487f9ac0d62b39aa175e81976fb599716aaa68db4c02985a6f0ffe522b0fb21b
-
-x 20cc05120202e684981bce1db74af493d218ed8e0f5e76fad46bfeb98c69e504113b0eb91771c602cb422ae09846fbfef7c47afd09689277
-z b07d84ff34dc5f0cbcc60037400ee04ba09f34d1d7a0c6a80672a3f6c1da630681d4207ce1325d301b36f0acaafd7579a108646f5a26b755
-
-x 72c4c3e4fcfd36389f558e0d4016f3f088145be47b2de85ee7ab963fcd8c7adf449d5b7c37ad8a32cf97ea9bde5c220fc896cf1b91633e19
-z 1e8f68736c3b259b661c0c1ec065a642e717f9e4d86003411b8e15ff89537d8e129c116d2f8a9e7e1b46879deedd66fa6ce2b60ab680cfb0
-
-x 8c524f059e7ebcf3af3072dbd2f76ebc530adba6d26240c8675b5451d5558db648e7a61fefb1369cf2939ba1fadcf8e40385db5d57cacace
-z a19188e6821f5cc2c53b7e59ae6f70e95fb929c0f282627ccfa2c6d9cb59dc871e9dcf3e2a8d6d66b7a6907d4d36c9de03c3d74325d8c1f1
-
-x dd47eb6f4f68cd3a9abd6af401bd6f3c795d89474dd41a89025b24c8349a0de417c3676bb6ee36002d7c8ff6b4fb4491e693cfa617e079f8
-z 871f46c93dea48a0d937b3f1f724f66615daa9200f0b48cee01c3b20e4a05dd6ce01bd7b2713e096cc2bd1c5ce7ca0c075aed0fc1ef6fa51
-
-x 577870fdb83454eed0711eb51d7bd91f9843769737566823e41d0668fad45c82fe069347769244af7230e6fbc40f5a71151279ae65e9893a
-z efabd464218df4a490b9870d541c45e9b7ab29bae25d9e976539a553995ded0edc5610916883642a032eae4e96eb9e4e1443f747dec98135
-
-x 8ba84194db2aad7b46005423b1251555ea931b933e0083fee76b9863fb528927f27a4a0617b8d75de306103b592a0fbd51b72bfbb051ee2d
-z 3a29e940174d846df65d51070295f535a03e988fc401ef62f5dd2456cf52668390e61e7b6912186d6d5260f6d6977004003bb106abbdaf02
-
-x 9f17e0943b4e39051abfd8f4512ef177fd5c368ebdf4b0af49df2e1d89e30c4e68ec474d81203964bfe9c1fecc1279e5e4f598ac97b48cb0
-z d794adb47cff3f7666dd0a934896015e59f278d9b1d6dc7a06328da96d6e6520670598129b7e1b26f9537216364199cf5c0010f23692ec90
-
-x a6b51625066e4cccb7d45dff5b182e2a6bf4b1cce7090a187d38dd39f08afad6f868c0277bf70d5fb88b6e67432526e4feb39ae707e34990
-z 67315efb85e16a1e97130092cc351759d9c18261845329f63eba1e77d91ad2c7df51ffa50b655de81bc807ea2b3e137214a2b08b400f2b7a
-
-x 28a0fe53cf73a0419fdb4cb493c6425be8aa812c3693411816c90621097a9d5687feb16ebf874a30ec849297742b7aab5921427d7b474190
-z 69300770a5bc2c9c599431e5f879ef3f3ec065e3a2cfe82e3499018add58acada581e9e81d40799fc74674b9721da018a64138519abdb108
-
-x fad58259395fd5bbcfca35b095253a3a121b62f1694e14cd9e2f85bd08e8a15d1dff98e3b81eeec678821a1ee9d6192c8351bde45ce0581f
-z bee7e0d6d4de419981ba2aa3964adfc7545e21b72b65c774b2029c22e06f251cebf04cdffd23e2051b57f986cbf7e56f047050714a275e72
-
-x 91e548171a8136d2d26e6bea02cb16ec9591e9cd5b913184b22b43d1029bdb214ef737f6e45f473f7d95b8fde075645c3b0c2dd2bd224278
-z abe2936ecf2ac3012455dcac906f691f2d96490539c9621658fd7f66790bbfe0d2df07165ea80e0c3282642d45b63b7db476b53e4f94f1c5
-
-x a52c855daa9ede16ea8de7c681436d5d31eda6ca5b441f972e5cf5639a1c56f689fcb411965271853de2893f22b81d7d0facafdb49292e39
-z 382480e92d44199fe5f7c357ad2e5a7277beab1a3055d48e679516151ca85ee3cb498b172087d588738daac2ec1da9638552d76be97626ad
-
-x c65888cdc1a575fc9a06dce8800607f56fe88839948b7e4e2713aae44b0ae6b7c6b68786b11b430d22766e9e4d76af118a972729c67c06b7
-z 31311e4ff9600089b533cdac6c05de3ddfe6a450ee7fc90cde1bb297e2deb750336ac3ed2f6fa9b88ece846be6f6aeb392f6753eb6fa475e
-
-x a61c81d621df61ece4b7274f63ae4e9f2e2df1d603fc9303ee361962b2d70bd783ff1b5d8f3ed27f17e7773b2b1c85af7fbd70387bdef5d3
-z a014ef20adc291c0238be3759ceb9f9645524b961761c8a991ce67efbddda568359fe36e762980d75a58a7ba10b803c9f883fe4d2239a08b
-
-x 96ced952366c324c5fccd48ac5d475cc1944e7e455dc093f0d9680d6d6abf1e45c76a286ac46acb4de061b9eb673a2d3124e6c3b921ad71f
-z 6debaeff6a7d2bb2c1389cb3338fc87b2a32e651ecb8d43fc012efc9b9c59c79487b742f0b30d0b64ac283af0d3b877102c6a7ff0f606eb9
-
-###--------------------------------------------------------------------------
-test inv
-
-x d665678f17043846f953fb09c88295d7fd0a53bc70ec7d396aff56e7dfa376f3a338f0da0af9e07b66d3ff7443e3829b541bd667201999d4
-z 6839ab730bf666c6ca987d254d83bf32b981b466c147f04b823981da75e12c9ded469a0a462861a987c13f05739f47596401fec25a5eee5c
-
-x bb8d567f6163a92603a388405121bd58abfcf05c596bf0624bf65b6a8fe03e6940648382fe01e5ab58e37ce235f4acbfb9e02624001c49da
-z 3f60d0fa0036da2db915e232bd841d09f006d4ba018c1d268af86d36990579d669ee63393b95c202645dcb1225fe9e64d14270905e63eb79
-
-x d456692d8e00bf9cd86d22a9f4ad9e9879e6298274854ae82729ebbdb0cc46877caeb381506dbb097b10c180d615661189da65d431e3003b
-z 6e0f5a173fb60be882a2b570200515dc7ad473e2192470ba89e6dda6cfdd6ff77026a1d76acdded7b5881a54d68605140a4ffceae70906d5
-
-x 359ab073b7465de1358a5772aef79db09118541c062421cb30a972525a351f16b5545daed5f9ce8e91a283818df6cdbf443831fbe5f3e848
-z 2b0ea74e6f4533498eb3f34247a9674f3a2cf2ab0e4fde65ff11b0d1e756430bc5452ca4b85bd3a1f10f6e4e3b1874df8d19f390a9021757
-
-x 3509fb8b7688f354738d4a8ca4091f66c880db794aacec6115e675090394ca77e1c83b955aaf4d8e75c6e4e9200be1ce5693532a561d970d
-z cafa18317193054cff7884bada249422ba889c19693d66610fb774fb4bdfeac0e67a5ba6f84ace126c125c46b4cfd627ee777e231a6ffc1f
-
-x 42e2babc095d88b61caa8883e91fd045106db9c4eeb4d945703c1dee3229c58869e21f73909ae2f3c4437d301a2a3724d67f6ad310f63835
-z 28c43a594b6471412f504dc10fd79d2c04ec029a7723cfa0a90aef036991f1b56cf156e2cbc7533671086edb54036e9f4ddc9bfe2e3ffcda
-
-x 9c01d006213bcfda413517ec815e8cebc06707f5649398a9d14a5d64754375c1ded8aaefd838e8eba84746de07a0f9b32caa2325c4c8e540
-z 0a3b64374ac2149d602a9f0ee4fcf6d814c476f451531a086b04b0dd598287b1758f77780b7de08573326a9767e816309d871fb1962bb1a4
-
-x 7bbd8a2de4bd2ffee4e93d0dd2fa9c5d4abcf9ab86c097921fe7d603b7ffdd07006c7d79d1a10267edce9b3069b134bed727c8f0ed1aca13
-z c909ffafbcc09a96723b9afba8ec0d00d5ce0c9d85de3c1e4de24cf44fb934bd0d2397b380885b7419cbbeac339fc85e2161f08c2f3515d7
-
-x 6a64650ccf103604c3b030415f7114c88c7094fbd0fd2f2b6b907a27fe104ef4e0684c17ff9f26f15eee5e7442e679ecad3e49a0629cb5c3
-z 9db77e47433997640b4c0916c5123e8a4d9c7c0bcd12b2dafccbababd6c9dbc3f4ec7991ea68b3ad4ffc6f0be4920764c65d98bdeba8a811
-
-x c3823c71f6c0f3679cb9c776e437e718f856c8fde038418942d062423113352aeb60ab84138f2bf73f268386cab0f2a1419660e966c24187
-z 558bff4fffa85d6f67ad44938f5b4473d250a87a120af9ff645a7db37a43808abe30c19c90bac94adb190840078214518e189d6c9fc5bef2
-
-x 44bd920b0eaf47695f93d063cd85c43c58470c23796f4a106b298d5f2b091210d103e9575c369bb0be66b2323d89cc29602a8071697931c6
-z 67464f2dab3a95c9ac7c783017105df7d561d7ae499ad89c4698da2c0710a1654c89966a7bd30d2d5c0511ed9f020309cde84cecd66be8d0
-
-x a6b12fc35e62532ea7c1fd49dd834bb7957da914ec3daf2e4f446b54916d016054cb59ffd4e3d9eecd4a18b08033ee8d9ff84db072cc4f86
-z cc70960f0bb743da1b23d11eb87530a820484a861abd68d2ed7079b487d88481d915b1b34c29d9938b5fa54d05c75cb1aebf0b722a6770b6
-
-x 1773dc978cd9f94186b83fd5e10a456b48058acd9e3bbacbecee2cfd0f8303c64721ca64c2913d57764336ea055700c2fcafc60d9f4b817e
-z 49e443096eb28c167ee62c63bfe4079418fa8e7f9e58757e13327680890b02ce7c9e5bbbc51366e0b3f5315edc456b6f65a09ea1b1a24438
-
-x 552158406db36accc32edde2f0ce46e23a1d406f60e54ca6a789386df36a57434c826c9586c4b371df3179f675e5956fe7dc3022f785d9e0
-z e0025a1007d3dff5e44947a0292bee8db5abbd1a0fca1d3ab0a64a37925396cd96c21af54d36656eb0b60c63fd5651622ec5487d53f976e4
-
-x 6b006d36f60750bb5c59f6eb31e2efe6098ab67de7a7a8a27201652380a295c408ec78351c2a799d62227dffd4731b7605e5c462dce2c1e8
-z 21785aae5f73da711f6144894728627824b685fac3d95068a9d0c4e0ee058301a8953322a5ee5be75452164a55477f1a987103a718bf98ca
-
-x 700cb76911e718ce8829f8d767c53e333dd2f7f20d2c020d1da3cc9ce96b9f6c7aad67450d5aab8f8c60e8ad77d4b5fdb86fae92a0ac30fe
-z 257f202b457f19f27ceed047e6778204c2b71646fcc96e19c6f07518780bb5b1c456fd6e93ce2f1cb0aea1a225137511dc71e446c1fe22c3
-
-x 0c909e0326649d4d375452c5b233a86e90b0fa88b20aa54e02685edd02b70aa022ed8af31e994b70b20101a5cfd8e16ba53c702840b4a16b
-z 98c41073ea843b4b5ad6b0589699f48a1576e3d834f8e595b8859069b71bf5e16126aa93b20259ff0a03976ff6d7f78239ec1059f8cf1193
-
-x 4529761361781e67037eae69c5ca9977b1e21468834eb83cd369471e5092249015cd263563bff9348a0f51e4a8517e27236ed1ecfe30a780
-z e20d5896be18bb273bb0ba84f6c070de45378bac6d793685e654764e5aa847d48403a68560b48dcb12573ac737366ae701072300615b4659
-
-x 6fae83f7eadeaca22b6781f400b01f9de186b12e31fdf56e0ebe98a8420baacf5069ffdf26d0215c16b64027dd69ff29709a64cfe8f52dcb
-z daa266a02c4500d989670eb63ab78219892d9c1ca2e17f4b5200cf1d920cfece5e80050be77f81a616de840bf19c23835ed17d57aeeea0f5
-
-x 23ca16e8b4c15f8f2b216441d851368d185a7f8587f398b0cf775875678241094538708da0cb2260c5e056b59c003c30c8f84f5088d0c99c
-z 9de1360b4718fc762e6ffab46827c5e4672a77d797aa608b31c132d1ad8138e7a64ba1f4278a07a6088f8cec9a01ea9bc1427c55241433c5
-
-###--------------------------------------------------------------------------
-test xdh
-
-## These are taken from RFC7748.
-
-k 3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3
-X 06fce640fa3487bfda5f6cf2d5263f8aad88334cbd07437f020f08f9814dc031ddbdc38c19c6da2583fa5429db94ada18aa7a7fb4ef8a086
-Z ce3e4ff95a60dc6697da1db1d85e6afbdf79b50a2412d7546d5f239fe14fbaadeb445fc66a01b0779d98223961111e21766282f73dd96b6f
-
-k 203d494428b8399352665ddca42f9de8fef600908e0d461cb021f8c538345dd77c3e4806e25f46d3315c44e0a5b4371282dd2c8d5be3095f
-X 0fbcc2f993cd56d3305b0b7d9e55d4c1a8fb5dbb52f8e9a1e9b6201b165d015894e56c4d3570bee52fe205e28a78b91cdfbde71ce8d157db
-Z 884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d
-
-
-k 9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b
-X 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-Z 9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0
-
-k 1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d
-X 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-Z 3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609
-
-k 9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b
-X 3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b43027d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609
-Z 07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d
-
-k 1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d
-X 9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0
-Z 07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282bb60c0b56fd2464c335543936521c24403085d59a449a5037514a879d
-
-###--------------------------------------------------------------------------
-test xdh-mct
-
-## These are taken from RFC7748.
-
-k 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-X 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-n 1
-Z 3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113
-
-k 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-X 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-n 1000
-Z aa3b4749d55b9daf1e5b00288826c467274ce3ebbdd5c17b975e09d4af6c67cf10d087202db88286e2b79fceea3ec353ef54faa26e219f38
-
-## This one takes aaaaages.
-##k 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-##X 0500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
-##n 1000000
-##Z 077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37
+++ /dev/null
-/*
- * x448.c: Hamburg's X448 key-exchange function
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Remove the test rig code: a replacement is in a separate source file.
- *
- * * Strip out the key-management definitions.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * The X448 key-agreement algorithm
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-#include "montladder.h"
-#include "fgoldi.h"
-#include "x448.h"
-
-/*----- Important constants -----------------------------------------------*/
-
-const octet x448_base[56] = { 5, 0, /* ... */ };
-
-#define A0 39081
-
-/*----- Main code ---------------------------------------------------------*/
-
-/* --- @x448@ --- *
- *
- * Arguments: @octet zz[X448_OUTSZ]@ = where to put the result
- * @const octet k[X448_KEYSZ]@ = pointer to private key
- * @const octet qx[X448_PUBSZ]@ = pointer to public value
- *
- * Returns: ---
- *
- * Use: Calculates X448 of @k@ and @qx@.
- */
-
-void x448(octet zz[X448_OUTSZ],
- const octet k[X448_KEYSZ],
- const octet qx[X448_PUBSZ])
-{
- uint32 kw[14];
- fgoldi x1;
- unsigned i;
-
- /* Load and clamp the key. The low bits are cleared to kill the small
- * subgroups on the curve and its twist, and a high bit is set to guard
- * against careless implementations, though this isn't one of those.
- */
- for (i = 0; i < 14; i++) kw[i] = LOAD32_L(k + 4*i);
- kw[0] &= 0xfffffffc; kw[13] |= 0x80000000;
-
- /* And run the ladder. */
- fgoldi_load(&x1, qx);
-#define MULA0(z, x) do { fgoldi_mulconst((z), (x), A0); } while (0)
- MONT_LADDER(fgoldi, MULA0, kw, 14, 32, &x1, &x1);
-#undef MULA0
- fgoldi_store(zz, &x1);
-}
-
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#include <mLib/report.h>
-#include <mLib/str.h>
-#include <mLib/testrig.h>
-
-static int vrf_x448(dstr dv[])
-{
- dstr dz = DSTR_INIT;
- int ok = 1;
-
- if (dv[0].len != 56) die(1, "bad key length");
- if (dv[1].len != 56) die(1, "bad public length");
- if (dv[2].len != 56) die(1, "bad result length");
-
- dstr_ensure(&dz, 56); dz.len = 56;
- x448((octet *)dz.buf,
- (const octet *)dv[0].buf,
- (const octet *)dv[1].buf);
- if (memcmp(dz.buf, dv[2].buf, 56) != 0) {
- ok = 0;
- fprintf(stderr, "failed!");
- fprintf(stderr, "\n\t k = "); type_hex.dump(&dv[0], stderr);
- fprintf(stderr, "\n\t p = "); type_hex.dump(&dv[1], stderr);
- fprintf(stderr, "\n\twant = "); type_hex.dump(&dv[2], stderr);
- fprintf(stderr, "\n\tcalc = "); type_hex.dump(&dz, stderr);
- fprintf(stderr, "\n");
- }
-
- dstr_destroy(&dz);
- return (ok);
-}
-
-static int vrf_mct(dstr dv[])
-{
- octet b0[56], b1[56], *k = b0, *x = b1, *t;
- unsigned long i, niter;
- dstr d = DSTR_INIT;
- int ok = 1;
-
- if (dv[0].len != sizeof(b0)) { fprintf(stderr, "k len\n"); exit(2); }
- if (dv[1].len != sizeof(b1)) { fprintf(stderr, "x len\n"); exit(2); }
- if (dv[3].len != sizeof(b0)) { fprintf(stderr, "result len\n"); exit(2); }
- memcpy(b0, dv[0].buf, sizeof(b0));
- memcpy(b1, dv[1].buf, sizeof(b1));
- niter = *(unsigned long *)dv[2].buf;
- dstr_ensure(&d, 56); d.len = 56; t = (octet *)d.buf;
-
- for (i = 0; i < niter; i++) {
- x448(x, k, x);
- t = x; x = k; k = t;
- }
- memcpy(d.buf, k, d.len);
-
- if (memcmp(d.buf, dv[3].buf, d.len) != 0) {
- ok = 0;
- fprintf(stderr, "failed...");
- fprintf(stderr, "\n\tinitial k = "); type_hex.dump(&dv[0], stderr);
- fprintf(stderr, "\n\tinitial x = "); type_hex.dump(&dv[1], stderr);
- fprintf(stderr, "\n\titerations = %lu", niter);
- fprintf(stderr, "\n\texpected = "); type_hex.dump(&dv[3], stderr);
- fprintf(stderr, "\n\tcalculated = "); type_hex.dump(&d, stderr);
- fputc('\n', stderr);
- }
-
- dstr_destroy(&d);
- return (ok);
-}
-
-static test_chunk tests[] = {
- { "x448", vrf_x448, { &type_hex, &type_hex, &type_hex } },
- { "x448-mct", vrf_mct,
- { &type_hex, &type_hex, &type_ulong, &type_hex } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, tests, SRCDIR "/t/x448");
- return (0);
-}
-
-#endif
-
-/*----- That's all, folks -------------------------------------------------*/
+++ /dev/null
-/*
- * x448.h: Hamburg's X448 key-exchange function
- */
-/*
- * This file is Free Software. It has been modified to as part of its
- * incorporation into secnet.
- *
- * Copyright 2017 Mark Wooding
- *
- * You may redistribute this file and/or modify it under the terms of
- * the permissive licence shown below.
- *
- * You may redistribute secnet as a whole and/or modify it under the
- * terms of the GNU General Public License as published by the Free
- * Software Foundation; either version 3, or (at your option) any
- * later version.
- *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, see
- * https://www.gnu.org/licenses/gpl.html.
- */
-/*
- * Imported from Catacomb, and modified for Secnet (2017-04-30):
- *
- * * Use `fake-mLib-bits.h' in place of the real <mLib/bits.h>.
- *
- * * Strip out the key-management definitions.
- *
- * The file's original comment headers are preserved below.
- */
-/* -*-c-*-
- *
- * The X448 key-agreement algorithm
- *
- * (c) 2017 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of Catacomb.
- *
- * Catacomb is free software; you can redistribute it and/or modify
- * it under the terms of the GNU Library General Public License as
- * published by the Free Software Foundation; either version 2 of the
- * License, or (at your option) any later version.
- *
- * Catacomb is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU Library General Public License for more details.
- *
- * You should have received a copy of the GNU Library General Public
- * License along with Catacomb; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef CATACOMB_X448_H
-#define CATACOMB_X448_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-/*----- Notes on the X448 key-agreement algorithm -------------------------*
- *
- * This is X448, as described in RFC7748, based on the elliptic curve defined
- * in Mike Hamburg, `Ed448-Goldilocks, a new elliptic curve', EUROCRYPT 2016,
- * https://eprint.iacr.org/2015/625/.
- *
- * The RFC-specified operation is simpler than the Diffie--Hellman function
- * described in Hamburg's paper, since it doesn't involve the `Decaf'
- * cofactor elimination procedure. Indeed, it looks very much like X25519
- * with Hamburg's curve slotted in in place of Bernstein's.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include "fake-mLib-bits.h"
-
-/*----- Important constants -----------------------------------------------*/
-
-#define X448_KEYSZ 56
-#define X448_PUBSZ 56
-#define X448_OUTSZ 56
-
-extern const octet x448_base[56];
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @x448@ --- *
- *
- * Arguments: @octet zz[X448_OUTSZ]@ = where to put the result
- * @const octet k[X448_KEYSZ]@ = pointer to private key
- * @const octet qx[X448_PUBSZ]@ = pointer to public value
- *
- * Returns: ---
- *
- * Use: Calculates X448 of @k@ and @qx@.
- */
-
-extern void x448(octet /*zz*/[X448_OUTSZ],
- const octet /*k*/[X448_KEYSZ],
- const octet /*qx*/[X448_PUBSZ]);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
~mdw / secnet / commitdiff