+++ /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
~mdw / secnet / blobdiff