/*----- Licensing notice --------------------------------------------------*
*
- * This file is part of Catacomb.
+ * This file is part of secnet.
+ * See README for full list of copyright holders.
+ *
+ * secnet is free software; you can redistribute it and/or modify it
+ * under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version d of the License, or
+ * (at your option) any later version.
+ *
+ * secnet 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
+ * version 3 along with secnet; if not, see
+ * https://www.gnu.org/licenses/gpl.html.
+ *
+ * This file was originally part of Catacomb, but has been automatically
+ * modified for incorporation into secnet: see `import-catacomb-crypto'
+ * for details.
*
* Catacomb is free software; you can redistribute it and/or modify
* it under the terms of the GNU Library General Public License as
/*----- Header files ------------------------------------------------------*/
-#include "config.h"
-
#include "fgoldi.h"
/*----- Basic setup -------------------------------------------------------*
* (hence the name).
*/
-#if FGOLDI_IMPL == 28
+typedef fgoldi_piece piece;
+
/* 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 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
-#elif FGOLDI_IMPL == 12
-/* We represent an element of GF(p) as 40 signed integer pieces x_i: x =
- * SUM_{0<=i<40} x_i 2^ceil(224i/20). Pieces i with i == 0 (mod 5) are 12
- * bits wide; the others are 11 bits wide, so they form eight groups of 56
- * bits.
- */
-
-typedef int16 piece; typedef int32 dblpiece;
-typedef uint16 upiece; typedef uint32 udblpiece;
-#define PIECEWD(i) ((i)%5 ? 11 : 12)
-#define NPIECE 40
-#define P p12
-
-#define B12 0x1000u
-#define B11 0x0800u
-#define B10 0x0400u
-#define M12 0xfffu
-#define M11 0x7ffu
-#define M10 0x3ffu
-#define M8 0xffu
-
-#endif
-
/*----- Debugging machinery -----------------------------------------------*/
-#if defined(FGOLDI_DEBUG) || defined(TEST_RIG)
+#if defined(FGOLDI_DEBUG)
#include <stdio.h>
void fgoldi_load(fgoldi *z, const octet xv[56])
{
-#if FGOLDI_IMPL == 28
unsigned i;
uint32 xw[14];
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;
-
-#elif FGOLDI_IMPL == 12
-
- unsigned i, j, n, w, b;
- uint32 a;
- int c;
-
- /* First, convert the bytes into nonnegative pieces. */
- for (i = j = a = n = 0, w = PIECEWD(0); i < 56; i++) {
- a |= (uint32)xv[i] << n; n += 8;
- if (n >= w) {
- z->P[j++] = a&MASK(w);
- a >>= w; n -= w; w = PIECEWD(j);
- }
- }
-
- /* Convert the nonnegative pieces into a balanced signed representation, so
- * each piece ends up in the interval |z_i| <= 2^11 + 1.
- */
- b = z->P[39]&B10; z->P[39] -= b << 1; c = b >> 10;
- for (i = NPIECE - 1; i--; ) {
- w = PIECEWD(i) - 1;
- b = z->P[i]&BIT(w);
- z->P[i] -= b << 1;
- z->P[i + 1] += b >> w;
- }
- z->P[0] += c; z->P[20] += c;
-
-#endif
}
/* --- @fgoldi_store@ --- *
void fgoldi_store(octet zv[56], const fgoldi *x)
{
-#if FGOLDI_IMPL == 28
piece y[NPIECE], yy[NPIECE], c, d;
uint32 u, v;
STORE32_L(zv + 4*i, u);
STORE32_L(zv + 4*i + 28, v);
}
-
-#elif FGOLDI_IMPL == 12
-
- piece y[NPIECE], yy[NPIECE], c, d;
- uint32 a;
- mask32 m, mm;
- unsigned i, j, n, w;
-
- 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| <= 2^14. We start off by cutting
- * off and reducing the carry c_39 from the topmost piece, y_39. This
- * leaves 0 <= y_39 < 2^11; and we'll have |c_39| <= 16. We'll add this
- * onto y_0 and y_20, and propagate the carries. It's very clear that
- * we'll end up with |y + (φ + 1) c_39 - φ^2/2| << φ^2.
- *
- * Here, the y_i are signed, so we must be cautious about bithacking them.
- */
- c = ASR(piece, y[39], 11); y[39] = (piece)y[39]&M11; y[20] += c;
- for (i = 0; i < NPIECE; i++) {
- w = PIECEWD(i); m = (1 << w) - 1;
- y[i] += c; c = ASR(piece, y[i], w); y[i] = (upiece)y[i]&m;
- }
-
- /* 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.
- */
- mm = SIGN(c);
- 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 ^ (mm&M12)); yy[ 0] = d&M12; d >>= 12;
- for (i = 1; i < 20; i++) {
- w = PIECEWD(i); m = MASK(w);
- d += y[ i] + (mm&m); yy[ i] = d&m; d >>= w;
- }
- d += y[20] + (1 ^ (mm&M12)); yy[20] = d&M12; d >>= 12;
- for (i = 21; i < 40; i++) {
- w = PIECEWD(i); m = MASK(w);
- d += y[ i] + (mm&m); yy[ i] = d&m; d >>= w;
- }
-
- /* 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);
-
- /* Convert that back into octets. */
- for (i = j = a = n = 0; i < NPIECE; i++) {
- a |= (uint32)y[i] << n; n += PIECEWD(i);
- while (n >= 8) { zv[j++] = a&M8; a >>= 8; n -= 8; }
- }
-
-#endif
}
/* --- @fgoldi_set@ --- *
for (i = 0; i < NPIECE; i++) z->P[i] = x->P[i] - y->P[i];
}
+/* --- @fgoldi_neg@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *x@ = an operand
+ *
+ * Returns: ---
+ *
+ * Use: Set @z = -x@.
+ */
+
+void fgoldi_neg(fgoldi *z, const fgoldi *x)
+{
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = -x->P[i];
+}
+
/*----- Constant-time utilities -------------------------------------------*/
+/* --- @fgoldi_pick2@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *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 fgoldi_pick2(fgoldi *z, const fgoldi *x, const fgoldi *y, uint32 m)
+{
+ mask32 mm = FIX_MASK32(m);
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = PICK2(x->P[i], y->P[i], mm);
+}
+
+/* --- @fgoldi_pickn@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result
+ * @const fgoldi *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 fgoldi_pickn(fgoldi *z, const fgoldi *v, size_t n, size_t i)
+{
+ uint32 b = (uint32)1 << (31 - i);
+ mask32 m;
+ unsigned j;
+
+ for (j = 0; j < NPIECE; j++) z->P[j] = 0;
+ while (n--) {
+ m = SIGN(b);
+ for (j = 0; j < NPIECE; j++) CONDPICK(z->P[j], v->P[j], m);
+ v++; b <<= 1;
+ }
+}
+
/* --- @fgoldi_condswap@ --- *
*
* Arguments: @fgoldi *x, *y@ = two operands
for (i = 0; i < NPIECE; i++) CONDSWAP(x->P[i], y->P[i], mm);
}
-/*----- Multiplication ----------------------------------------------------*/
+/* --- @fgoldi_condneg@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
+ * @const fgoldi *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 fgoldi_condneg(fgoldi *z, const fgoldi *x, uint32 m)
+{
+ mask32 m_xor = FIX_MASK32(m);
+ piece m_add = m&1;
+# define CONDNEG(x) (((x) ^ m_xor) + m_add)
+
+ unsigned i;
+ for (i = 0; i < NPIECE; i++) z->P[i] = CONDNEG(x->P[i]);
+
+#undef CONDNEG
+}
-#if FGOLDI_IMPL == 28
+/*----- 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
(z)[8] += _c; \
} while (0)
-#elif FGOLDI_IMPL == 12
-
-static void carry_reduce(dblpiece x[NPIECE])
-{
- /* Initial bounds: we assume |x_i| < 2^31 - 2^27. */
-
- unsigned i, j;
- dblpiece c;
-
- /* The result is nearly canonical, because we do sequential carry
- * propagation, because smaller processors are more likely to prefer the
- * smaller working set than the instruction-level parallelism.
- *
- * Start at x_37; truncate it to 10 bits, and propagate the carry to x_38.
- * Truncate x_38 to 10 bits, and add the carry onto x_39. Truncate x_39 to
- * 10 bits, and add the carry onto x_0 and x_20. And so on.
- *
- * Once we reach x_37 for the second time, we start with |x_37| <= 2^10.
- * The carry into x_37 is at most 2^21; so the carry out into x_38 has
- * magnitude at most 2^10. In turn, |x_38| <= 2^10 before the carry, so is
- * now no more than 2^11 in magnitude, and the carry out into x_39 is at
- * most 1. This leaves |x_39| <= 2^10 + 1 after carry propagation.
- *
- * Be careful with the bit hacking because the quantities involved are
- * signed.
- */
-
- /* For each piece, we bias it so that floor division (as done by an
- * arithmetic right shift) and modulus (as done by bitwise-AND) does the
- * right thing.
- */
-#define CARRY(i, wd, b, m) do { \
- x[i] += (b); \
- c = ASR(dblpiece, x[i], (wd)); \
- x[i] = (dblpiece)((udblpiece)x[i]&(m)) - (b); \
-} while (0)
-
- { CARRY(37, 11, B10, M11); }
- { x[38] += c; CARRY(38, 11, B10, M11); }
- { x[39] += c; CARRY(39, 11, B10, M11); }
- x[20] += c;
- for (i = 0; i < 35; ) {
- { x[i] += c; CARRY( i, 12, B11, M12); i++; }
- for (j = i + 4; i < j; ) { x[i] += c; CARRY( i, 11, B10, M11); i++; }
- }
- { x[i] += c; CARRY( i, 12, B11, M12); i++; }
- while (i < 39) { x[i] += c; CARRY( i, 11, B10, M11); i++; }
- x[39] += c;
-}
-
-#endif
-
/* --- @fgoldi_mulconst@ --- *
*
* Arguments: @fgoldi *z@ = where to put the result (may alias @x@)
dblpiece zz[NPIECE], aa = a;
for (i = 0; i < NPIECE; i++) zz[i] = aa*x->P[i];
-#if FGOLDI_IMPL == 28
CARRY_REDUCE(z->P, zz);
-#elif FGOLDI_IMPL == 12
- carry_reduce(zz);
- for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-#endif
}
/* --- @fgoldi_mul@ --- *
*c = y->P + NPIECE/2, *d = y->P;
unsigned i, j;
-#if FGOLDI_IMPL == 28
-
# define M(x,i, y,j) ((dblpiece)(x)[i]*(y)[j])
-#elif FGOLDI_IMPL == 12
-
- static const unsigned short off[39] = {
- 0, 12, 23, 34, 45, 56, 68, 79, 90, 101,
- 112, 124, 135, 146, 157, 168, 180, 191, 202, 213,
- 224, 236, 247, 258, 269, 280, 292, 303, 314, 325,
- 336, 348, 359, 370, 381, 392, 404, 415, 426
- };
-
-#define M(x,i, y,j) \
- (((dblpiece)(x)[i]*(y)[j]) << (off[i] + off[j] - off[(i) + (j)]))
-
-#endif
-
/* Behold the magic.
*
* Write x = a φ + b, and y = c φ + d. Then x y = a c φ^2 +
#undef M
-#if FGOLDI_IMPL == 28
/* 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
*/
for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-#elif FGOLDI_IMPL == 12
- carry_reduce(zz);
- for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-#endif
}
/* --- @fgoldi_sqr@ --- *
void fgoldi_sqr(fgoldi *z, const fgoldi *x)
{
-#if FGOLDI_IMPL == 28
dblpiece zz[NPIECE], u[NPIECE];
piece ab[NPIECE];
/* Finally, carrying. */
for (i = 0; i < 2; i++) CARRY_REDUCE(zz, zz);
for (i = 0; i < NPIECE; i++) z->P[i] = zz[i];
-
-#elif FGOLDI_IMPL == 12
- fgoldi_mul(z, x, x);
-#endif
}
/*----- More advanced operations ------------------------------------------*/
#undef SQRN
}
-/*----- Test rig ----------------------------------------------------------*/
-
-#ifdef TEST_RIG
-
-#include <mLib/report.h>
-#include <mLib/str.h>
-#include <mLib/testrig.h>
-
-static void fixdstr(dstr *d)
-{
- if (d->len > 56)
- die(1, "invalid length for fgoldi");
- else if (d->len < 56) {
- dstr_ensure(d, 56);
- memset(d->buf + d->len, 0, 56 - d->len);
- d->len = 56;
- }
-}
-
-static void cvt_fgoldi(const char *buf, dstr *d)
-{
- dstr dd = DSTR_INIT;
-
- type_hex.cvt(buf, &dd); fixdstr(&dd);
- dstr_ensure(d, sizeof(fgoldi)); d->len = sizeof(fgoldi);
- fgoldi_load((fgoldi *)d->buf, (const octet *)dd.buf);
- dstr_destroy(&dd);
-}
-
-static void dump_fgoldi(dstr *d, FILE *fp)
- { fdump(stderr, "???", (const piece *)d->buf); }
-
-static void cvt_fgoldi_ref(const char *buf, dstr *d)
- { type_hex.cvt(buf, d); fixdstr(d); }
-
-static void dump_fgoldi_ref(dstr *d, FILE *fp)
-{
- fgoldi x;
-
- fgoldi_load(&x, (const octet *)d->buf);
- fdump(stderr, "???", x.P);
-}
-
-static int eq(const fgoldi *x, dstr *d)
- { octet b[56]; fgoldi_store(b, x); return (memcmp(b, d->buf, 56) == 0); }
-
-static const test_type
- type_fgoldi = { cvt_fgoldi, dump_fgoldi },
- type_fgoldi_ref = { cvt_fgoldi_ref, dump_fgoldi_ref };
-
-#define TEST_UNOP(op) \
- static int vrf_##op(dstr dv[]) \
- { \
- fgoldi *x = (fgoldi *)dv[0].buf; \
- fgoldi z, zz; \
- int ok = 1; \
- \
- fgoldi_##op(&z, x); \
- if (!eq(&z, &dv[1])) { \
- ok = 0; \
- fprintf(stderr, "failed!\n"); \
- fdump(stderr, "x", x->P); \
- fdump(stderr, "calc", z.P); \
- fgoldi_load(&zz, (const octet *)dv[1].buf); \
- fdump(stderr, "z", zz.P); \
- } \
- \
- return (ok); \
- }
-
-TEST_UNOP(sqr)
-TEST_UNOP(inv)
-
-#define TEST_BINOP(op) \
- static int vrf_##op(dstr dv[]) \
- { \
- fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf; \
- fgoldi z, zz; \
- int ok = 1; \
- \
- fgoldi_##op(&z, x, y); \
- if (!eq(&z, &dv[2])) { \
- ok = 0; \
- fprintf(stderr, "failed!\n"); \
- fdump(stderr, "x", x->P); \
- fdump(stderr, "y", y->P); \
- fdump(stderr, "calc", z.P); \
- fgoldi_load(&zz, (const octet *)dv[2].buf); \
- fdump(stderr, "z", zz.P); \
- } \
- \
- return (ok); \
- }
-
-TEST_BINOP(add)
-TEST_BINOP(sub)
-TEST_BINOP(mul)
+/* --- @fgoldi_quosqrt@ --- *
+ *
+ * Arguments: @fgoldi *z@ = where to put the result (may alias @x@ or @y@)
+ * @const fgoldi *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 int vrf_mulc(dstr dv[])
+int fgoldi_quosqrt(fgoldi *z, const fgoldi *x, const fgoldi *y)
{
- fgoldi *x = (fgoldi *)dv[0].buf;
- long a = *(const long *)dv[1].buf;
- fgoldi z, zz;
- int ok = 1;
-
- fgoldi_mulconst(&z, x, a);
- if (!eq(&z, &dv[2])) {
- ok = 0;
- fprintf(stderr, "failed!\n");
- fdump(stderr, "x", x->P);
- fprintf(stderr, "a = %ld\n", a);
- fdump(stderr, "calc", z.P);
- fgoldi_load(&zz, (const octet *)dv[2].buf);
- fdump(stderr, "z", zz.P);
- }
-
- return (ok);
-}
+ fgoldi t, u, v;
+ octet xb[56], b0[56];
+ int32 rc = -1;
+ mask32 m;
+ unsigned i;
-static int vrf_condswap(dstr dv[])
-{
- fgoldi *x = (fgoldi *)dv[0].buf, *y = (fgoldi *)dv[1].buf;
- fgoldi xx = *x, yy = *y;
- uint32 m = *(uint32 *)dv[2].buf;
- int ok = 1;
-
- fgoldi_condswap(&xx, &yy, m);
- if (!eq(&xx, &dv[3]) || !eq(&yy, &dv[4])) {
- ok = 0;
- fprintf(stderr, "failed!\n");
- fdump(stderr, "x", x->P);
- fdump(stderr, "y", y->P);
- fprintf(stderr, "m = 0x%08lx\n", (unsigned long)m);
- fdump(stderr, "calc xx", xx.P);
- fdump(stderr, "calc yy", yy.P);
- fgoldi_load(&xx, (const octet *)dv[3].buf);
- fgoldi_load(&yy, (const octet *)dv[4].buf);
- fdump(stderr, "want xx", xx.P);
- fdump(stderr, "want yy", yy.P);
- }
+#define SQRN(z, x, n) do { \
+ fgoldi_sqr((z), (x)); \
+ for (i = 1; i < (n); i++) fgoldi_sqr((z), (z)); \
+} while (0)
- return (ok);
-}
+ /* This is, fortunately, significantly easier than the equivalent problem
+ * in GF(2^255 - 19), since p == 3 (mod 4).
+ *
+ * If x/y is square, then so is v = y^2 x/y = x y, and therefore u has
+ * order r = (p - 1)/2. Let w = v^{(p-3)/4}. Then w^2 = v^{(p-3)/2} =
+ * u^{r-1} = 1/v = 1/x y. Clearly, then, (x w)^2 = x^2/x y = x/y, so x w
+ * is one of the square roots we seek.
+ *
+ * The addition chain, then, is a prefix of the previous one.
+ */
+ fgoldi_mul(&v, x, y);
-static int vrf_sub_mulc_add_sub_mul(dstr dv[])
-{
- fgoldi *u = (fgoldi *)dv[0].buf, *v = (fgoldi *)dv[1].buf,
- *w = (fgoldi *)dv[3].buf, *x = (fgoldi *)dv[4].buf,
- *y = (fgoldi *)dv[5].buf;
- long a = *(const long *)dv[2].buf;
- fgoldi umv, aumv, wpaumv, xmy, z, zz;
- int ok = 1;
-
- fgoldi_sub(&umv, u, v);
- fgoldi_mulconst(&aumv, &umv, a);
- fgoldi_add(&wpaumv, w, &aumv);
- fgoldi_sub(&xmy, x, y);
- fgoldi_mul(&z, &wpaumv, &xmy);
-
- if (!eq(&z, &dv[6])) {
- ok = 0;
- fprintf(stderr, "failed!\n");
- fdump(stderr, "u", u->P);
- fdump(stderr, "v", v->P);
- fdump(stderr, "u - v", umv.P);
- fprintf(stderr, "a = %ld\n", a);
- fdump(stderr, "a (u - v)", aumv.P);
- fdump(stderr, "w + a (u - v)", wpaumv.P);
- fdump(stderr, "x", x->P);
- fdump(stderr, "y", y->P);
- fdump(stderr, "x - y", xmy.P);
- fdump(stderr, "(x - y) (w + a (u - v))", z.P);
- fgoldi_load(&zz, (const octet *)dv[6].buf); fdump(stderr, "z", zz.P);
- }
+ fgoldi_sqr(&u, &v); /* 1 | 2 */
+ fgoldi_mul(&t, &u, &v); /* 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, &v); /* 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, &v); /* 233 | 2^223 - 1 */
+ SQRN(&u, &u, 223); /* 456 | 2^446 - 2^223 */
+ fgoldi_mul(&t, &u, &t); /* 457 | 2^446 - 2^222 - 1 */
- return (ok);
-}
+#undef SQRN
-static test_chunk tests[] = {
- { "add", vrf_add, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
- { "sub", vrf_sub, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
- { "mul", vrf_mul, { &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
- { "mulconst", vrf_mulc, { &type_fgoldi, &type_long, &type_fgoldi_ref } },
- { "condswap", vrf_condswap,
- { &type_fgoldi, &type_fgoldi, &type_uint32,
- &type_fgoldi_ref, &type_fgoldi_ref } },
- { "sqr", vrf_sqr, { &type_fgoldi, &type_fgoldi_ref } },
- { "inv", vrf_inv, { &type_fgoldi, &type_fgoldi_ref } },
- { "sub-mulc-add-sub-mul", vrf_sub_mulc_add_sub_mul,
- { &type_fgoldi, &type_fgoldi, &type_long, &type_fgoldi,
- &type_fgoldi, &type_fgoldi, &type_fgoldi_ref } },
- { 0, 0, { 0 } }
-};
-
-int main(int argc, char *argv[])
-{
- test_run(argc, argv, tests, SRCDIR "/t/fgoldi");
- return (0);
+ /* Now we must decide whether the answer was right. We should have z^2 =
+ * x/y, so y z^2 = x.
+ *
+ * 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.
+ */
+ fgoldi_mul(z, x, &t);
+ fgoldi_sqr(&t, z);
+ fgoldi_mul(&t, &t, y);
+ fgoldi_store(xb, x);
+ fgoldi_store(b0, &t);
+ m = -consttime_memeq(xb, b0, 56);
+ rc = PICK2(0, rc, m);
+ return (rc);
}
-#endif
-
/*----- That's all, folks -------------------------------------------------*/
~mdw / secnet / blobdiff