Improve bounds checks in modinv modules
This commit adds functions to verify and compare numbers in signed{30,62} notation,
and uses that to do more extensive bounds checking on various variables in the modinv
code.
This commit is contained in:
Pieter Wuille
parent
151aac00d3
commit
08d54964e5
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@ -20,6 +20,42 @@
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* implementation for N=30, using 30-bit signed limbs represented as int32_t.
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*/
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#ifdef VERIFY
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static const secp256k1_modinv32_signed30 SECP256K1_SIGNED30_ONE = {{1}};
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/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^30). */
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static void secp256k1_modinv32_mul_30(secp256k1_modinv32_signed30 *r, const secp256k1_modinv32_signed30 *a, int32_t factor) {
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const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
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int64_t c = 0;
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int i;
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for (i = 0; i < 8; ++i) {
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c += (int64_t)a->v[i] * factor;
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r->v[i] = (int32_t)c & M30; c >>= 30;
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}
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c += (int64_t)a->v[8] * factor;
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VERIFY_CHECK(c == (int32_t)c);
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r->v[8] = (int32_t)c;
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}
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/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. */
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static int secp256k1_modinv32_mul_cmp_30(const secp256k1_modinv32_signed30 *a, const secp256k1_modinv32_signed30 *b, int32_t factor) {
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int i;
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secp256k1_modinv32_signed30 am, bm;
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secp256k1_modinv32_mul_30(&am, a, 1); /* Normalize all but the top limb of a. */
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secp256k1_modinv32_mul_30(&bm, b, factor);
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for (i = 0; i < 8; ++i) {
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/* Verify that all but the top limb of a and b are normalized. */
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VERIFY_CHECK(am.v[i] >> 30 == 0);
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VERIFY_CHECK(bm.v[i] >> 30 == 0);
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}
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for (i = 8; i >= 0; --i) {
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if (am.v[i] < bm.v[i]) return -1;
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if (am.v[i] > bm.v[i]) return 1;
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}
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return 0;
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}
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#endif
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/* Take as input a signed30 number in range (-2*modulus,modulus), and add a multiple of the modulus
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* to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the
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* process. The input must have limbs in range (-2^30,2^30). The output will have limbs in range
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@ -30,6 +66,17 @@ static void secp256k1_modinv32_normalize_30(secp256k1_modinv32_signed30 *r, int3
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r5 = r->v[5], r6 = r->v[6], r7 = r->v[7], r8 = r->v[8];
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int32_t cond_add, cond_negate;
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#ifdef VERIFY
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/* Verify that all limbs are in range (-2^30,2^30). */
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int i;
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for (i = 0; i < 9; ++i) {
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VERIFY_CHECK(r->v[i] >= -M30);
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VERIFY_CHECK(r->v[i] <= M30);
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}
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, &modinfo->modulus, -2) > 0); /* r > -2*modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, &modinfo->modulus, 1) < 0); /* r < modulus */
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#endif
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/* In a first step, add the modulus if the input is negative, and then negate if requested.
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* This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input
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* limbs are in range (-2^30,2^30), this cannot overflow an int32_t. Note that the right
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@ -96,6 +143,20 @@ static void secp256k1_modinv32_normalize_30(secp256k1_modinv32_signed30 *r, int3
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r->v[6] = r6;
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r->v[7] = r7;
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r->v[8] = r8;
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#ifdef VERIFY
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VERIFY_CHECK(r0 >> 30 == 0);
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VERIFY_CHECK(r1 >> 30 == 0);
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VERIFY_CHECK(r2 >> 30 == 0);
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VERIFY_CHECK(r3 >> 30 == 0);
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VERIFY_CHECK(r4 >> 30 == 0);
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VERIFY_CHECK(r5 >> 30 == 0);
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VERIFY_CHECK(r6 >> 30 == 0);
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VERIFY_CHECK(r7 >> 30 == 0);
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VERIFY_CHECK(r8 >> 30 == 0);
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, &modinfo->modulus, 0) >= 0); /* r >= 0 */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, &modinfo->modulus, 1) < 0); /* r < modulus */
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#endif
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}
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/* Data type for transition matrices (see section 3 of explanation).
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@ -155,12 +216,19 @@ static int32_t secp256k1_modinv32_divsteps_30(int32_t eta, uint32_t f0, uint32_t
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g >>= 1;
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u <<= 1;
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v <<= 1;
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/* Bounds on eta that follow from the bounds on iteration count (max 25*30 divsteps). */
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VERIFY_CHECK(eta >= -751 && eta <= 751);
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}
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/* Return data in t and return value. */
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t->u = (int32_t)u;
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t->v = (int32_t)v;
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t->q = (int32_t)q;
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t->r = (int32_t)r;
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/* The determinant of t must be a power of two. This guarantees that multiplication with t
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* does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
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* will be divided out again). As each divstep's individual matrix has determinant 2, the
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* aggregate of 30 of them will have determinant 2^30. */
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VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30);
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return eta;
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}
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@ -211,6 +279,8 @@ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint
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VERIFY_CHECK((g & 1) == 1);
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VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i));
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VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i));
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/* Bounds on eta that follow from the bounds on iteration count (max 25*30 divsteps). */
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VERIFY_CHECK(eta >= -751 && eta <= 751);
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/* If eta is negative, negate it and replace f,g with g,-f. */
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if (eta < 0) {
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uint32_t tmp;
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@ -224,6 +294,7 @@ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint
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* can be done as its sign will flip once that happens. */
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limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
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/* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */
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VERIFY_CHECK(limit > 0 && limit <= 30);
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m = (UINT32_MAX >> (32 - limit)) & 255U;
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/* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */
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w = (g * inv256[(f >> 1) & 127]) & m;
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@ -238,6 +309,11 @@ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint
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t->v = (int32_t)v;
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t->q = (int32_t)q;
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t->r = (int32_t)r;
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/* The determinant of t must be a power of two. This guarantees that multiplication with t
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* does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
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* will be divided out again). As each divstep's individual matrix has determinant 2, the
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* aggregate of 30 of them will have determinant 2^30. */
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VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30);
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return eta;
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}
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@ -254,6 +330,16 @@ static void secp256k1_modinv32_update_de_30(secp256k1_modinv32_signed30 *d, secp
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int32_t di, ei, md, me, sd, se;
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int64_t cd, ce;
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int i;
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#ifdef VERIFY
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, &modinfo->modulus, 1) < 0); /* d < modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, &modinfo->modulus, 1) < 0); /* e < modulus */
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VERIFY_CHECK((labs(u) + labs(v)) >= 0); /* |u|+|v| doesn't overflow */
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VERIFY_CHECK((labs(q) + labs(r)) >= 0); /* |q|+|r| doesn't overflow */
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VERIFY_CHECK((labs(u) + labs(v)) <= M30 + 1); /* |u|+|v| <= 2^30 */
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VERIFY_CHECK((labs(q) + labs(r)) <= M30 + 1); /* |q|+|r| <= 2^30 */
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#endif
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/* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */
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sd = d->v[8] >> 31;
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se = e->v[8] >> 31;
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@ -288,6 +374,12 @@ static void secp256k1_modinv32_update_de_30(secp256k1_modinv32_signed30 *d, secp
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/* What remains is limb 9 of t*[d,e]+modulus*[md,me]; store it as output limb 8. */
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d->v[8] = (int32_t)cd;
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e->v[8] = (int32_t)ce;
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#ifdef VERIFY
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, &modinfo->modulus, 1) < 0); /* d < modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, &modinfo->modulus, 1) < 0); /* e < modulus */
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#endif
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}
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/* Compute (t/2^30) * [f, g], where t is a transition matrix for 30 divsteps.
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@ -341,13 +433,35 @@ static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_m
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/* Update d,e using that transition matrix. */
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secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo);
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/* Update f,g using that transition matrix. */
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#ifdef VERIFY
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
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#endif
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secp256k1_modinv32_update_fg_30(&f, &g, &t);
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#ifdef VERIFY
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
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#endif
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}
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/* At this point sufficient iterations have been performed that g must have reached 0
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* and (if g was not originally 0) f must now equal +/- GCD of the initial f, g
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* values i.e. +/- 1, and d now contains +/- the modular inverse. */
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VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4] | g.v[5] | g.v[6] | g.v[7] | g.v[8]) == 0);
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#ifdef VERIFY
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/* g == 0 */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &SECP256K1_SIGNED30_ONE, 0) == 0);
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/* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &SECP256K1_SIGNED30_ONE, -1) == 0 ||
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secp256k1_modinv32_mul_cmp_30(&f, &SECP256K1_SIGNED30_ONE, 1) == 0 ||
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(secp256k1_modinv32_mul_cmp_30(x, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
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secp256k1_modinv32_mul_cmp_30(&d, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
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(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) == 0 ||
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secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) == 0)));
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#endif
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/* Optionally negate d, normalize to [0,modulus), and return it. */
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secp256k1_modinv32_normalize_30(&d, f.v[8], modinfo);
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@ -361,6 +475,9 @@ static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256
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secp256k1_modinv32_signed30 e = {{1, 0, 0, 0, 0, 0, 0, 0, 0}};
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secp256k1_modinv32_signed30 f = modinfo->modulus;
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secp256k1_modinv32_signed30 g = *x;
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#ifdef VERIFY
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int i = 0;
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#endif
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int j;
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int32_t eta = -1;
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int32_t cond;
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@ -373,6 +490,12 @@ static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256
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/* Update d,e using that transition matrix. */
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secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo);
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/* Update f,g using that transition matrix. */
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#ifdef VERIFY
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
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#endif
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secp256k1_modinv32_update_fg_30(&f, &g, &t);
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/* If the bottom limb of g is 0, there is a chance g=0. */
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if (g.v[0] == 0) {
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@ -384,10 +507,28 @@ static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256
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/* If so, we're done. */
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if (cond == 0) break;
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}
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#ifdef VERIFY
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VERIFY_CHECK(++i < 25); /* We should never need more than 25*30 = 750 divsteps */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
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#endif
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}
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/* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of
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* the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */
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#ifdef VERIFY
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/* g == 0 */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, &SECP256K1_SIGNED30_ONE, 0) == 0);
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/* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */
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VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, &SECP256K1_SIGNED30_ONE, -1) == 0 ||
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secp256k1_modinv32_mul_cmp_30(&f, &SECP256K1_SIGNED30_ONE, 1) == 0 ||
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(secp256k1_modinv32_mul_cmp_30(x, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
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secp256k1_modinv32_mul_cmp_30(&d, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
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(secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, 1) == 0 ||
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secp256k1_modinv32_mul_cmp_30(&f, &modinfo->modulus, -1) == 0)));
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#endif
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/* Optionally negate d, normalize to [0,modulus), and return it. */
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secp256k1_modinv32_normalize_30(&d, f.v[8], modinfo);
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@ -18,6 +18,50 @@
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* implementation for N=62, using 62-bit signed limbs represented as int64_t.
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*/
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#ifdef VERIFY
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/* Helper function to compute the absolute value of an int64_t.
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* (we don't use abs/labs/llabs as it depends on the int sizes). */
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static int64_t secp256k1_modinv64_abs(int64_t v) {
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VERIFY_CHECK(v > INT64_MIN);
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if (v < 0) return -v;
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return v;
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}
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static const secp256k1_modinv64_signed62 SECP256K1_SIGNED62_ONE = {{1}};
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/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^62). */
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static void secp256k1_modinv64_mul_62(secp256k1_modinv64_signed62 *r, const secp256k1_modinv64_signed62 *a, int64_t factor) {
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const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
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int128_t c = 0;
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int i;
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for (i = 0; i < 4; ++i) {
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c += (int128_t)a->v[i] * factor;
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r->v[i] = (int64_t)c & M62; c >>= 62;
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}
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c += (int128_t)a->v[4] * factor;
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VERIFY_CHECK(c == (int64_t)c);
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r->v[4] = (int64_t)c;
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}
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/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. */
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static int secp256k1_modinv64_mul_cmp_62(const secp256k1_modinv64_signed62 *a, const secp256k1_modinv64_signed62 *b, int64_t factor) {
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int i;
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secp256k1_modinv64_signed62 am, bm;
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secp256k1_modinv64_mul_62(&am, a, 1); /* Normalize all but the top limb of a. */
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secp256k1_modinv64_mul_62(&bm, b, factor);
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for (i = 0; i < 4; ++i) {
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/* Verify that all but the top limb of a and b are normalized. */
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VERIFY_CHECK(am.v[i] >> 62 == 0);
|
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VERIFY_CHECK(bm.v[i] >> 62 == 0);
|
||||
}
|
||||
for (i = 4; i >= 0; --i) {
|
||||
if (am.v[i] < bm.v[i]) return -1;
|
||||
if (am.v[i] > bm.v[i]) return 1;
|
||||
}
|
||||
return 0;
|
||||
}
|
||||
#endif
|
||||
|
||||
/* Take as input a signed62 number in range (-2*modulus,modulus), and add a multiple of the modulus
|
||||
* to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the
|
||||
* process. The input must have limbs in range (-2^62,2^62). The output will have limbs in range
|
||||
|
|
@ -27,6 +71,17 @@ static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int6
|
|||
int64_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4];
|
||||
int64_t cond_add, cond_negate;
|
||||
|
||||
#ifdef VERIFY
|
||||
/* Verify that all limbs are in range (-2^62,2^62). */
|
||||
int i;
|
||||
for (i = 0; i < 5; ++i) {
|
||||
VERIFY_CHECK(r->v[i] >= -M62);
|
||||
VERIFY_CHECK(r->v[i] <= M62);
|
||||
}
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, &modinfo->modulus, -2) > 0); /* r > -2*modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, &modinfo->modulus, 1) < 0); /* r < modulus */
|
||||
#endif
|
||||
|
||||
/* In a first step, add the modulus if the input is negative, and then negate if requested.
|
||||
* This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input
|
||||
* limbs are in range (-2^62,2^62), this cannot overflow an int64_t. Note that the right
|
||||
|
|
@ -69,6 +124,16 @@ static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int6
|
|||
r->v[2] = r2;
|
||||
r->v[3] = r3;
|
||||
r->v[4] = r4;
|
||||
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(r0 >> 62 == 0);
|
||||
VERIFY_CHECK(r1 >> 62 == 0);
|
||||
VERIFY_CHECK(r2 >> 62 == 0);
|
||||
VERIFY_CHECK(r3 >> 62 == 0);
|
||||
VERIFY_CHECK(r4 >> 62 == 0);
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, &modinfo->modulus, 0) >= 0); /* r >= 0 */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, &modinfo->modulus, 1) < 0); /* r < modulus */
|
||||
#endif
|
||||
}
|
||||
|
||||
/* Data type for transition matrices (see section 3 of explanation).
|
||||
|
|
@ -128,12 +193,19 @@ static int64_t secp256k1_modinv64_divsteps_62(int64_t eta, uint64_t f0, uint64_t
|
|||
g >>= 1;
|
||||
u <<= 1;
|
||||
v <<= 1;
|
||||
/* Bounds on eta that follow from the bounds on iteration count (max 12*62 divsteps). */
|
||||
VERIFY_CHECK(eta >= -745 && eta <= 745);
|
||||
}
|
||||
/* Return data in t and return value. */
|
||||
t->u = (int64_t)u;
|
||||
t->v = (int64_t)v;
|
||||
t->q = (int64_t)q;
|
||||
t->r = (int64_t)r;
|
||||
/* The determinant of t must be a power of two. This guarantees that multiplication with t
|
||||
* does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
|
||||
* will be divided out again). As each divstep's individual matrix has determinant 2, the
|
||||
* aggregate of 62 of them will have determinant 2^62. */
|
||||
VERIFY_CHECK((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 62);
|
||||
return eta;
|
||||
}
|
||||
|
||||
|
|
@ -184,6 +256,8 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint
|
|||
VERIFY_CHECK((g & 1) == 1);
|
||||
VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i));
|
||||
VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i));
|
||||
/* Bounds on eta that follow from the bounds on iteration count (max 12*62 divsteps). */
|
||||
VERIFY_CHECK(eta >= -745 && eta <= 745);
|
||||
/* If eta is negative, negate it and replace f,g with g,-f. */
|
||||
if (eta < 0) {
|
||||
uint64_t tmp;
|
||||
|
|
@ -197,6 +271,7 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint
|
|||
* can be done as its sign will flip once that happens. */
|
||||
limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
|
||||
/* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */
|
||||
VERIFY_CHECK(limit > 0 && limit <= 62);
|
||||
m = (UINT64_MAX >> (64 - limit)) & 255U;
|
||||
/* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */
|
||||
w = (g * inv256[(f >> 1) & 127]) & m;
|
||||
|
|
@ -211,6 +286,11 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint
|
|||
t->v = (int64_t)v;
|
||||
t->q = (int64_t)q;
|
||||
t->r = (int64_t)r;
|
||||
/* The determinant of t must be a power of two. This guarantees that multiplication with t
|
||||
* does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
|
||||
* will be divided out again). As each divstep's individual matrix has determinant 2, the
|
||||
* aggregate of 62 of them will have determinant 2^62. */
|
||||
VERIFY_CHECK((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 62);
|
||||
return eta;
|
||||
}
|
||||
|
||||
|
|
@ -228,6 +308,16 @@ static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp
|
|||
const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
|
||||
int64_t md, me, sd, se;
|
||||
int128_t cd, ce;
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, &modinfo->modulus, 1) < 0); /* d < modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, &modinfo->modulus, 1) < 0); /* e < modulus */
|
||||
VERIFY_CHECK((secp256k1_modinv64_abs(u) + secp256k1_modinv64_abs(v)) >= 0); /* |u|+|v| doesn't overflow */
|
||||
VERIFY_CHECK((secp256k1_modinv64_abs(q) + secp256k1_modinv64_abs(r)) >= 0); /* |q|+|r| doesn't overflow */
|
||||
VERIFY_CHECK((secp256k1_modinv64_abs(u) + secp256k1_modinv64_abs(v)) <= M62 + 1); /* |u|+|v| <= 2^62 */
|
||||
VERIFY_CHECK((secp256k1_modinv64_abs(q) + secp256k1_modinv64_abs(r)) <= M62 + 1); /* |q|+|r| <= 2^62 */
|
||||
#endif
|
||||
/* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */
|
||||
sd = d4 >> 63;
|
||||
se = e4 >> 63;
|
||||
|
|
@ -276,6 +366,12 @@ static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp
|
|||
/* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */
|
||||
d->v[4] = (int64_t)cd;
|
||||
e->v[4] = (int64_t)ce;
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, &modinfo->modulus, 1) < 0); /* d < modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, &modinfo->modulus, 1) < 0); /* e < modulus */
|
||||
#endif
|
||||
}
|
||||
|
||||
/* Compute (t/2^62) * [f, g], where t is a transition matrix for 62 divsteps.
|
||||
|
|
@ -337,13 +433,35 @@ static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_m
|
|||
/* Update d,e using that transition matrix. */
|
||||
secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo);
|
||||
/* Update f,g using that transition matrix. */
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
|
||||
#endif
|
||||
secp256k1_modinv64_update_fg_62(&f, &g, &t);
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
|
||||
#endif
|
||||
}
|
||||
|
||||
/* At this point sufficient iterations have been performed that g must have reached 0
|
||||
* and (if g was not originally 0) f must now equal +/- GCD of the initial f, g
|
||||
* values i.e. +/- 1, and d now contains +/- the modular inverse. */
|
||||
VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4]) == 0);
|
||||
#ifdef VERIFY
|
||||
/* g == 0 */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &SECP256K1_SIGNED62_ONE, 0) == 0);
|
||||
/* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &SECP256K1_SIGNED62_ONE, -1) == 0 ||
|
||||
secp256k1_modinv64_mul_cmp_62(&f, &SECP256K1_SIGNED62_ONE, 1) == 0 ||
|
||||
(secp256k1_modinv64_mul_cmp_62(x, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
|
||||
secp256k1_modinv64_mul_cmp_62(&d, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
|
||||
(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) == 0 ||
|
||||
secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) == 0)));
|
||||
#endif
|
||||
|
||||
/* Optionally negate d, normalize to [0,modulus), and return it. */
|
||||
secp256k1_modinv64_normalize_62(&d, f.v[4], modinfo);
|
||||
|
|
@ -358,6 +476,9 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256
|
|||
secp256k1_modinv64_signed62 f = modinfo->modulus;
|
||||
secp256k1_modinv64_signed62 g = *x;
|
||||
int j;
|
||||
#ifdef VERIFY
|
||||
int i = 0;
|
||||
#endif
|
||||
int64_t eta = -1;
|
||||
int64_t cond;
|
||||
|
||||
|
|
@ -369,6 +490,12 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256
|
|||
/* Update d,e using that transition matrix. */
|
||||
secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo);
|
||||
/* Update f,g using that transition matrix. */
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
|
||||
#endif
|
||||
secp256k1_modinv64_update_fg_62(&f, &g, &t);
|
||||
/* If the bottom limb of g is zero, there is a chance that g=0. */
|
||||
if (g.v[0] == 0) {
|
||||
|
|
@ -380,10 +507,28 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256
|
|||
/* If so, we're done. */
|
||||
if (cond == 0) break;
|
||||
}
|
||||
#ifdef VERIFY
|
||||
VERIFY_CHECK(++i < 12); /* We should never need more than 12*62 = 744 divsteps */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) > 0); /* f > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) <= 0); /* f <= modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, -1) > 0); /* g > -modulus */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &modinfo->modulus, 1) < 0); /* g < modulus */
|
||||
#endif
|
||||
}
|
||||
|
||||
/* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of
|
||||
* the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */
|
||||
#ifdef VERIFY
|
||||
/* g == 0 */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, &SECP256K1_SIGNED62_ONE, 0) == 0);
|
||||
/* |f| == 1, or (x == 0 and d == 0 and |f|=modulus) */
|
||||
VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, &SECP256K1_SIGNED62_ONE, -1) == 0 ||
|
||||
secp256k1_modinv64_mul_cmp_62(&f, &SECP256K1_SIGNED62_ONE, 1) == 0 ||
|
||||
(secp256k1_modinv64_mul_cmp_62(x, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
|
||||
secp256k1_modinv64_mul_cmp_62(&d, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
|
||||
(secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, 1) == 0 ||
|
||||
secp256k1_modinv64_mul_cmp_62(&f, &modinfo->modulus, -1) == 0)));
|
||||
#endif
|
||||
|
||||
/* Optionally negate d, normalize to [0,modulus), and return it. */
|
||||
secp256k1_modinv64_normalize_62(&d, f.v[4], modinfo);
|
||||
|
|
|
|||
Loading…
Reference in New Issue