X-Git-Url: https://git.openssl.org/gitweb/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fec%2Fec2_mult.c;h=9955948dfd1e6e282630b78d4b3925f73ac3e3e1;hp=41b4c957156a4998461ae39c800b00587d1ca904;hb=c695ebe2a09cb7f9aaec3c435ab94d36a6d6aece;hpb=102c8f47bf899bfc76047bdde396d40ea3b6ce7c diff --git a/crypto/ec/ec2_mult.c b/crypto/ec/ec2_mult.c index 41b4c95715..9955948dfd 100644 --- a/crypto/ec/ec2_mult.c +++ b/crypto/ec/ec2_mult.c @@ -9,25 +9,12 @@ * The ECC Code is licensed pursuant to the OpenSSL open source * license provided below. * - * In addition, Sun covenants to all licensees who provide a reciprocal - * covenant with respect to their own patents if any, not to sue under - * current and future patent claims necessarily infringed by the making, - * using, practicing, selling, offering for sale and/or otherwise - * disposing of the ECC Code as delivered hereunder (or portions thereof), - * provided that such covenant shall not apply: - * 1) for code that a licensee deletes from the ECC Code; - * 2) separates from the ECC Code; or - * 3) for infringements caused by: - * i) the modification of the ECC Code or - * ii) the combination of the ECC Code with other software or - * devices where such combination causes the infringement. - * * The software is originally written by Sheueling Chang Shantz and * Douglas Stebila of Sun Microsystems Laboratories. * */ /* ==================================================================== - * Copyright (c) 1998-2002 The OpenSSL Project. All rights reserved. + * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions @@ -84,15 +71,18 @@ #include "ec_lcl.h" +#ifndef OPENSSL_NO_EC2M + -/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective +/*- + * Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective * coordinates. * Uses algorithm Mdouble in appendix of * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * modified to not require precomputation of c=b^{2^{m-1}}. */ -static int Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) +static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) { BIGNUM *t1; int ret = 0; @@ -117,13 +107,14 @@ static int Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx) return ret; } -/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery +/*- + * Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery * projective coordinates. * Uses algorithm Madd in appendix of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). */ -static int Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, +static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx) { BIGNUM *t1, *t2; @@ -151,17 +142,17 @@ static int Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, return ret; } -/* Compute the affine coordinates x2, y2=z2 for the point (x1/z1) and (x2/x2) in - * Montgomery projective coordinates. - * Uses algorithm Mxy in appendix of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". +/*- + * Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) + * using Montgomery point multiplication algorithm Mxy() in appendix of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). * Returns: * 0 on error * 1 if return value should be the point at infinity * 2 otherwise */ -static int Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, +static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx) { BIGNUM *t3, *t4, *t5; @@ -169,8 +160,8 @@ static int Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM * if (BN_is_zero(z1)) { - if (!BN_zero(x2)) return 0; - if (!BN_zero(z2)) return 0; + BN_zero(x2); + BN_zero(z2); return 1; } @@ -220,22 +211,27 @@ static int Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM * return ret; } -/* Computes scalar*point and stores the result in r. + +/*- + * Computes scalar*point and stores the result in r. * point can not equal r. - * Uses algorithm 2P of - * Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over - * GF(2^m) without precomputation". + * Uses a modified algorithm 2P of + * Lopez, J. and Dahab, R. "Fast multiplication on elliptic curves over + * GF(2^m) without precomputation" (CHES '99, LNCS 1717). + * + * To protect against side-channel attack the function uses constant time swap, + * avoiding conditional branches. */ -static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, +static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx) { BIGNUM *x1, *x2, *z1, *z2; - int ret = 0, i, j; - BN_ULONG mask; + int ret = 0, i; + BN_ULONG mask,word; if (r == point) { - ECerr(EC_F_EC_POINT_MUL, EC_R_INVALID_ARGUMENT); + ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT); return 0; } @@ -258,6 +254,11 @@ static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scal x2 = &r->X; z2 = &r->Y; + bn_wexpand(x1, group->field.top); + bn_wexpand(z1, group->field.top); + bn_wexpand(x2, group->field.top); + bn_wexpand(z2, group->field.top); + if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */ if (!BN_one(z1)) goto err; /* z1 = 1 */ if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */ @@ -265,39 +266,36 @@ static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scal if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */ /* find top most bit and go one past it */ - i = scalar->top - 1; j = BN_BITS2 - 1; + i = scalar->top - 1; mask = BN_TBIT; - while (!(scalar->d[i] & mask)) { mask >>= 1; j--; } - mask >>= 1; j--; + word = scalar->d[i]; + while (!(word & mask)) mask >>= 1; + mask >>= 1; /* if top most bit was at word break, go to next word */ if (!mask) { - i--; j = BN_BITS2 - 1; + i--; mask = BN_TBIT; } for (; i >= 0; i--) { - for (; j >= 0; j--) + word = scalar->d[i]; + while (mask) { - if (scalar->d[i] & mask) - { - if (!Madd(group, &point->X, x1, z1, x2, z2, ctx)) goto err; - if (!Mdouble(group, x2, z2, ctx)) goto err; - } - else - { - if (!Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; - if (!Mdouble(group, x1, z1, ctx)) goto err; - } + BN_consttime_swap(word & mask, x1, x2, group->field.top); + BN_consttime_swap(word & mask, z1, z2, group->field.top); + if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err; + if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err; + BN_consttime_swap(word & mask, x1, x2, group->field.top); + BN_consttime_swap(word & mask, z1, z2, group->field.top); mask >>= 1; } - j = BN_BITS2 - 1; mask = BN_TBIT; } /* convert out of "projective" coordinates */ - i = Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); + i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx); if (i == 0) goto err; else if (i == 1) { @@ -310,8 +308,8 @@ static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scal } /* GF(2^m) field elements should always have BIGNUM::neg = 0 */ - r->X.neg = 0; - r->Y.neg = 0; + BN_set_negative(&r->X, 0); + BN_set_negative(&r->Y, 0); ret = 1; @@ -321,16 +319,19 @@ static int point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scal } -/* Computes the sum +/*- + * Computes the sum * scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1] * gracefully ignoring NULL scalar values. */ -int ec_GF2m_mont_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, +int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) { BN_CTX *new_ctx = NULL; - int ret = 0, i; + int ret = 0; + size_t i; EC_POINT *p=NULL; + EC_POINT *acc = NULL; if (ctx == NULL) { @@ -340,48 +341,60 @@ int ec_GF2m_mont_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, } /* This implementation is more efficient than the wNAF implementation for 2 - * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points. + * or fewer points. Use the ec_wNAF_mul implementation for 3 or more points, + * or if we can perform a fast multiplication based on precomputation. */ - if ((scalar && (num > 1)) || (num > 2)) + if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group))) { ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx); goto err; } if ((p = EC_POINT_new(group)) == NULL) goto err; + if ((acc = EC_POINT_new(group)) == NULL) goto err; - if (!EC_POINT_set_to_infinity(group, r)) goto err; + if (!EC_POINT_set_to_infinity(group, acc)) goto err; if (scalar) { - if (!point_multiply(group, p, scalar, group->generator, ctx)) goto err; - if (scalar->neg) if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, r, r, p, ctx)) goto err; + if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err; + if (BN_is_negative(scalar)) + if (!group->meth->invert(group, p, ctx)) goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) goto err; } for (i = 0; i < num; i++) { - if (!point_multiply(group, p, scalars[i], points[i], ctx)) goto err; - if (scalars[i]->neg) if (!group->meth->invert(group, p, ctx)) goto err; - if (!group->meth->add(group, r, r, p, ctx)) goto err; + if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err; + if (BN_is_negative(scalars[i])) + if (!group->meth->invert(group, p, ctx)) goto err; + if (!group->meth->add(group, acc, acc, p, ctx)) goto err; } + if (!EC_POINT_copy(r, acc)) goto err; + ret = 1; err: if (p) EC_POINT_free(p); + if (acc) EC_POINT_free(acc); if (new_ctx != NULL) BN_CTX_free(new_ctx); return ret; } -/* Precomputation for point multiplication. */ -int ec_GF2m_mont_precompute_mult(EC_GROUP *group, BN_CTX *ctx) +/* Precomputation for point multiplication: fall back to wNAF methods + * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */ + +int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx) { - /* There is no precomputation to do for Montgomery scalar multiplication but - * since this implementation falls back to the wNAF multiplication for more than - * two points, call the wNAF implementation's precompute. - */ return ec_wNAF_precompute_mult(group, ctx); - } + } + +int ec_GF2m_have_precompute_mult(const EC_GROUP *group) + { + return ec_wNAF_have_precompute_mult(group); + } + +#endif