Loading CHANGES +10 −3 Original line number Diff line number Diff line Loading @@ -12,6 +12,10 @@ *) applies to 0.9.6a/0.9.6b/0.9.6c and 0.9.7 +) applies to 0.9.7 only +) Use wNAFs in EC_POINTs_mul() for improved efficiency (about 10% better than before for single multiplications over P-192 or P-224). [Bodo Moeller] -) [In 0.9.6c-engine release:] Add support for Broadcom crypto accelerator cards, backported from 0.9.7. Loading Loading @@ -943,9 +947,12 @@ des-cbc 3624.96k 5258.21k 5530.91k 5624.30k 5628.26k don't write to the wrong index in ERR_set_error_data. [Bodo Moeller] +) Function EC_POINTs_mul for simultaneous scalar multiplication of an arbitrary number of elliptic curve points, optionally including the generator defined for the EC_GROUP. +) Function EC_POINTs_mul for multiple scalar multiplication of an arbitrary number of elliptic curve points \sum scalars[i]*points[i], optionally including the generator defined for the EC_GROUP: scalar*generator + \sum scalars[i]*points[i]. EC_POINT_mul is a simple wrapper function for the typical case that the point list has just one item (besides the optional generator). Loading crypto/ec/ec.h +1 −0 Original line number Diff line number Diff line Loading @@ -177,6 +177,7 @@ void ERR_load_EC_strings(void); /* Error codes for the EC functions. */ /* Function codes. */ #define EC_F_COMPUTE_WNAF 143 #define EC_F_EC_GFP_MONT_FIELD_DECODE 133 #define EC_F_EC_GFP_MONT_FIELD_ENCODE 134 #define EC_F_EC_GFP_MONT_FIELD_MUL 131 Loading crypto/ec/ec_err.c +1 −0 Original line number Diff line number Diff line Loading @@ -66,6 +66,7 @@ #ifndef OPENSSL_NO_ERR static ERR_STRING_DATA EC_str_functs[]= { {ERR_PACK(0,EC_F_COMPUTE_WNAF,0), "COMPUTE_WNAF"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_DECODE,0), "ec_GFp_mont_field_decode"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_ENCODE,0), "ec_GFp_mont_field_encode"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_MUL,0), "ec_GFp_mont_field_mul"}, Loading crypto/ec/ec_mult.c +361 −10 Original line number Diff line number Diff line Loading @@ -58,11 +58,369 @@ #include "ec_lcl.h" /* TODO: width-m NAFs */ /* TODO: optional precomputation of multiples of the generator */ #if 1 /* * wNAF-based interleaving multi-exponentation method */ /* Determine the width-(w+1) Non-Adjacent Form of 'scalar'. * This is an array r[] of values that are either zero or odd with an * absolute value less than 2^w satisfying * scalar = \sum_j r[j]*2^j * where at most one of any w+1 consecutive digits is non-zero. */ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx) { BIGNUM *c; int ok = 0; signed char *r = NULL; int sign = 1; int bit, next_bit, mask; size_t len, j; BN_CTX_start(ctx); c = BN_CTX_get(ctx); if (c == NULL) goto err; if (w <= 0 || w > 7) /* 'unsigned char' can represent integers with absolute values less than 2^7 */ { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } bit = 1 << w; /* at most 128 */ next_bit = bit << 1; /* at most 256 */ mask = next_bit - 1; /* at most 255 */ if (!BN_copy(c, scalar)) goto err; if (c->neg) { sign = -1; c->neg = 0; } len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */ r = OPENSSL_malloc(len); if (r == NULL) goto err; j = 0; while (!BN_is_zero(c)) { int u = 0; if (BN_is_odd(c)) { if (c->d == NULL || c->top == 0) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } u = c->d[0] & mask; if (u & bit) { u -= next_bit; /* u < 0 */ if (!BN_add_word(c, -u)) goto err; } else { /* u > 0 */ if (!BN_sub_word(c, u)) goto err; } if (u <= -bit || u >= bit || !(u & 1) || c->neg) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } } r[j++] = sign * u; if (BN_is_odd(c)) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } if (!BN_rshift1(c, c)) goto err; } if (j > len) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } len = j; ok = 1; err: BN_CTX_end(ctx); if (!ok) { OPENSSL_free(r); r = NULL; } if (ok) *ret_len = len; return r; } /* TODO: table should be optimised for the wNAF-based implementation */ #define EC_window_bits_for_scalar_size(b) \ ((b) >= 2000 ? 6 : \ (b) >= 800 ? 5 : \ (b) >= 300 ? 4 : \ (b) >= 70 ? 3 : \ (b) >= 20 ? 2 : \ 1) /* Compute * \sum scalars[i]*points[i], * also including * scalar*generator * in the addition if scalar != NULL */ int EC_POINTs_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; EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t totalnum; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; size_t *wsize = NULL; /* individual window sizes */ size_t *wNAF_len = NULL; size_t max_len = 0; signed char **wNAF = NULL; /* individual wNAFs */ size_t num_val; EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ int ret = 0; if (scalar != NULL) { generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); return 0; } } for (i = 0; i < num; i++) { if (group->meth != points[i]->meth) { ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } } totalnum = num + (scalar != NULL); wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); wNAF = OPENSSL_malloc(totalnum * sizeof wNAF[0] + 1); if (wNAF != NULL) { wNAF[0] = NULL; /* preliminary pivot */ } if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err; /* num_val := total number of points to precompute */ num_val = 0; for (i = 0; i < totalnum; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); num_val += 1u << (wsize[i] - 1); } /* all precomputed points go into a single array 'val', * 'val_sub[i]' is a pointer to the subarray for the i-th point */ val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); if (val == NULL) goto err; val[num_val] = NULL; /* pivot element */ val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); if (val_sub == NULL) goto err; /* allocate points for precomputation */ v = val; for (i = 0; i < totalnum; i++) { val_sub[i] = v; for (j = 0; j < (1u << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); if (*v == NULL) goto err; v++; } } if (!(v == val + num_val)) { ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR); goto err; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } tmp = EC_POINT_new(group); if (tmp == NULL) goto err; /* prepare precomputed values: * val_sub[i][0] := points[i] * val_sub[i][1] := 3 * points[i] * val_sub[i][2] := 5 * points[i] * ... */ for (i = 0; i < totalnum; i++) { if (i < num) { if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; } else { if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; } if (wsize[i] > 1) { if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; for (j = 1; j < (1u << (wsize[i] - 1)); j++) { if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; } } wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i], ctx); if (wNAF[i] == NULL) goto err; if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; } #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; #endif r_is_at_infinity = 1; for (k = max_len - 1; k >= 0; k--) { if (!r_is_at_infinity) { if (!EC_POINT_dbl(group, r, r, ctx)) goto err; } for (i = 0; i < totalnum; i++) { if (wNAF_len[i] > k) { int digit = wNAF[i][k]; int is_neg; if (digit) { is_neg = digit < 0; if (is_neg) digit = -digit; if (is_neg != r_is_inverted) { if (!r_is_at_infinity) { if (!EC_POINT_invert(group, r, ctx)) goto err; } r_is_inverted = !r_is_inverted; } /* digit > 0 */ if (r_is_at_infinity) { if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; r_is_at_infinity = 0; } else { if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; } } } } } if (r_is_at_infinity) { if (!EC_POINT_set_to_infinity(group, r)) goto err; } else { if (r_is_inverted) if (!EC_POINT_invert(group, r, ctx)) goto err; } ret = 1; err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (tmp != NULL) EC_POINT_free(tmp); if (wsize != NULL) OPENSSL_free(wsize); if (wNAF_len != NULL) OPENSSL_free(wNAF_len); if (wNAF != NULL) { signed char **w; for (w = wNAF; *w != NULL; w++) OPENSSL_free(*w); OPENSSL_free(wNAF); } if (val != NULL) { for (v = val; *v != NULL; v++) EC_POINT_clear_free(*v); OPENSSL_free(val); } if (val_sub != NULL) { OPENSSL_free(val_sub); } return ret; } #else /* * Basic interleaving multi-exponentation method */ #define EC_window_bits_for_scalar_size(b) \ ((b) >= 2000 ? 6 : \ (b) >= 800 ? 5 : \ Loading Loading @@ -143,14 +501,6 @@ * w = 1 if 19 >= b */ /* Compute * \sum scalars[i]*points[i], * also including * scalar*generator * in the addition if scalar != NULL */ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) { Loading Loading @@ -369,6 +719,7 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, } return ret; } #endif int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) Loading Loading
CHANGES +10 −3 Original line number Diff line number Diff line Loading @@ -12,6 +12,10 @@ *) applies to 0.9.6a/0.9.6b/0.9.6c and 0.9.7 +) applies to 0.9.7 only +) Use wNAFs in EC_POINTs_mul() for improved efficiency (about 10% better than before for single multiplications over P-192 or P-224). [Bodo Moeller] -) [In 0.9.6c-engine release:] Add support for Broadcom crypto accelerator cards, backported from 0.9.7. Loading Loading @@ -943,9 +947,12 @@ des-cbc 3624.96k 5258.21k 5530.91k 5624.30k 5628.26k don't write to the wrong index in ERR_set_error_data. [Bodo Moeller] +) Function EC_POINTs_mul for simultaneous scalar multiplication of an arbitrary number of elliptic curve points, optionally including the generator defined for the EC_GROUP. +) Function EC_POINTs_mul for multiple scalar multiplication of an arbitrary number of elliptic curve points \sum scalars[i]*points[i], optionally including the generator defined for the EC_GROUP: scalar*generator + \sum scalars[i]*points[i]. EC_POINT_mul is a simple wrapper function for the typical case that the point list has just one item (besides the optional generator). Loading
crypto/ec/ec.h +1 −0 Original line number Diff line number Diff line Loading @@ -177,6 +177,7 @@ void ERR_load_EC_strings(void); /* Error codes for the EC functions. */ /* Function codes. */ #define EC_F_COMPUTE_WNAF 143 #define EC_F_EC_GFP_MONT_FIELD_DECODE 133 #define EC_F_EC_GFP_MONT_FIELD_ENCODE 134 #define EC_F_EC_GFP_MONT_FIELD_MUL 131 Loading
crypto/ec/ec_err.c +1 −0 Original line number Diff line number Diff line Loading @@ -66,6 +66,7 @@ #ifndef OPENSSL_NO_ERR static ERR_STRING_DATA EC_str_functs[]= { {ERR_PACK(0,EC_F_COMPUTE_WNAF,0), "COMPUTE_WNAF"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_DECODE,0), "ec_GFp_mont_field_decode"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_ENCODE,0), "ec_GFp_mont_field_encode"}, {ERR_PACK(0,EC_F_EC_GFP_MONT_FIELD_MUL,0), "ec_GFp_mont_field_mul"}, Loading
crypto/ec/ec_mult.c +361 −10 Original line number Diff line number Diff line Loading @@ -58,11 +58,369 @@ #include "ec_lcl.h" /* TODO: width-m NAFs */ /* TODO: optional precomputation of multiples of the generator */ #if 1 /* * wNAF-based interleaving multi-exponentation method */ /* Determine the width-(w+1) Non-Adjacent Form of 'scalar'. * This is an array r[] of values that are either zero or odd with an * absolute value less than 2^w satisfying * scalar = \sum_j r[j]*2^j * where at most one of any w+1 consecutive digits is non-zero. */ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len, BN_CTX *ctx) { BIGNUM *c; int ok = 0; signed char *r = NULL; int sign = 1; int bit, next_bit, mask; size_t len, j; BN_CTX_start(ctx); c = BN_CTX_get(ctx); if (c == NULL) goto err; if (w <= 0 || w > 7) /* 'unsigned char' can represent integers with absolute values less than 2^7 */ { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } bit = 1 << w; /* at most 128 */ next_bit = bit << 1; /* at most 256 */ mask = next_bit - 1; /* at most 255 */ if (!BN_copy(c, scalar)) goto err; if (c->neg) { sign = -1; c->neg = 0; } len = BN_num_bits(c) + 1; /* wNAF may be one digit longer than binary representation */ r = OPENSSL_malloc(len); if (r == NULL) goto err; j = 0; while (!BN_is_zero(c)) { int u = 0; if (BN_is_odd(c)) { if (c->d == NULL || c->top == 0) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } u = c->d[0] & mask; if (u & bit) { u -= next_bit; /* u < 0 */ if (!BN_add_word(c, -u)) goto err; } else { /* u > 0 */ if (!BN_sub_word(c, u)) goto err; } if (u <= -bit || u >= bit || !(u & 1) || c->neg) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } } r[j++] = sign * u; if (BN_is_odd(c)) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } if (!BN_rshift1(c, c)) goto err; } if (j > len) { ECerr(EC_F_COMPUTE_WNAF, ERR_R_INTERNAL_ERROR); goto err; } len = j; ok = 1; err: BN_CTX_end(ctx); if (!ok) { OPENSSL_free(r); r = NULL; } if (ok) *ret_len = len; return r; } /* TODO: table should be optimised for the wNAF-based implementation */ #define EC_window_bits_for_scalar_size(b) \ ((b) >= 2000 ? 6 : \ (b) >= 800 ? 5 : \ (b) >= 300 ? 4 : \ (b) >= 70 ? 3 : \ (b) >= 20 ? 2 : \ 1) /* Compute * \sum scalars[i]*points[i], * also including * scalar*generator * in the addition if scalar != NULL */ int EC_POINTs_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; EC_POINT *generator = NULL; EC_POINT *tmp = NULL; size_t totalnum; size_t i, j; int k; int r_is_inverted = 0; int r_is_at_infinity = 1; size_t *wsize = NULL; /* individual window sizes */ size_t *wNAF_len = NULL; size_t max_len = 0; signed char **wNAF = NULL; /* individual wNAFs */ size_t num_val; EC_POINT **val = NULL; /* precomputation */ EC_POINT **v; EC_POINT ***val_sub = NULL; /* pointers to sub-arrays of 'val' */ int ret = 0; if (scalar != NULL) { generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_EC_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); return 0; } } for (i = 0; i < num; i++) { if (group->meth != points[i]->meth) { ECerr(EC_F_EC_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } } totalnum = num + (scalar != NULL); wsize = OPENSSL_malloc(totalnum * sizeof wsize[0]); wNAF_len = OPENSSL_malloc(totalnum * sizeof wNAF_len[0]); wNAF = OPENSSL_malloc(totalnum * sizeof wNAF[0] + 1); if (wNAF != NULL) { wNAF[0] = NULL; /* preliminary pivot */ } if (wsize == NULL || wNAF_len == NULL || wNAF == NULL) goto err; /* num_val := total number of points to precompute */ num_val = 0; for (i = 0; i < totalnum; i++) { size_t bits; bits = i < num ? BN_num_bits(scalars[i]) : BN_num_bits(scalar); wsize[i] = EC_window_bits_for_scalar_size(bits); num_val += 1u << (wsize[i] - 1); } /* all precomputed points go into a single array 'val', * 'val_sub[i]' is a pointer to the subarray for the i-th point */ val = OPENSSL_malloc((num_val + 1) * sizeof val[0]); if (val == NULL) goto err; val[num_val] = NULL; /* pivot element */ val_sub = OPENSSL_malloc(totalnum * sizeof val_sub[0]); if (val_sub == NULL) goto err; /* allocate points for precomputation */ v = val; for (i = 0; i < totalnum; i++) { val_sub[i] = v; for (j = 0; j < (1u << (wsize[i] - 1)); j++) { *v = EC_POINT_new(group); if (*v == NULL) goto err; v++; } } if (!(v == val + num_val)) { ECerr(EC_F_EC_POINTS_MUL, ERR_R_INTERNAL_ERROR); goto err; } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } tmp = EC_POINT_new(group); if (tmp == NULL) goto err; /* prepare precomputed values: * val_sub[i][0] := points[i] * val_sub[i][1] := 3 * points[i] * val_sub[i][2] := 5 * points[i] * ... */ for (i = 0; i < totalnum; i++) { if (i < num) { if (!EC_POINT_copy(val_sub[i][0], points[i])) goto err; } else { if (!EC_POINT_copy(val_sub[i][0], generator)) goto err; } if (wsize[i] > 1) { if (!EC_POINT_dbl(group, tmp, val_sub[i][0], ctx)) goto err; for (j = 1; j < (1u << (wsize[i] - 1)); j++) { if (!EC_POINT_add(group, val_sub[i][j], val_sub[i][j - 1], tmp, ctx)) goto err; } } wNAF[i + 1] = NULL; /* make sure we always have a pivot */ wNAF[i] = compute_wNAF((i < num ? scalars[i] : scalar), wsize[i], &wNAF_len[i], ctx); if (wNAF[i] == NULL) goto err; if (wNAF_len[i] > max_len) max_len = wNAF_len[i]; } #if 1 /* optional; EC_window_bits_for_scalar_size assumes we do this step */ if (!EC_POINTs_make_affine(group, num_val, val, ctx)) goto err; #endif r_is_at_infinity = 1; for (k = max_len - 1; k >= 0; k--) { if (!r_is_at_infinity) { if (!EC_POINT_dbl(group, r, r, ctx)) goto err; } for (i = 0; i < totalnum; i++) { if (wNAF_len[i] > k) { int digit = wNAF[i][k]; int is_neg; if (digit) { is_neg = digit < 0; if (is_neg) digit = -digit; if (is_neg != r_is_inverted) { if (!r_is_at_infinity) { if (!EC_POINT_invert(group, r, ctx)) goto err; } r_is_inverted = !r_is_inverted; } /* digit > 0 */ if (r_is_at_infinity) { if (!EC_POINT_copy(r, val_sub[i][digit >> 1])) goto err; r_is_at_infinity = 0; } else { if (!EC_POINT_add(group, r, r, val_sub[i][digit >> 1], ctx)) goto err; } } } } } if (r_is_at_infinity) { if (!EC_POINT_set_to_infinity(group, r)) goto err; } else { if (r_is_inverted) if (!EC_POINT_invert(group, r, ctx)) goto err; } ret = 1; err: if (new_ctx != NULL) BN_CTX_free(new_ctx); if (tmp != NULL) EC_POINT_free(tmp); if (wsize != NULL) OPENSSL_free(wsize); if (wNAF_len != NULL) OPENSSL_free(wNAF_len); if (wNAF != NULL) { signed char **w; for (w = wNAF; *w != NULL; w++) OPENSSL_free(*w); OPENSSL_free(wNAF); } if (val != NULL) { for (v = val; *v != NULL; v++) EC_POINT_clear_free(*v); OPENSSL_free(val); } if (val_sub != NULL) { OPENSSL_free(val_sub); } return ret; } #else /* * Basic interleaving multi-exponentation method */ #define EC_window_bits_for_scalar_size(b) \ ((b) >= 2000 ? 6 : \ (b) >= 800 ? 5 : \ Loading Loading @@ -143,14 +501,6 @@ * w = 1 if 19 >= b */ /* Compute * \sum scalars[i]*points[i], * also including * scalar*generator * in the addition if scalar != NULL */ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) { Loading Loading @@ -369,6 +719,7 @@ int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, } return ret; } #endif int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, const EC_POINT *point, const BIGNUM *p_scalar, BN_CTX *ctx) Loading
