From 3ba1f111470257c218d46f0aaa74cfba2c068c35 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Bodo=20M=C3=B6ller?= Date: Thu, 15 Nov 2001 22:32:11 +0000 Subject: [PATCH] Improve EC efficiency. --- CHANGES | 13 +- crypto/ec/ec.h | 1 + crypto/ec/ec_err.c | 1 + crypto/ec/ec_mult.c | 371 ++++++++++++++++++++++++++++++++++++++++++-- 4 files changed, 373 insertions(+), 13 deletions(-) diff --git a/CHANGES b/CHANGES index 26cf061a6d..f51029ef77 100644 --- a/CHANGES +++ b/CHANGES @@ -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. @@ -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). diff --git a/crypto/ec/ec.h b/crypto/ec/ec.h index 066c384798..a52d4edf14 100644 --- a/crypto/ec/ec.h +++ b/crypto/ec/ec.h @@ -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 diff --git a/crypto/ec/ec_err.c b/crypto/ec/ec_err.c index 49aff3139d..394cdc021f 100644 --- a/crypto/ec/ec_err.c +++ b/crypto/ec/ec_err.c @@ -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"}, diff --git a/crypto/ec/ec_mult.c b/crypto/ec/ec_mult.c index e075a1ee07..60429e0d1e 100644 --- a/crypto/ec/ec_mult.c +++ b/crypto/ec/ec_mult.c @@ -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 : \ @@ -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) { @@ -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) -- 2.34.1