ec/ecp_nistz256.c: improve ECDSA sign by 30-40%.

This is based on RT#3810, which added dedicated modular inversion.
ECDSA verify results improves as well, but not as much.
Reviewed-by: NRich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/5001)

crypto/ec/ec_err.c

@@ -48,6 +48,8 @@ static const ERR_STRING_DATA EC_str_functs[] = {
      "ECPKParameters_print_fp"},
     {ERR_PACK(ERR_LIB_EC, EC_F_ECP_NISTZ256_GET_AFFINE, 0),
      "ecp_nistz256_get_affine"},
+    {ERR_PACK(ERR_LIB_EC, EC_F_ECP_NISTZ256_INV_MOD_ORD, 0),
+     "ecp_nistz256_inv_mod_ord"},
     {ERR_PACK(ERR_LIB_EC, EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, 0),
      "ecp_nistz256_mult_precompute"},
     {ERR_PACK(ERR_LIB_EC, EC_F_ECP_NISTZ256_POINTS_MUL, 0),

crypto/ec/ec_lcl.h

@@ -155,6 +155,9 @@ struct ec_method_st {
     /* custom ECDH operation */
     int (*ecdh_compute_key)(unsigned char **pout, size_t *poutlen,
                             const EC_POINT *pub_key, const EC_KEY *ecdh);
+    /* Inverse modulo order */
+    int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r, BIGNUM *x,
+                                 BN_CTX *ctx);
 };
 
 /*
@@ -520,7 +523,6 @@ void ec_GFp_nistp_points_make_affine_internal(size_t num, void *point_array,
 void ec_GFp_nistp_recode_scalar_bits(unsigned char *sign,
                                      unsigned char *digit, unsigned char in);
 #endif
-int ec_precompute_mont_data(EC_GROUP *);
 int ec_group_simple_order_bits(const EC_GROUP *group);
 
 #ifdef ECP_NISTZ256_ASM
@@ -604,3 +606,6 @@ int X25519(uint8_t out_shared_key[32], const uint8_t private_key[32],
            const uint8_t peer_public_value[32]);
 void X25519_public_from_private(uint8_t out_public_value[32],
                                 const uint8_t private_key[32]);
+
+int EC_GROUP_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
+                            BIGNUM *x, BN_CTX *ctx);

crypto/ec/ec_lib.c

@@ -261,6 +261,8 @@ int EC_METHOD_get_field_type(const EC_METHOD *meth)
     return meth->field_type;
 }
 
+static int ec_precompute_mont_data(EC_GROUP *);
+
 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
                            const BIGNUM *order, const BIGNUM *cofactor)
 {
@@ -961,7 +963,7 @@ int EC_GROUP_have_precompute_mult(const EC_GROUP *group)
  * ec_precompute_mont_data sets |group->mont_data| from |group->order| and
  * returns one on success. On error it returns zero.
  */
-int ec_precompute_mont_data(EC_GROUP *group)
+static int ec_precompute_mont_data(EC_GROUP *group)
 {
     BN_CTX *ctx = BN_CTX_new();
     int ret = 0;
@@ -1006,3 +1008,12 @@ int ec_group_simple_order_bits(const EC_GROUP *group)
         return 0;
     return BN_num_bits(group->order);
 }
+
+int EC_GROUP_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
+                            BIGNUM *x, BN_CTX *ctx)
+{
+    if (group->meth->field_inverse_mod_ord != NULL)
+        return group->meth->field_inverse_mod_ord(group, res, x, ctx);
+    else
+        return 0;
+}

crypto/ec/ecdsa_ossl.c

@@ -153,30 +153,33 @@ static int ecdsa_sign_setup(EC_KEY *eckey, BN_CTX *ctx_in,
     }
     while (BN_is_zero(r));
 
-    /* compute the inverse of k */
-    if (EC_GROUP_get_mont_data(group) != NULL) {
-        /*
-         * We want inverse in constant time, therefore we utilize the fact
-         * order must be prime and use Fermat's Little Theorem instead.
-         */
-        if (!BN_set_word(X, 2)) {
-            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
-            goto err;
-        }
-        if (!BN_mod_sub(X, order, X, order, ctx)) {
-            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
-            goto err;
-        }
-        BN_set_flags(X, BN_FLG_CONSTTIME);
-        if (!BN_mod_exp_mont_consttime
-            (k, k, X, order, ctx, EC_GROUP_get_mont_data(group))) {
-            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
-            goto err;
-        }
-    } else {
-        if (!BN_mod_inverse(k, k, order, ctx)) {
-            ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
-            goto err;
+    /* Check if optimized inverse is implemented */
+    if (EC_GROUP_do_inverse_ord(group, k, k, ctx) == 0) {
+        /* compute the inverse of k */
+        if (group->mont_data != NULL) {
+            /*
+             * We want inverse in constant time, therefore we utilize the fact
+             * order must be prime and use Fermats Little Theorem instead.
+             */
+            if (!BN_set_word(X, 2)) {
+                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
+                goto err;
+            }
+            if (!BN_mod_sub(X, order, X, order, ctx)) {
+                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
+                goto err;
+            }
+            BN_set_flags(X, BN_FLG_CONSTTIME);
+            if (!BN_mod_exp_mont_consttime(k, k, X, order, ctx,
+                                           group->mont_data)) {
+                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
+                goto err;
+            }
+        } else {
+            if (!BN_mod_inverse(k, k, order, ctx)) {
+                ECerr(EC_F_ECDSA_SIGN_SETUP, ERR_R_BN_LIB);
+                goto err;
+            }
         }
     }
 
@@ -407,9 +410,12 @@ int ossl_ecdsa_verify_sig(const unsigned char *dgst, int dgst_len,
         goto err;
     }
     /* calculate tmp1 = inv(S) mod order */
-    if (!BN_mod_inverse(u2, sig->s, order, ctx)) {
-        ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
-        goto err;
+    /* Check if optimized inverse is implemented */
+    if (EC_GROUP_do_inverse_ord(group, u2, sig->s, ctx) == 0) {
+        if (!BN_mod_inverse(u2, sig->s, order, ctx)) {
+            ECerr(EC_F_OSSL_ECDSA_VERIFY_SIG, ERR_R_BN_LIB);
+            goto err;
+        }
     }
     /* digest -> m */
     i = BN_num_bits(order);

crypto/ec/ecp_nistz256.c

 /*
  * Copyright 2014-2017 The OpenSSL Project Authors. All Rights Reserved.
  * Copyright (c) 2014, Intel Corporation. All Rights Reserved.
+ * Copyright (c) 2015, CloudFlare, Inc.
  *
  * Licensed under the OpenSSL license (the "License").  You may not use
  * this file except in compliance with the License.  You can obtain a copy
  * in the file LICENSE in the source distribution or at
  * https://www.openssl.org/source/license.html
  *
- * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1)
+ * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3)
  * (1) Intel Corporation, Israel Development Center, Haifa, Israel
  * (2) University of Haifa, Israel
+ * (3) CloudFlare, Inc.
  *
  * Reference:
  * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with
@@ -908,7 +910,7 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
  */
 #if defined(ECP_NISTZ256_AVX2)
 # if !(defined(__x86_64) || defined(__x86_64__) || \
-       defined(_M_AMD64) || defined(_MX64)) || \
+       defined(_M_AMD64) || defined(_M_X64)) || \
      !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
 #  undef ECP_NISTZ256_AVX2
 # else
@@ -1495,6 +1497,117 @@ static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
     return HAVEPRECOMP(group, nistz256);
 }
 
+#if defined(__x86_64) || defined(__x86_64__) || \
+    defined(_M_AMD64) || defined(_M_X64) || \
+    defined(__powerpc64__) || defined(_ARCH_PP64)
+/*
+ * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
+ */
+void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
+                               const BN_ULONG a[P256_LIMBS],
+                               const BN_ULONG b[P256_LIMBS]);
+void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
+                               const BN_ULONG a[P256_LIMBS],
+                               int rep);
+
+static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
+                                    BIGNUM *x, BN_CTX *ctx)
+{
+    /* RR = 2^512 mod ord(p256) */
+    static const BN_ULONG RR[P256_LIMBS]  = { TOBN(0x83244c95,0xbe79eea2),
+                                              TOBN(0x4699799c,0x49bd6fa6),
+                                              TOBN(0x2845b239,0x2b6bec59),
+                                              TOBN(0x66e12d94,0xf3d95620) };
+    /* The constant 1 (unlike ONE that is one in Montgomery representation) */
+    static const BN_ULONG one[P256_LIMBS] = { TOBN(0,1),TOBN(0,0),
+                                              TOBN(0,0),TOBN(0,0) };
+    /* expLo - the low 128bit of the exponent we use (ord(p256) - 2),
+     * split into 4bit windows */
+    static const unsigned char expLo[32]  = { 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,
+                                              0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
+                                              0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,
+                                              0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf };
+    /*
+     * We don't use entry 0 in the table, so we omit it and address
+     * with -1 offset.
+     */
+    BN_ULONG table[15][P256_LIMBS];
+    BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
+    int i, ret = 0;
+
+    /*
+     * Catch allocation failure early.
+     */
+    if (bn_wexpand(r, P256_LIMBS) == NULL) {
+        ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
+        goto err;
+    }
+
+    if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
+        BIGNUM *tmp;
+
+        if ((tmp = BN_CTX_get(ctx)) == NULL
+            || !BN_nnmod(tmp, x, group->order, ctx)) {
+            ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
+            goto err;
+        }
+        x = tmp;
+    }
+
+    if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
+        ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE);
+        goto err;
+    }
+
+    ecp_nistz256_ord_mul_mont(table[0], t, RR);
+    for (i = 2; i < 16; i += 2) {
+        ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
+        ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
+    }
+
+    /*
+     * The top 128bit of the exponent are highly redudndant, so we
+     * perform an optimized flow
+     */
+    ecp_nistz256_ord_sqr_mont(t, table[15-1], 4);   /* f0 */
+    ecp_nistz256_ord_mul_mont(t, t, table[15-1]);   /* ff */
+
+    ecp_nistz256_ord_sqr_mont(out, t, 8);           /* ff00 */
+    ecp_nistz256_ord_mul_mont(out, out, t);         /* ffff */
+
+    ecp_nistz256_ord_sqr_mont(t, out, 16);          /* ffff0000 */
+    ecp_nistz256_ord_mul_mont(t, t, out);           /* ffffffff */
+
+    ecp_nistz256_ord_sqr_mont(out, t, 64);          /* ffffffff0000000000000000 */
+    ecp_nistz256_ord_mul_mont(out, out, t);         /* ffffffff00000000ffffffff */
+
+    ecp_nistz256_ord_sqr_mont(out, out, 32);        /* ffffffff00000000ffffffff00000000 */
+    ecp_nistz256_ord_mul_mont(out, out, t);         /* ffffffff00000000ffffffffffffffff */
+
+    /*
+     * The bottom 128 bit of the exponent are easier done with a table
+     */
+    for(i = 0; i < 32; i++) {
+        ecp_nistz256_ord_sqr_mont(out, out, 4);
+        /* The exponent is public, no need in constant-time access */
+        ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
+    }
+    ecp_nistz256_ord_mul_mont(out, out, one);
+
+    /*
+     * Can't fail, but check return code to be consistent anyway.
+     */
+    if (!bn_set_words(r, out, P256_LIMBS))
+        goto err;
+
+    ret = 1;
+err:
+    return ret;
+}
+#else
+# define ecp_nistz256_inv_mod_ord NULL
+#endif
+
 const EC_METHOD *EC_GFp_nistz256_method(void)
 {
     static const EC_METHOD ret = {
@@ -1544,7 +1657,8 @@ const EC_METHOD *EC_GFp_nistz256_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        ecp_nistz256_inv_mod_ord                    /* can be #defined-ed NULL */
     };
 
     return &ret;

crypto/err/openssl.txt

@@ -458,6 +458,7 @@ EC_F_ECPARAMETERS_PRINT_FP:148:ECParameters_print_fp
 EC_F_ECPKPARAMETERS_PRINT:149:ECPKParameters_print
 EC_F_ECPKPARAMETERS_PRINT_FP:150:ECPKParameters_print_fp
 EC_F_ECP_NISTZ256_GET_AFFINE:240:ecp_nistz256_get_affine
+EC_F_ECP_NISTZ256_INV_MOD_ORD:275:ecp_nistz256_inv_mod_ord
 EC_F_ECP_NISTZ256_MULT_PRECOMPUTE:243:ecp_nistz256_mult_precompute
 EC_F_ECP_NISTZ256_POINTS_MUL:241:ecp_nistz256_points_mul
 EC_F_ECP_NISTZ256_PRE_COMP_NEW:244:ecp_nistz256_pre_comp_new

include/openssl/ecerr.h

@@ -50,6 +50,7 @@ int ERR_load_EC_strings(void);
 # define EC_F_ECPKPARAMETERS_PRINT                        149
 # define EC_F_ECPKPARAMETERS_PRINT_FP                     150
 # define EC_F_ECP_NISTZ256_GET_AFFINE                     240
+# define EC_F_ECP_NISTZ256_INV_MOD_ORD                    275
 # define EC_F_ECP_NISTZ256_MULT_PRECOMPUTE                243
 # define EC_F_ECP_NISTZ256_POINTS_MUL                     241
 # define EC_F_ECP_NISTZ256_PRE_COMP_NEW                   244