/* crypto/bn/bn_nist.c */ /* * Written by Nils Larsch for the OpenSSL project */ /* ==================================================================== * Copyright (c) 1998-2005 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 * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include "bn_lcl.h" #include "cryptlib.h" #define BN_NIST_192_TOP (192+BN_BITS2-1)/BN_BITS2 #define BN_NIST_224_TOP (224+BN_BITS2-1)/BN_BITS2 #define BN_NIST_256_TOP (256+BN_BITS2-1)/BN_BITS2 #define BN_NIST_384_TOP (384+BN_BITS2-1)/BN_BITS2 #define BN_NIST_521_TOP (521+BN_BITS2-1)/BN_BITS2 /* pre-computed tables are "carry-less" values of modulus*(i+1) */ #if BN_BITS2 == 64 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = { {0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL}, {0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL}, {0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFCULL, 0xFFFFFFFFFFFFFFFFULL} }; static const BN_ULONG _nist_p_192_sqr[] = { 0x0000000000000001ULL, 0x0000000000000002ULL, 0x0000000000000001ULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL }; static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = { {0x0000000000000001ULL, 0xFFFFFFFF00000000ULL, 0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL}, {0x0000000000000002ULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFFULL} /* this one is * "carry-full" */ }; static const BN_ULONG _nist_p_224_sqr[] = { 0x0000000000000001ULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFFULL, 0x0000000200000000ULL, 0x0000000000000000ULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL }; static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = { {0xFFFFFFFFFFFFFFFFULL, 0x00000000FFFFFFFFULL, 0x0000000000000000ULL, 0xFFFFFFFF00000001ULL}, {0xFFFFFFFFFFFFFFFEULL, 0x00000001FFFFFFFFULL, 0x0000000000000000ULL, 0xFFFFFFFE00000002ULL}, {0xFFFFFFFFFFFFFFFDULL, 0x00000002FFFFFFFFULL, 0x0000000000000000ULL, 0xFFFFFFFD00000003ULL}, {0xFFFFFFFFFFFFFFFCULL, 0x00000003FFFFFFFFULL, 0x0000000000000000ULL, 0xFFFFFFFC00000004ULL}, {0xFFFFFFFFFFFFFFFBULL, 0x00000004FFFFFFFFULL, 0x0000000000000000ULL, 0xFFFFFFFB00000005ULL}, }; static const BN_ULONG _nist_p_256_sqr[] = { 0x0000000000000001ULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFFULL, 0x00000001FFFFFFFEULL, 0x00000001FFFFFFFEULL, 0x00000001FFFFFFFEULL, 0xFFFFFFFE00000001ULL, 0xFFFFFFFE00000002ULL }; static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = { {0x00000000FFFFFFFFULL, 0xFFFFFFFF00000000ULL, 0xFFFFFFFFFFFFFFFEULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL}, {0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL}, {0x00000002FFFFFFFDULL, 0xFFFFFFFD00000000ULL, 0xFFFFFFFFFFFFFFFCULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL}, {0x00000003FFFFFFFCULL, 0xFFFFFFFC00000000ULL, 0xFFFFFFFFFFFFFFFBULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL}, {0x00000004FFFFFFFBULL, 0xFFFFFFFB00000000ULL, 0xFFFFFFFFFFFFFFFAULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL}, }; static const BN_ULONG _nist_p_384_sqr[] = { 0xFFFFFFFE00000001ULL, 0x0000000200000000ULL, 0xFFFFFFFE00000000ULL, 0x0000000200000000ULL, 0x0000000000000001ULL, 0x0000000000000000ULL, 0x00000001FFFFFFFEULL, 0xFFFFFFFE00000000ULL, 0xFFFFFFFFFFFFFFFDULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL }; static const BN_ULONG _nist_p_521[] = { 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0x00000000000001FFULL }; static const BN_ULONG _nist_p_521_sqr[] = { 0x0000000000000001ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0x0000000000000000ULL, 0xFFFFFFFFFFFFFC00ULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0xFFFFFFFFFFFFFFFFULL, 0x000000000003FFFFULL }; #elif BN_BITS2 == 32 static const BN_ULONG _nist_p_192[][BN_NIST_192_TOP] = { {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} }; static const BN_ULONG _nist_p_192_sqr[] = { 0x00000001, 0x00000000, 0x00000002, 0x00000000, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF }; static const BN_ULONG _nist_p_224[][BN_NIST_224_TOP] = { {0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF} }; static const BN_ULONG _nist_p_224_sqr[] = { 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000002, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF }; static const BN_ULONG _nist_p_256[][BN_NIST_256_TOP] = { {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xFFFFFFFF}, {0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000001, 0x00000000, 0x00000000, 0x00000002, 0xFFFFFFFE}, {0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000002, 0x00000000, 0x00000000, 0x00000003, 0xFFFFFFFD}, {0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000003, 0x00000000, 0x00000000, 0x00000004, 0xFFFFFFFC}, {0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000004, 0x00000000, 0x00000000, 0x00000005, 0xFFFFFFFB}, }; static const BN_ULONG _nist_p_256_sqr[] = { 0x00000001, 0x00000000, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0xFFFFFFFE, 0x00000001, 0x00000001, 0xFFFFFFFE, 0x00000002, 0xFFFFFFFE }; static const BN_ULONG _nist_p_384[][BN_NIST_384_TOP] = { {0xFFFFFFFF, 0x00000000, 0x00000000, 0xFFFFFFFF, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFD, 0x00000002, 0x00000000, 0xFFFFFFFD, 0xFFFFFFFC, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFC, 0x00000003, 0x00000000, 0xFFFFFFFC, 0xFFFFFFFB, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, {0xFFFFFFFB, 0x00000004, 0x00000000, 0xFFFFFFFB, 0xFFFFFFFA, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF}, }; static const BN_ULONG _nist_p_384_sqr[] = { 0x00000001, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000000, 0xFFFFFFFE, 0x00000000, 0x00000002, 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFFFE, 0x00000001, 0x00000000, 0xFFFFFFFE, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF }; static const BN_ULONG _nist_p_521[] = { 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x000001FF }; static const BN_ULONG _nist_p_521_sqr[] = { 0x00000001, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0xFFFFFC00, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x0003FFFF }; #else # error "unsupported BN_BITS2" #endif static const BIGNUM _bignum_nist_p_192 = { (BN_ULONG *)_nist_p_192[0], BN_NIST_192_TOP, BN_NIST_192_TOP, 0, BN_FLG_STATIC_DATA }; static const BIGNUM _bignum_nist_p_224 = { (BN_ULONG *)_nist_p_224[0], BN_NIST_224_TOP, BN_NIST_224_TOP, 0, BN_FLG_STATIC_DATA }; static const BIGNUM _bignum_nist_p_256 = { (BN_ULONG *)_nist_p_256[0], BN_NIST_256_TOP, BN_NIST_256_TOP, 0, BN_FLG_STATIC_DATA }; static const BIGNUM _bignum_nist_p_384 = { (BN_ULONG *)_nist_p_384[0], BN_NIST_384_TOP, BN_NIST_384_TOP, 0, BN_FLG_STATIC_DATA }; static const BIGNUM _bignum_nist_p_521 = { (BN_ULONG *)_nist_p_521, BN_NIST_521_TOP, BN_NIST_521_TOP, 0, BN_FLG_STATIC_DATA }; const BIGNUM *BN_get0_nist_prime_192(void) { return &_bignum_nist_p_192; } const BIGNUM *BN_get0_nist_prime_224(void) { return &_bignum_nist_p_224; } const BIGNUM *BN_get0_nist_prime_256(void) { return &_bignum_nist_p_256; } const BIGNUM *BN_get0_nist_prime_384(void) { return &_bignum_nist_p_384; } const BIGNUM *BN_get0_nist_prime_521(void) { return &_bignum_nist_p_521; } static void nist_cp_bn_0(BN_ULONG *buf, BN_ULONG *a, int top, int max) { int i; BN_ULONG *_tmp1 = (buf), *_tmp2 = (a); #ifdef BN_DEBUG OPENSSL_assert(top <= max); #endif for (i = (top); i != 0; i--) *_tmp1++ = *_tmp2++; for (i = (max) - (top); i != 0; i--) *_tmp1++ = (BN_ULONG)0; } static void nist_cp_bn(BN_ULONG *buf, BN_ULONG *a, int top) { int i; BN_ULONG *_tmp1 = (buf), *_tmp2 = (a); for (i = (top); i != 0; i--) *_tmp1++ = *_tmp2++; } #if BN_BITS2 == 64 # define bn_cp_64(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0; # define bn_64_set_0(to, n) (to)[n] = (BN_ULONG)0; /* * two following macros are implemented under assumption that they * are called in a sequence with *ascending* n, i.e. as they are... */ # define bn_cp_32_naked(to, n, from, m) (((n)&1)?(to[(n)/2]|=((m)&1)?(from[(m)/2]&BN_MASK2h):(from[(m)/2]<<32))\ :(to[(n)/2] =((m)&1)?(from[(m)/2]>>32):(from[(m)/2]&BN_MASK2l))) # define bn_32_set_0(to, n) (((n)&1)?(to[(n)/2]&=BN_MASK2l):(to[(n)/2]=0)); # define bn_cp_32(to,n,from,m) ((m)>=0)?bn_cp_32_naked(to,n,from,m):bn_32_set_0(to,n) #else # define bn_cp_64(to, n, from, m) \ { \ bn_cp_32(to, (n)*2, from, (m)*2); \ bn_cp_32(to, (n)*2+1, from, (m)*2+1); \ } # define bn_64_set_0(to, n) \ { \ bn_32_set_0(to, (n)*2); \ bn_32_set_0(to, (n)*2+1); \ } # if BN_BITS2 == 32 # define bn_cp_32(to, n, from, m) (to)[n] = (m>=0)?((from)[m]):0; # define bn_32_set_0(to, n) (to)[n] = (BN_ULONG)0; # endif #endif /* BN_BITS2 != 64 */ #define nist_set_192(to, from, a1, a2, a3) \ { \ bn_cp_64(to, 0, from, (a3) - 3) \ bn_cp_64(to, 1, from, (a2) - 3) \ bn_cp_64(to, 2, from, (a1) - 3) \ } int BN_nist_mod_192(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx) { int top = a->top, i; int carry; register BN_ULONG *r_d, *a_d = a->d; BN_ULONG t_d[BN_NIST_192_TOP], buf[BN_NIST_192_TOP], c_d[BN_NIST_192_TOP], *res; PTR_SIZE_INT mask; static const BIGNUM _bignum_nist_p_192_sqr = { (BN_ULONG *)_nist_p_192_sqr, sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]), sizeof(_nist_p_192_sqr) / sizeof(_nist_p_192_sqr[0]), 0, BN_FLG_STATIC_DATA }; field = &_bignum_nist_p_192; /* just to make sure */ if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_192_sqr) >= 0) return BN_nnmod(r, a, field, ctx); i = BN_ucmp(field, a); if (i == 0) { BN_zero(r); return 1; } else if (i > 0) return (r == a) ? 1 : (BN_copy(r, a) != NULL); if (r != a) { if (!bn_wexpand(r, BN_NIST_192_TOP)) return 0; r_d = r->d; nist_cp_bn(r_d, a_d, BN_NIST_192_TOP); } else r_d = a_d; nist_cp_bn_0(buf, a_d + BN_NIST_192_TOP, top - BN_NIST_192_TOP, BN_NIST_192_TOP); nist_set_192(t_d, buf, 0, 3, 3); carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP); nist_set_192(t_d, buf, 4, 4, 0); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP); nist_set_192(t_d, buf, 5, 5, 5) carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_192_TOP); if (carry > 0) carry = (int)bn_sub_words(r_d, r_d, _nist_p_192[carry - 1], BN_NIST_192_TOP); else carry = 1; /* * we need 'if (carry==0 || result>=modulus) result-=modulus;' * as comparison implies subtraction, we can write * 'tmp=result-modulus; if (!carry || !borrow) result=tmp;' * this is what happens below, but without explicit if:-) a. */ mask = 0 - (PTR_SIZE_INT) bn_sub_words(c_d, r_d, _nist_p_192[0], BN_NIST_192_TOP); mask &= 0 - (PTR_SIZE_INT) carry; res = (BN_ULONG *) (((PTR_SIZE_INT) c_d & ~mask) | ((PTR_SIZE_INT) r_d & mask)); nist_cp_bn(r_d, res, BN_NIST_192_TOP); r->top = BN_NIST_192_TOP; bn_correct_top(r); return 1; } typedef BN_ULONG (*bn_addsub_f) (BN_ULONG *, const BN_ULONG *, const BN_ULONG *, int); #define nist_set_224(to, from, a1, a2, a3, a4, a5, a6, a7) \ { \ bn_cp_32(to, 0, from, (a7) - 7) \ bn_cp_32(to, 1, from, (a6) - 7) \ bn_cp_32(to, 2, from, (a5) - 7) \ bn_cp_32(to, 3, from, (a4) - 7) \ bn_cp_32(to, 4, from, (a3) - 7) \ bn_cp_32(to, 5, from, (a2) - 7) \ bn_cp_32(to, 6, from, (a1) - 7) \ } int BN_nist_mod_224(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx) { int top = a->top, i; int carry; BN_ULONG *r_d, *a_d = a->d; BN_ULONG t_d[BN_NIST_224_TOP], buf[BN_NIST_224_TOP], c_d[BN_NIST_224_TOP], *res; PTR_SIZE_INT mask; union { bn_addsub_f f; PTR_SIZE_INT p; } u; static const BIGNUM _bignum_nist_p_224_sqr = { (BN_ULONG *)_nist_p_224_sqr, sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]), sizeof(_nist_p_224_sqr) / sizeof(_nist_p_224_sqr[0]), 0, BN_FLG_STATIC_DATA }; field = &_bignum_nist_p_224; /* just to make sure */ if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_224_sqr) >= 0) return BN_nnmod(r, a, field, ctx); i = BN_ucmp(field, a); if (i == 0) { BN_zero(r); return 1; } else if (i > 0) return (r == a) ? 1 : (BN_copy(r, a) != NULL); if (r != a) { if (!bn_wexpand(r, BN_NIST_224_TOP)) return 0; r_d = r->d; nist_cp_bn(r_d, a_d, BN_NIST_224_TOP); } else r_d = a_d; #if BN_BITS2==64 /* copy upper 256 bits of 448 bit number ... */ nist_cp_bn_0(t_d, a_d + (BN_NIST_224_TOP - 1), top - (BN_NIST_224_TOP - 1), BN_NIST_224_TOP); /* ... and right shift by 32 to obtain upper 224 bits */ nist_set_224(buf, t_d, 14, 13, 12, 11, 10, 9, 8); /* truncate lower part to 224 bits too */ r_d[BN_NIST_224_TOP - 1] &= BN_MASK2l; #else nist_cp_bn_0(buf, a_d + BN_NIST_224_TOP, top - BN_NIST_224_TOP, BN_NIST_224_TOP); #endif nist_set_224(t_d, buf, 10, 9, 8, 7, 0, 0, 0); carry = (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP); nist_set_224(t_d, buf, 0, 13, 12, 11, 0, 0, 0); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_224_TOP); nist_set_224(t_d, buf, 13, 12, 11, 10, 9, 8, 7); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP); nist_set_224(t_d, buf, 0, 0, 0, 0, 13, 12, 11); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_224_TOP); #if BN_BITS2==64 carry = (int)(r_d[BN_NIST_224_TOP - 1] >> 32); #endif u.f = bn_sub_words; if (carry > 0) { carry = (int)bn_sub_words(r_d, r_d, _nist_p_224[carry - 1], BN_NIST_224_TOP); #if BN_BITS2==64 carry = (int)(~(r_d[BN_NIST_224_TOP - 1] >> 32)) & 1; #endif } else if (carry < 0) { /* * it's a bit more comlicated logic in this case. if bn_add_words * yields no carry, then result has to be adjusted by unconditionally * *adding* the modulus. but if it does, then result has to be * compared to the modulus and conditionally adjusted by * *subtracting* the latter. */ carry = (int)bn_add_words(r_d, r_d, _nist_p_224[-carry - 1], BN_NIST_224_TOP); mask = 0 - (PTR_SIZE_INT) carry; u.p = ((PTR_SIZE_INT) bn_sub_words & mask) | ((PTR_SIZE_INT) bn_add_words & ~mask); } else carry = 1; /* otherwise it's effectively same as in BN_nist_mod_192... */ mask = 0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_224[0], BN_NIST_224_TOP); mask &= 0 - (PTR_SIZE_INT) carry; res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) | ((PTR_SIZE_INT) r_d & mask)); nist_cp_bn(r_d, res, BN_NIST_224_TOP); r->top = BN_NIST_224_TOP; bn_correct_top(r); return 1; } #define nist_set_256(to, from, a1, a2, a3, a4, a5, a6, a7, a8) \ { \ bn_cp_32(to, 0, from, (a8) - 8) \ bn_cp_32(to, 1, from, (a7) - 8) \ bn_cp_32(to, 2, from, (a6) - 8) \ bn_cp_32(to, 3, from, (a5) - 8) \ bn_cp_32(to, 4, from, (a4) - 8) \ bn_cp_32(to, 5, from, (a3) - 8) \ bn_cp_32(to, 6, from, (a2) - 8) \ bn_cp_32(to, 7, from, (a1) - 8) \ } int BN_nist_mod_256(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx) { int i, top = a->top; int carry = 0; register BN_ULONG *a_d = a->d, *r_d; BN_ULONG t_d[BN_NIST_256_TOP], buf[BN_NIST_256_TOP], c_d[BN_NIST_256_TOP], *res; PTR_SIZE_INT mask; union { bn_addsub_f f; PTR_SIZE_INT p; } u; static const BIGNUM _bignum_nist_p_256_sqr = { (BN_ULONG *)_nist_p_256_sqr, sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]), sizeof(_nist_p_256_sqr) / sizeof(_nist_p_256_sqr[0]), 0, BN_FLG_STATIC_DATA }; field = &_bignum_nist_p_256; /* just to make sure */ if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_256_sqr) >= 0) return BN_nnmod(r, a, field, ctx); i = BN_ucmp(field, a); if (i == 0) { BN_zero(r); return 1; } else if (i > 0) return (r == a) ? 1 : (BN_copy(r, a) != NULL); if (r != a) { if (!bn_wexpand(r, BN_NIST_256_TOP)) return 0; r_d = r->d; nist_cp_bn(r_d, a_d, BN_NIST_256_TOP); } else r_d = a_d; nist_cp_bn_0(buf, a_d + BN_NIST_256_TOP, top - BN_NIST_256_TOP, BN_NIST_256_TOP); /* * S1 */ nist_set_256(t_d, buf, 15, 14, 13, 12, 11, 0, 0, 0); /* * S2 */ nist_set_256(c_d, buf, 0, 15, 14, 13, 12, 0, 0, 0); carry = (int)bn_add_words(t_d, t_d, c_d, BN_NIST_256_TOP); /* left shift */ { register BN_ULONG *ap, t, c; ap = t_d; c = 0; for (i = BN_NIST_256_TOP; i != 0; --i) { t = *ap; *(ap++) = ((t << 1) | c) & BN_MASK2; c = (t & BN_TBIT) ? 1 : 0; } carry <<= 1; carry |= c; } carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * S3 */ nist_set_256(t_d, buf, 15, 14, 0, 0, 0, 10, 9, 8); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * S4 */ nist_set_256(t_d, buf, 8, 13, 15, 14, 13, 11, 10, 9); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * D1 */ nist_set_256(t_d, buf, 10, 8, 0, 0, 0, 13, 12, 11); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * D2 */ nist_set_256(t_d, buf, 11, 9, 0, 0, 15, 14, 13, 12); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * D3 */ nist_set_256(t_d, buf, 12, 0, 10, 9, 8, 15, 14, 13); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* * D4 */ nist_set_256(t_d, buf, 13, 0, 11, 10, 9, 0, 15, 14); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_256_TOP); /* see BN_nist_mod_224 for explanation */ u.f = bn_sub_words; if (carry > 0) carry = (int)bn_sub_words(r_d, r_d, _nist_p_256[carry - 1], BN_NIST_256_TOP); else if (carry < 0) { carry = (int)bn_add_words(r_d, r_d, _nist_p_256[-carry - 1], BN_NIST_256_TOP); mask = 0 - (PTR_SIZE_INT) carry; u.p = ((PTR_SIZE_INT) bn_sub_words & mask) | ((PTR_SIZE_INT) bn_add_words & ~mask); } else carry = 1; mask = 0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_256[0], BN_NIST_256_TOP); mask &= 0 - (PTR_SIZE_INT) carry; res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) | ((PTR_SIZE_INT) r_d & mask)); nist_cp_bn(r_d, res, BN_NIST_256_TOP); r->top = BN_NIST_256_TOP; bn_correct_top(r); return 1; } #define nist_set_384(to,from,a1,a2,a3,a4,a5,a6,a7,a8,a9,a10,a11,a12) \ { \ bn_cp_32(to, 0, from, (a12) - 12) \ bn_cp_32(to, 1, from, (a11) - 12) \ bn_cp_32(to, 2, from, (a10) - 12) \ bn_cp_32(to, 3, from, (a9) - 12) \ bn_cp_32(to, 4, from, (a8) - 12) \ bn_cp_32(to, 5, from, (a7) - 12) \ bn_cp_32(to, 6, from, (a6) - 12) \ bn_cp_32(to, 7, from, (a5) - 12) \ bn_cp_32(to, 8, from, (a4) - 12) \ bn_cp_32(to, 9, from, (a3) - 12) \ bn_cp_32(to, 10, from, (a2) - 12) \ bn_cp_32(to, 11, from, (a1) - 12) \ } int BN_nist_mod_384(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx) { int i, top = a->top; int carry = 0; register BN_ULONG *r_d, *a_d = a->d; BN_ULONG t_d[BN_NIST_384_TOP], buf[BN_NIST_384_TOP], c_d[BN_NIST_384_TOP], *res; PTR_SIZE_INT mask; union { bn_addsub_f f; PTR_SIZE_INT p; } u; static const BIGNUM _bignum_nist_p_384_sqr = { (BN_ULONG *)_nist_p_384_sqr, sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]), sizeof(_nist_p_384_sqr) / sizeof(_nist_p_384_sqr[0]), 0, BN_FLG_STATIC_DATA }; field = &_bignum_nist_p_384; /* just to make sure */ if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_384_sqr) >= 0) return BN_nnmod(r, a, field, ctx); i = BN_ucmp(field, a); if (i == 0) { BN_zero(r); return 1; } else if (i > 0) return (r == a) ? 1 : (BN_copy(r, a) != NULL); if (r != a) { if (!bn_wexpand(r, BN_NIST_384_TOP)) return 0; r_d = r->d; nist_cp_bn(r_d, a_d, BN_NIST_384_TOP); } else r_d = a_d; nist_cp_bn_0(buf, a_d + BN_NIST_384_TOP, top - BN_NIST_384_TOP, BN_NIST_384_TOP); /* * S1 */ nist_set_256(t_d, buf, 0, 0, 0, 0, 0, 23 - 4, 22 - 4, 21 - 4); /* left shift */ { register BN_ULONG *ap, t, c; ap = t_d; c = 0; for (i = 3; i != 0; --i) { t = *ap; *(ap++) = ((t << 1) | c) & BN_MASK2; c = (t & BN_TBIT) ? 1 : 0; } *ap = c; } carry = (int)bn_add_words(r_d + (128 / BN_BITS2), r_d + (128 / BN_BITS2), t_d, BN_NIST_256_TOP); /* * S2 */ carry += (int)bn_add_words(r_d, r_d, buf, BN_NIST_384_TOP); /* * S3 */ nist_set_384(t_d, buf, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23, 22, 21); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * S4 */ nist_set_384(t_d, buf, 19, 18, 17, 16, 15, 14, 13, 12, 20, 0, 23, 0); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * S5 */ nist_set_384(t_d, buf, 0, 0, 0, 0, 23, 22, 21, 20, 0, 0, 0, 0); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * S6 */ nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 23, 22, 21, 0, 0, 20); carry += (int)bn_add_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * D1 */ nist_set_384(t_d, buf, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 23); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * D2 */ nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 22, 21, 20, 0); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* * D3 */ nist_set_384(t_d, buf, 0, 0, 0, 0, 0, 0, 0, 23, 23, 0, 0, 0); carry -= (int)bn_sub_words(r_d, r_d, t_d, BN_NIST_384_TOP); /* see BN_nist_mod_224 for explanation */ u.f = bn_sub_words; if (carry > 0) carry = (int)bn_sub_words(r_d, r_d, _nist_p_384[carry - 1], BN_NIST_384_TOP); else if (carry < 0) { carry = (int)bn_add_words(r_d, r_d, _nist_p_384[-carry - 1], BN_NIST_384_TOP); mask = 0 - (PTR_SIZE_INT) carry; u.p = ((PTR_SIZE_INT) bn_sub_words & mask) | ((PTR_SIZE_INT) bn_add_words & ~mask); } else carry = 1; mask = 0 - (PTR_SIZE_INT) (*u.f) (c_d, r_d, _nist_p_384[0], BN_NIST_384_TOP); mask &= 0 - (PTR_SIZE_INT) carry; res = (BN_ULONG *)(((PTR_SIZE_INT) c_d & ~mask) | ((PTR_SIZE_INT) r_d & mask)); nist_cp_bn(r_d, res, BN_NIST_384_TOP); r->top = BN_NIST_384_TOP; bn_correct_top(r); return 1; } #define BN_NIST_521_RSHIFT (521%BN_BITS2) #define BN_NIST_521_LSHIFT (BN_BITS2-BN_NIST_521_RSHIFT) #define BN_NIST_521_TOP_MASK ((BN_ULONG)BN_MASK2>>BN_NIST_521_LSHIFT) int BN_nist_mod_521(BIGNUM *r, const BIGNUM *a, const BIGNUM *field, BN_CTX *ctx) { int top = a->top, i; BN_ULONG *r_d, *a_d = a->d, t_d[BN_NIST_521_TOP], val, tmp, *res; PTR_SIZE_INT mask; static const BIGNUM _bignum_nist_p_521_sqr = { (BN_ULONG *)_nist_p_521_sqr, sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]), sizeof(_nist_p_521_sqr) / sizeof(_nist_p_521_sqr[0]), 0, BN_FLG_STATIC_DATA }; field = &_bignum_nist_p_521; /* just to make sure */ if (BN_is_negative(a) || BN_ucmp(a, &_bignum_nist_p_521_sqr) >= 0) return BN_nnmod(r, a, field, ctx); i = BN_ucmp(field, a); if (i == 0) { BN_zero(r); return 1; } else if (i > 0) return (r == a) ? 1 : (BN_copy(r, a) != NULL); if (r != a) { if (!bn_wexpand(r, BN_NIST_521_TOP)) return 0; r_d = r->d; nist_cp_bn(r_d, a_d, BN_NIST_521_TOP); } else r_d = a_d; /* upper 521 bits, copy ... */ nist_cp_bn_0(t_d, a_d + (BN_NIST_521_TOP - 1), top - (BN_NIST_521_TOP - 1), BN_NIST_521_TOP); /* ... and right shift */ for (val = t_d[0], i = 0; i < BN_NIST_521_TOP - 1; i++) { t_d[i] = (val >> BN_NIST_521_RSHIFT | (tmp = t_d[i + 1]) << BN_NIST_521_LSHIFT) & BN_MASK2; val = tmp; } t_d[i] = val >> BN_NIST_521_RSHIFT; /* lower 521 bits */ r_d[i] &= BN_NIST_521_TOP_MASK; bn_add_words(r_d, r_d, t_d, BN_NIST_521_TOP); mask = 0 - (PTR_SIZE_INT) bn_sub_words(t_d, r_d, _nist_p_521, BN_NIST_521_TOP); res = (BN_ULONG *)(((PTR_SIZE_INT) t_d & ~mask) | ((PTR_SIZE_INT) r_d & mask)); nist_cp_bn(r_d, res, BN_NIST_521_TOP); r->top = BN_NIST_521_TOP; bn_correct_top(r); return 1; }