| /* |
| * Elliptic curves over GF(p): curve-specific data and functions |
| * |
| * Copyright (C) 2006-2013, Brainspark B.V. |
| * |
| * This file is part of PolarSSL (http://www.polarssl.org) |
| * Lead Maintainer: Paul Bakker <polarssl_maintainer at polarssl.org> |
| * |
| * All rights reserved. |
| * |
| * This program is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or |
| * (at your option) any later version. |
| * |
| * This program is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| * GNU General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License along |
| * with this program; if not, write to the Free Software Foundation, Inc., |
| * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| */ |
| |
| #include "polarssl/config.h" |
| |
| #if defined(POLARSSL_ECP_C) |
| |
| #include "polarssl/ecp.h" |
| |
| /* |
| * Domain parameters for secp192r1 |
| */ |
| #define SECP192R1_P \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF" |
| #define SECP192R1_B \ |
| "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1" |
| #define SECP192R1_GX \ |
| "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012" |
| #define SECP192R1_GY \ |
| "07192B95FFC8DA78631011ED6B24CDD573F977A11E794811" |
| #define SECP192R1_N \ |
| "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831" |
| |
| /* |
| * Domain parameters for secp224r1 |
| */ |
| #define SECP224R1_P \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001" |
| #define SECP224R1_B \ |
| "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4" |
| #define SECP224R1_GX \ |
| "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21" |
| #define SECP224R1_GY \ |
| "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34" |
| #define SECP224R1_N \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D" |
| |
| /* |
| * Domain parameters for secp256r1 |
| */ |
| #define SECP256R1_P \ |
| "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF" |
| #define SECP256R1_B \ |
| "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B" |
| #define SECP256R1_GX \ |
| "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296" |
| #define SECP256R1_GY \ |
| "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5" |
| #define SECP256R1_N \ |
| "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551" |
| |
| /* |
| * Domain parameters for secp384r1 |
| */ |
| #define SECP384R1_P \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \ |
| "FFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF" |
| #define SECP384R1_B \ |
| "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE814112" \ |
| "0314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF" |
| #define SECP384R1_GX \ |
| "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B98" \ |
| "59F741E082542A385502F25DBF55296C3A545E3872760AB7" |
| #define SECP384R1_GY \ |
| "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147C" \ |
| "E9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F" |
| #define SECP384R1_N \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \ |
| "C7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973" |
| |
| /* |
| * Domain parameters for secp521r1 |
| */ |
| #define SECP521R1_P \ |
| "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \ |
| "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" |
| #define SECP521R1_B \ |
| "00000051953EB9618E1C9A1F929A21A0B68540EEA2DA725B" \ |
| "99B315F3B8B489918EF109E156193951EC7E937B1652C0BD" \ |
| "3BB1BF073573DF883D2C34F1EF451FD46B503F00" |
| #define SECP521R1_GX \ |
| "000000C6858E06B70404E9CD9E3ECB662395B4429C648139" \ |
| "053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127" \ |
| "A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66" |
| #define SECP521R1_GY \ |
| "0000011839296A789A3BC0045C8A5FB42C7D1BD998F54449" \ |
| "579B446817AFBD17273E662C97EE72995EF42640C550B901" \ |
| "3FAD0761353C7086A272C24088BE94769FD16650" |
| #define SECP521R1_N \ |
| "000001FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF" \ |
| "FFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148" \ |
| "F709A5D03BB5C9B8899C47AEBB6FB71E91386409" |
| |
| /* |
| * Domain parameters for brainpoolP256r1 (RFC 5639 3.4) |
| */ |
| #define BP256R1_P \ |
| "A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377" |
| #define BP256R1_A \ |
| "7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9" |
| #define BP256R1_B \ |
| "26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6" |
| #define BP256R1_GX \ |
| "8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262" |
| #define BP256R1_GY \ |
| "547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997" |
| #define BP256R1_N \ |
| "A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7" |
| |
| /* |
| * Domain parameters for brainpoolP384r1 (RFC 5639 3.6) |
| */ |
| #define BP384R1_P \ |
| "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB711" \ |
| "23ACD3A729901D1A71874700133107EC53" |
| #define BP384R1_A \ |
| "7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F9" \ |
| "0F8AA5814A503AD4EB04A8C7DD22CE2826" |
| #define BP384R1_B \ |
| "04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62" \ |
| "D57CB4390295DBC9943AB78696FA504C11" |
| #define BP384R1_GX \ |
| "1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10" \ |
| "E8E826E03436D646AAEF87B2E247D4AF1E" |
| #define BP384R1_GY \ |
| "8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129" \ |
| "280E4646217791811142820341263C5315" |
| #define BP384R1_N \ |
| "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425" \ |
| "A7CF3AB6AF6B7FC3103B883202E9046565" |
| |
| /* |
| * Domain parameters for brainpoolP512r1 (RFC 5639 3.7) |
| */ |
| #define BP512R1_P \ |
| "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \ |
| "717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3" |
| #define BP512R1_A \ |
| "7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863" \ |
| "BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA" |
| #define BP512R1_B \ |
| "3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117" \ |
| "A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723" |
| #define BP512R1_GX \ |
| "81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D009" \ |
| "8EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822" |
| #define BP512R1_GY \ |
| "7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F81" \ |
| "11B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892" |
| #define BP512R1_N \ |
| "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308" \ |
| "70553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069" |
| |
| /* |
| * Import an ECP group from ASCII strings, general case (A used) |
| */ |
| static int ecp_group_read_string_gen( ecp_group *grp, int radix, |
| const char *p, const char *a, const char *b, |
| const char *gx, const char *gy, const char *n) |
| { |
| int ret; |
| |
| MPI_CHK( mpi_read_string( &grp->P, radix, p ) ); |
| MPI_CHK( mpi_read_string( &grp->A, radix, a ) ); |
| MPI_CHK( mpi_read_string( &grp->B, radix, b ) ); |
| MPI_CHK( ecp_point_read_string( &grp->G, radix, gx, gy ) ); |
| MPI_CHK( mpi_read_string( &grp->N, radix, n ) ); |
| |
| grp->pbits = mpi_msb( &grp->P ); |
| grp->nbits = mpi_msb( &grp->N ); |
| |
| cleanup: |
| if( ret != 0 ) |
| ecp_group_free( grp ); |
| |
| return( ret ); |
| } |
| |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| /* Forward declarations */ |
| int ecp_mod_p192( mpi * ); |
| int ecp_mod_p224( mpi * ); |
| int ecp_mod_p256( mpi * ); |
| int ecp_mod_p384( mpi * ); |
| int ecp_mod_p521( mpi * ); |
| #endif |
| |
| /* |
| * Set a group using well-known domain parameters |
| */ |
| int ecp_use_known_dp( ecp_group *grp, ecp_group_id id ) |
| { |
| grp->id = id; |
| |
| switch( id ) |
| { |
| #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) |
| case POLARSSL_ECP_DP_SECP192R1: |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| grp->modp = ecp_mod_p192; |
| #endif |
| return( ecp_group_read_string( grp, 16, |
| SECP192R1_P, SECP192R1_B, |
| SECP192R1_GX, SECP192R1_GY, SECP192R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) |
| case POLARSSL_ECP_DP_SECP224R1: |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| grp->modp = ecp_mod_p224; |
| #endif |
| return( ecp_group_read_string( grp, 16, |
| SECP224R1_P, SECP224R1_B, |
| SECP224R1_GX, SECP224R1_GY, SECP224R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) |
| case POLARSSL_ECP_DP_SECP256R1: |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| grp->modp = ecp_mod_p256; |
| #endif |
| return( ecp_group_read_string( grp, 16, |
| SECP256R1_P, SECP256R1_B, |
| SECP256R1_GX, SECP256R1_GY, SECP256R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) |
| case POLARSSL_ECP_DP_SECP384R1: |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| grp->modp = ecp_mod_p384; |
| #endif |
| return( ecp_group_read_string( grp, 16, |
| SECP384R1_P, SECP384R1_B, |
| SECP384R1_GX, SECP384R1_GY, SECP384R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) |
| case POLARSSL_ECP_DP_SECP521R1: |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| grp->modp = ecp_mod_p521; |
| #endif |
| return( ecp_group_read_string( grp, 16, |
| SECP521R1_P, SECP521R1_B, |
| SECP521R1_GX, SECP521R1_GY, SECP521R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_BP256R1_ENABLED) |
| case POLARSSL_ECP_DP_BP256R1: |
| return( ecp_group_read_string_gen( grp, 16, |
| BP256R1_P, BP256R1_A, BP256R1_B, |
| BP256R1_GX, BP256R1_GY, BP256R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_BP256R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_BP384R1_ENABLED) |
| case POLARSSL_ECP_DP_BP384R1: |
| return( ecp_group_read_string_gen( grp, 16, |
| BP384R1_P, BP384R1_A, BP384R1_B, |
| BP384R1_GX, BP384R1_GY, BP384R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_BP384R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_BP512R1_ENABLED) |
| case POLARSSL_ECP_DP_BP512R1: |
| return( ecp_group_read_string_gen( grp, 16, |
| BP512R1_P, BP512R1_A, BP512R1_B, |
| BP512R1_GX, BP512R1_GY, BP512R1_N ) ); |
| #endif /* POLARSSL_ECP_DP_BP512R1_ENABLED */ |
| |
| default: |
| ecp_group_free( grp ); |
| return( POLARSSL_ERR_ECP_FEATURE_UNAVAILABLE ); |
| } |
| } |
| |
| #if defined(POLARSSL_ECP_NIST_OPTIM) |
| /* |
| * Fast reduction modulo the primes used by the NIST curves. |
| * |
| * These functions are critical for speed, but not needed for correct |
| * operations. So, we make the choice to heavily rely on the internals of our |
| * bignum library, which creates a tight coupling between these functions and |
| * our MPI implementation. However, the coupling between the ECP module and |
| * MPI remains loose, since these functions can be deactivated at will. |
| */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP192R1_ENABLED) |
| /* |
| * Compared to the way things are presented in FIPS 186-3 D.2, |
| * we proceed in columns, from right (least significant chunk) to left, |
| * adding chunks to N in place, and keeping a carry for the next chunk. |
| * This avoids moving things around in memory, and uselessly adding zeros, |
| * compared to the more straightforward, line-oriented approach. |
| * |
| * For this prime we need to handle data in chunks of 64 bits. |
| * Since this is always a multiple of our basic t_uint, we can |
| * use a t_uint * to designate such a chunk, and small loops to handle it. |
| */ |
| |
| /* Add 64-bit chunks (dst += src) and update carry */ |
| static inline void add64( t_uint *dst, t_uint *src, t_uint *carry ) |
| { |
| unsigned char i; |
| t_uint c = 0; |
| for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++, src++ ) |
| { |
| *dst += c; c = ( *dst < c ); |
| *dst += *src; c += ( *dst < *src ); |
| } |
| *carry += c; |
| } |
| |
| /* Add carry to a 64-bit chunk and update carry */ |
| static inline void carry64( t_uint *dst, t_uint *carry ) |
| { |
| unsigned char i; |
| for( i = 0; i < 8 / sizeof( t_uint ); i++, dst++ ) |
| { |
| *dst += *carry; |
| *carry = ( *dst < *carry ); |
| } |
| } |
| |
| #define WIDTH 8 / sizeof( t_uint ) |
| #define A( i ) N->p + i * WIDTH |
| #define ADD( i ) add64( p, A( i ), &c ) |
| #define NEXT p += WIDTH; carry64( p, &c ) |
| #define LAST p += WIDTH; *p = c; while( ++p < end ) *p = 0 |
| |
| /* |
| * Fast quasi-reduction modulo p192 (FIPS 186-3 D.2.1) |
| */ |
| int ecp_mod_p192( mpi *N ) |
| { |
| int ret; |
| t_uint c = 0; |
| t_uint *p, *end; |
| |
| /* Make sure we have enough blocks so that A(5) is legal */ |
| MPI_CHK( mpi_grow( N, 6 * WIDTH ) ); |
| |
| p = N->p; |
| end = p + N->n; |
| |
| ADD( 3 ); ADD( 5 ); NEXT; // A0 += A3 + A5 |
| ADD( 3 ); ADD( 4 ); ADD( 5 ); NEXT; // A1 += A3 + A4 + A5 |
| ADD( 4 ); ADD( 5 ); LAST; // A2 += A4 + A5 |
| |
| cleanup: |
| return( ret ); |
| } |
| |
| #undef WIDTH |
| #undef A |
| #undef ADD |
| #undef NEXT |
| #undef LAST |
| #endif /* POLARSSL_ECP_DP_SECP192R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) || \ |
| defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) || \ |
| defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) |
| /* |
| * The reader is advised to first understand ecp_mod_p192() since the same |
| * general structure is used here, but with additional complications: |
| * (1) chunks of 32 bits, and (2) subtractions. |
| */ |
| |
| /* |
| * For these primes, we need to handle data in chunks of 32 bits. |
| * This makes it more complicated if we use 64 bits limbs in MPI, |
| * which prevents us from using a uniform access method as for p192. |
| * |
| * So, we define a mini abstraction layer to access 32 bit chunks, |
| * load them in 'cur' for work, and store them back from 'cur' when done. |
| * |
| * While at it, also define the size of N in terms of 32-bit chunks. |
| */ |
| #define LOAD32 cur = A( i ); |
| |
| #if defined(POLARSSL_HAVE_INT8) /* 8 bit */ |
| |
| #define MAX32 N->n / 4 |
| #define A( j ) (uint32_t)( N->p[4*j+0] ) | \ |
| ( N->p[4*j+1] << 8 ) | \ |
| ( N->p[4*j+2] << 16 ) | \ |
| ( N->p[4*j+3] << 24 ) |
| #define STORE32 N->p[4*i+0] = (t_uint)( cur ); \ |
| N->p[4*i+1] = (t_uint)( cur >> 8 ); \ |
| N->p[4*i+2] = (t_uint)( cur >> 16 ); \ |
| N->p[4*i+3] = (t_uint)( cur >> 24 ); |
| |
| #elif defined(POLARSSL_HAVE_INT16) /* 16 bit */ |
| |
| #define MAX32 N->n / 2 |
| #define A( j ) (uint32_t)( N->p[2*j] ) | ( N->p[2*j+1] << 16 ) |
| #define STORE32 N->p[2*i+0] = (t_uint)( cur ); \ |
| N->p[2*i+1] = (t_uint)( cur >> 16 ); |
| |
| #elif defined(POLARSSL_HAVE_INT32) /* 32 bit */ |
| |
| #define MAX32 N->n |
| #define A( j ) N->p[j] |
| #define STORE32 N->p[i] = cur; |
| |
| #else /* 64-bit */ |
| |
| #define MAX32 N->n * 2 |
| #define A( j ) j % 2 ? (uint32_t)( N->p[j/2] >> 32 ) : (uint32_t)( N->p[j/2] ) |
| #define STORE32 \ |
| if( i % 2 ) { \ |
| N->p[i/2] &= 0x00000000FFFFFFFF; \ |
| N->p[i/2] |= ((t_uint) cur) << 32; \ |
| } else { \ |
| N->p[i/2] &= 0xFFFFFFFF00000000; \ |
| N->p[i/2] |= (t_uint) cur; \ |
| } |
| |
| #endif /* sizeof( t_uint ) */ |
| |
| /* |
| * Helpers for addition and subtraction of chunks, with signed carry. |
| */ |
| static inline void add32( uint32_t *dst, uint32_t src, signed char *carry ) |
| { |
| *dst += src; |
| *carry += ( *dst < src ); |
| } |
| |
| static inline void sub32( uint32_t *dst, uint32_t src, signed char *carry ) |
| { |
| *carry -= ( *dst < src ); |
| *dst -= src; |
| } |
| |
| #define ADD( j ) add32( &cur, A( j ), &c ); |
| #define SUB( j ) sub32( &cur, A( j ), &c ); |
| |
| /* |
| * Helpers for the main 'loop' |
| * (see fix_negative for the motivation of C) |
| */ |
| #define INIT( b ) \ |
| int ret; \ |
| signed char c = 0, cc; \ |
| uint32_t cur; \ |
| size_t i = 0, bits = b; \ |
| mpi C; \ |
| t_uint Cp[ b / 8 / sizeof( t_uint) + 1 ]; \ |
| \ |
| C.s = 1; \ |
| C.n = b / 8 / sizeof( t_uint) + 1; \ |
| C.p = Cp; \ |
| memset( Cp, 0, C.n * sizeof( t_uint ) ); \ |
| \ |
| MPI_CHK( mpi_grow( N, b * 2 / 8 / sizeof( t_uint ) ) ); \ |
| LOAD32; |
| |
| #define NEXT \ |
| STORE32; i++; LOAD32; \ |
| cc = c; c = 0; \ |
| if( cc < 0 ) \ |
| sub32( &cur, -cc, &c ); \ |
| else \ |
| add32( &cur, cc, &c ); \ |
| |
| #define LAST \ |
| STORE32; i++; \ |
| cur = c > 0 ? c : 0; STORE32; \ |
| cur = 0; while( ++i < MAX32 ) { STORE32; } \ |
| if( c < 0 ) fix_negative( N, c, &C, bits ); |
| |
| /* |
| * If the result is negative, we get it in the form |
| * c * 2^(bits + 32) + N, with c negative and N positive shorter than 'bits' |
| */ |
| static inline int fix_negative( mpi *N, signed char c, mpi *C, size_t bits ) |
| { |
| int ret; |
| |
| /* C = - c * 2^(bits + 32) */ |
| #if !defined(POLARSSL_HAVE_INT64) |
| ((void) bits); |
| #else |
| if( bits == 224 ) |
| C->p[ C->n - 1 ] = ((t_uint) -c) << 32; |
| else |
| #endif |
| C->p[ C->n - 1 ] = (t_uint) -c; |
| |
| /* N = - ( C - N ) */ |
| MPI_CHK( mpi_sub_abs( N, C, N ) ); |
| N->s = -1; |
| |
| cleanup: |
| |
| return( ret ); |
| } |
| |
| #if defined(POLARSSL_ECP_DP_SECP224R1_ENABLED) |
| /* |
| * Fast quasi-reduction modulo p224 (FIPS 186-3 D.2.2) |
| */ |
| int ecp_mod_p224( mpi *N ) |
| { |
| INIT( 224 ); |
| |
| SUB( 7 ); SUB( 11 ); NEXT; // A0 += -A7 - A11 |
| SUB( 8 ); SUB( 12 ); NEXT; // A1 += -A8 - A12 |
| SUB( 9 ); SUB( 13 ); NEXT; // A2 += -A9 - A13 |
| SUB( 10 ); ADD( 7 ); ADD( 11 ); NEXT; // A3 += -A10 + A7 + A11 |
| SUB( 11 ); ADD( 8 ); ADD( 12 ); NEXT; // A4 += -A11 + A8 + A12 |
| SUB( 12 ); ADD( 9 ); ADD( 13 ); NEXT; // A5 += -A12 + A9 + A13 |
| SUB( 13 ); ADD( 10 ); LAST; // A6 += -A13 + A10 |
| |
| cleanup: |
| return( ret ); |
| } |
| #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP256R1_ENABLED) |
| /* |
| * Fast quasi-reduction modulo p256 (FIPS 186-3 D.2.3) |
| */ |
| int ecp_mod_p256( mpi *N ) |
| { |
| INIT( 256 ); |
| |
| ADD( 8 ); ADD( 9 ); |
| SUB( 11 ); SUB( 12 ); SUB( 13 ); SUB( 14 ); NEXT; // A0 |
| |
| ADD( 9 ); ADD( 10 ); |
| SUB( 12 ); SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A1 |
| |
| ADD( 10 ); ADD( 11 ); |
| SUB( 13 ); SUB( 14 ); SUB( 15 ); NEXT; // A2 |
| |
| ADD( 11 ); ADD( 11 ); ADD( 12 ); ADD( 12 ); ADD( 13 ); |
| SUB( 15 ); SUB( 8 ); SUB( 9 ); NEXT; // A3 |
| |
| ADD( 12 ); ADD( 12 ); ADD( 13 ); ADD( 13 ); ADD( 14 ); |
| SUB( 9 ); SUB( 10 ); NEXT; // A4 |
| |
| ADD( 13 ); ADD( 13 ); ADD( 14 ); ADD( 14 ); ADD( 15 ); |
| SUB( 10 ); SUB( 11 ); NEXT; // A5 |
| |
| ADD( 14 ); ADD( 14 ); ADD( 15 ); ADD( 15 ); ADD( 14 ); ADD( 13 ); |
| SUB( 8 ); SUB( 9 ); NEXT; // A6 |
| |
| ADD( 15 ); ADD( 15 ); ADD( 15 ); ADD( 8 ); |
| SUB( 10 ); SUB( 11 ); SUB( 12 ); SUB( 13 ); LAST; // A7 |
| |
| cleanup: |
| return( ret ); |
| } |
| #endif /* POLARSSL_ECP_DP_SECP256R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP384R1_ENABLED) |
| /* |
| * Fast quasi-reduction modulo p384 (FIPS 186-3 D.2.4) |
| */ |
| int ecp_mod_p384( mpi *N ) |
| { |
| INIT( 384 ); |
| |
| ADD( 12 ); ADD( 21 ); ADD( 20 ); |
| SUB( 23 ); NEXT; // A0 |
| |
| ADD( 13 ); ADD( 22 ); ADD( 23 ); |
| SUB( 12 ); SUB( 20 ); NEXT; // A2 |
| |
| ADD( 14 ); ADD( 23 ); |
| SUB( 13 ); SUB( 21 ); NEXT; // A2 |
| |
| ADD( 15 ); ADD( 12 ); ADD( 20 ); ADD( 21 ); |
| SUB( 14 ); SUB( 22 ); SUB( 23 ); NEXT; // A3 |
| |
| ADD( 21 ); ADD( 21 ); ADD( 16 ); ADD( 13 ); ADD( 12 ); ADD( 20 ); ADD( 22 ); |
| SUB( 15 ); SUB( 23 ); SUB( 23 ); NEXT; // A4 |
| |
| ADD( 22 ); ADD( 22 ); ADD( 17 ); ADD( 14 ); ADD( 13 ); ADD( 21 ); ADD( 23 ); |
| SUB( 16 ); NEXT; // A5 |
| |
| ADD( 23 ); ADD( 23 ); ADD( 18 ); ADD( 15 ); ADD( 14 ); ADD( 22 ); |
| SUB( 17 ); NEXT; // A6 |
| |
| ADD( 19 ); ADD( 16 ); ADD( 15 ); ADD( 23 ); |
| SUB( 18 ); NEXT; // A7 |
| |
| ADD( 20 ); ADD( 17 ); ADD( 16 ); |
| SUB( 19 ); NEXT; // A8 |
| |
| ADD( 21 ); ADD( 18 ); ADD( 17 ); |
| SUB( 20 ); NEXT; // A9 |
| |
| ADD( 22 ); ADD( 19 ); ADD( 18 ); |
| SUB( 21 ); NEXT; // A10 |
| |
| ADD( 23 ); ADD( 20 ); ADD( 19 ); |
| SUB( 22 ); LAST; // A11 |
| |
| cleanup: |
| return( ret ); |
| } |
| #endif /* POLARSSL_ECP_DP_SECP384R1_ENABLED */ |
| |
| #undef A |
| #undef LOAD32 |
| #undef STORE32 |
| #undef MAX32 |
| #undef INIT |
| #undef NEXT |
| #undef LAST |
| |
| #endif /* POLARSSL_ECP_DP_SECP224R1_ENABLED || |
| POLARSSL_ECP_DP_SECP256R1_ENABLED || |
| POLARSSL_ECP_DP_SECP384R1_ENABLED */ |
| |
| #if defined(POLARSSL_ECP_DP_SECP521R1_ENABLED) |
| /* |
| * Here we have an actual Mersenne prime, so things are more straightforward. |
| * However, chunks are aligned on a 'weird' boundary (521 bits). |
| */ |
| |
| /* Size of p521 in terms of t_uint */ |
| #define P521_WIDTH ( 521 / 8 / sizeof( t_uint ) + 1 ) |
| |
| /* Bits to keep in the most significant t_uint */ |
| #if defined(POLARSSL_HAVE_INT8) |
| #define P521_MASK 0x01 |
| #else |
| #define P521_MASK 0x01FF |
| #endif |
| |
| /* |
| * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) |
| * Write N as A1 + 2^521 A0, return A0 + A1 |
| */ |
| int ecp_mod_p521( mpi *N ) |
| { |
| int ret; |
| size_t i; |
| mpi M; |
| t_uint Mp[P521_WIDTH + 1]; |
| /* Worst case for the size of M is when t_uint is 16 bits: |
| * we need to hold bits 513 to 1056, which is 34 limbs, that is |
| * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ |
| |
| if( N->n < P521_WIDTH ) |
| return( 0 ); |
| |
| /* M = A1 */ |
| M.s = 1; |
| M.n = N->n - ( P521_WIDTH - 1 ); |
| if( M.n > P521_WIDTH + 1 ) |
| M.n = P521_WIDTH + 1; |
| M.p = Mp; |
| memcpy( Mp, N->p + P521_WIDTH - 1, M.n * sizeof( t_uint ) ); |
| MPI_CHK( mpi_shift_r( &M, 521 % ( 8 * sizeof( t_uint ) ) ) ); |
| |
| /* N = A0 */ |
| N->p[P521_WIDTH - 1] &= P521_MASK; |
| for( i = P521_WIDTH; i < N->n; i++ ) |
| N->p[i] = 0; |
| |
| /* N = A0 + A1 */ |
| MPI_CHK( mpi_add_abs( N, N, &M ) ); |
| |
| cleanup: |
| return( ret ); |
| } |
| |
| #undef P521_WIDTH |
| #undef P521_MASK |
| #endif /* POLARSSL_ECP_DP_SECP521R1_ENABLED */ |
| |
| #endif /* POLARSSL_ECP_NIST_OPTIM */ |
| |
| #endif |