| 1 | /* |
| 2 | * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. |
| 3 | * Use is subject to license terms. |
| 4 | * |
| 5 | * This library is free software; you can redistribute it and/or |
| 6 | * modify it under the terms of the GNU Lesser General Public |
| 7 | * License as published by the Free Software Foundation; either |
| 8 | * version 2.1 of the License, or (at your option) any later version. |
| 9 | * |
| 10 | * This library is distributed in the hope that it will be useful, |
| 11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 13 | * Lesser General Public License for more details. |
| 14 | * |
| 15 | * You should have received a copy of the GNU Lesser General Public License |
| 16 | * along with this library; if not, write to the Free Software Foundation, |
| 17 | * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| 18 | * |
| 19 | * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| 20 | * or visit www.oracle.com if you need additional information or have any |
| 21 | * questions. |
| 22 | */ |
| 23 | |
| 24 | /* ********************************************************************* |
| 25 | * |
| 26 | * The Original Code is the elliptic curve math library. |
| 27 | * |
| 28 | * The Initial Developer of the Original Code is |
| 29 | * Sun Microsystems, Inc. |
| 30 | * Portions created by the Initial Developer are Copyright (C) 2003 |
| 31 | * the Initial Developer. All Rights Reserved. |
| 32 | * |
| 33 | * Contributor(s): |
| 34 | * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories |
| 35 | * |
| 36 | *********************************************************************** */ |
| 37 | |
| 38 | /* Uses Montgomery reduction for field arithmetic. See mpi/mpmontg.c for |
| 39 | * code implementation. */ |
| 40 | |
| 41 | #include "mpi.h" |
| 42 | #include "mplogic.h" |
| 43 | #include "mpi-priv.h" |
| 44 | #include "ecl-priv.h" |
| 45 | #include "ecp.h" |
| 46 | #ifndef _KERNEL |
| 47 | #include <stdlib.h> |
| 48 | #include <stdio.h> |
| 49 | #endif |
| 50 | |
| 51 | /* Construct a generic GFMethod for arithmetic over prime fields with |
| 52 | * irreducible irr. */ |
| 53 | GFMethod * |
| 54 | GFMethod_consGFp_mont(const mp_int *irr) |
| 55 | { |
| 56 | mp_err res = MP_OKAY; |
| 57 | int i; |
| 58 | GFMethod *meth = NULL; |
| 59 | mp_mont_modulus *mmm; |
| 60 | |
| 61 | meth = GFMethod_consGFp(irr); |
| 62 | if (meth == NULL) |
| 63 | return NULL; |
| 64 | |
| 65 | #ifdef _KERNEL |
| 66 | mmm = (mp_mont_modulus *) kmem_alloc(sizeof(mp_mont_modulus), |
| 67 | FLAG(irr)); |
| 68 | #else |
| 69 | mmm = (mp_mont_modulus *) malloc(sizeof(mp_mont_modulus)); |
| 70 | #endif |
| 71 | if (mmm == NULL) { |
| 72 | res = MP_MEM; |
| 73 | goto CLEANUP; |
| 74 | } |
| 75 | |
| 76 | meth->field_mul = &ec_GFp_mul_mont; |
| 77 | meth->field_sqr = &ec_GFp_sqr_mont; |
| 78 | meth->field_div = &ec_GFp_div_mont; |
| 79 | meth->field_enc = &ec_GFp_enc_mont; |
| 80 | meth->field_dec = &ec_GFp_dec_mont; |
| 81 | meth->extra1 = mmm; |
| 82 | meth->extra2 = NULL; |
| 83 | meth->extra_free = &ec_GFp_extra_free_mont; |
| 84 | |
| 85 | mmm->N = meth->irr; |
| 86 | i = mpl_significant_bits(&meth->irr); |
| 87 | i += MP_DIGIT_BIT - 1; |
| 88 | mmm->b = i - i % MP_DIGIT_BIT; |
| 89 | mmm->n0prime = 0 - s_mp_invmod_radix(MP_DIGIT(&meth->irr, 0)); |
| 90 | |
| 91 | CLEANUP: |
| 92 | if (res != MP_OKAY) { |
| 93 | GFMethod_free(meth); |
| 94 | return NULL; |
| 95 | } |
| 96 | return meth; |
| 97 | } |
| 98 | |
| 99 | /* Wrapper functions for generic prime field arithmetic. */ |
| 100 | |
| 101 | /* Field multiplication using Montgomery reduction. */ |
| 102 | mp_err |
| 103 | ec_GFp_mul_mont(const mp_int *a, const mp_int *b, mp_int *r, |
| 104 | const GFMethod *meth) |
| 105 | { |
| 106 | mp_err res = MP_OKAY; |
| 107 | |
| 108 | #ifdef MP_MONT_USE_MP_MUL |
| 109 | /* if MP_MONT_USE_MP_MUL is defined, then the function s_mp_mul_mont |
| 110 | * is not implemented and we have to use mp_mul and s_mp_redc directly |
| 111 | */ |
| 112 | MP_CHECKOK(mp_mul(a, b, r)); |
| 113 | MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1)); |
| 114 | #else |
| 115 | mp_int s; |
| 116 | |
| 117 | MP_DIGITS(&s) = 0; |
| 118 | /* s_mp_mul_mont doesn't allow source and destination to be the same */ |
| 119 | if ((a == r) || (b == r)) { |
| 120 | MP_CHECKOK(mp_init(&s, FLAG(a))); |
| 121 | MP_CHECKOK(s_mp_mul_mont |
| 122 | (a, b, &s, (mp_mont_modulus *) meth->extra1)); |
| 123 | MP_CHECKOK(mp_copy(&s, r)); |
| 124 | mp_clear(&s); |
| 125 | } else { |
| 126 | return s_mp_mul_mont(a, b, r, (mp_mont_modulus *) meth->extra1); |
| 127 | } |
| 128 | #endif |
| 129 | CLEANUP: |
| 130 | return res; |
| 131 | } |
| 132 | |
| 133 | /* Field squaring using Montgomery reduction. */ |
| 134 | mp_err |
| 135 | ec_GFp_sqr_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| 136 | { |
| 137 | return ec_GFp_mul_mont(a, a, r, meth); |
| 138 | } |
| 139 | |
| 140 | /* Field division using Montgomery reduction. */ |
| 141 | mp_err |
| 142 | ec_GFp_div_mont(const mp_int *a, const mp_int *b, mp_int *r, |
| 143 | const GFMethod *meth) |
| 144 | { |
| 145 | mp_err res = MP_OKAY; |
| 146 | |
| 147 | /* if A=aZ represents a encoded in montgomery coordinates with Z and # |
| 148 | * and \ respectively represent multiplication and division in |
| 149 | * montgomery coordinates, then A\B = (a/b)Z = (A/B)Z and Binv = |
| 150 | * (1/b)Z = (1/B)(Z^2) where B # Binv = Z */ |
| 151 | MP_CHECKOK(ec_GFp_div(a, b, r, meth)); |
| 152 | MP_CHECKOK(ec_GFp_enc_mont(r, r, meth)); |
| 153 | if (a == NULL) { |
| 154 | MP_CHECKOK(ec_GFp_enc_mont(r, r, meth)); |
| 155 | } |
| 156 | CLEANUP: |
| 157 | return res; |
| 158 | } |
| 159 | |
| 160 | /* Encode a field element in Montgomery form. See s_mp_to_mont in |
| 161 | * mpi/mpmontg.c */ |
| 162 | mp_err |
| 163 | ec_GFp_enc_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| 164 | { |
| 165 | mp_mont_modulus *mmm; |
| 166 | mp_err res = MP_OKAY; |
| 167 | |
| 168 | mmm = (mp_mont_modulus *) meth->extra1; |
| 169 | MP_CHECKOK(mpl_lsh(a, r, mmm->b)); |
| 170 | MP_CHECKOK(mp_mod(r, &mmm->N, r)); |
| 171 | CLEANUP: |
| 172 | return res; |
| 173 | } |
| 174 | |
| 175 | /* Decode a field element from Montgomery form. */ |
| 176 | mp_err |
| 177 | ec_GFp_dec_mont(const mp_int *a, mp_int *r, const GFMethod *meth) |
| 178 | { |
| 179 | mp_err res = MP_OKAY; |
| 180 | |
| 181 | if (a != r) { |
| 182 | MP_CHECKOK(mp_copy(a, r)); |
| 183 | } |
| 184 | MP_CHECKOK(s_mp_redc(r, (mp_mont_modulus *) meth->extra1)); |
| 185 | CLEANUP: |
| 186 | return res; |
| 187 | } |
| 188 | |
| 189 | /* Free the memory allocated to the extra fields of Montgomery GFMethod |
| 190 | * object. */ |
| 191 | void |
| 192 | (GFMethod *meth) |
| 193 | { |
| 194 | if (meth->extra1 != NULL) { |
| 195 | #ifdef _KERNEL |
| 196 | kmem_free(meth->extra1, sizeof(mp_mont_modulus)); |
| 197 | #else |
| 198 | free(meth->extra1); |
| 199 | #endif |
| 200 | meth->extra1 = NULL; |
| 201 | } |
| 202 | } |
| 203 | |