| /* |
| * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. |
| * Use is subject to license terms. |
| * |
| * This library is free software; you can redistribute it and/or |
| * modify it under the terms of the GNU Lesser General Public |
| * License as published by the Free Software Foundation; either |
| * version 2.1 of the License, or (at your option) any later version. |
| * |
| * This library 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 |
| * Lesser General Public License for more details. |
| * |
| * You should have received a copy of the GNU Lesser General Public License |
| * along with this library; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* ********************************************************************* |
| * |
| * The Original Code is the elliptic curve math library for prime field curves. |
| * |
| * The Initial Developer of the Original Code is |
| * Sun Microsystems, Inc. |
| * Portions created by the Initial Developer are Copyright (C) 2003 |
| * the Initial Developer. All Rights Reserved. |
| * |
| * Contributor(s): |
| * Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories |
| * |
| *********************************************************************** */ |
| |
| #include "ecp.h" |
| #include "mpi.h" |
| #include "mplogic.h" |
| #include "mpi-priv.h" |
| #ifndef _KERNEL |
| #include <stdlib.h> |
| #endif |
| |
| #define ECP224_DIGITS ECL_CURVE_DIGITS(224) |
| |
| /* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses |
| * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software |
| * Implementation of the NIST Elliptic Curves over Prime Fields. */ |
| mp_err |
| ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| mp_size a_used = MP_USED(a); |
| |
| int r3b; |
| mp_digit carry; |
| #ifdef ECL_THIRTY_TWO_BIT |
| mp_digit a6a = 0, a6b = 0, |
| a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0; |
| mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a; |
| #else |
| mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0; |
| mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0; |
| mp_digit r0, r1, r2, r3; |
| #endif |
| |
| /* reduction not needed if a is not larger than field size */ |
| if (a_used < ECP224_DIGITS) { |
| if (a == r) return MP_OKAY; |
| return mp_copy(a, r); |
| } |
| /* for polynomials larger than twice the field size, use regular |
| * reduction */ |
| if (a_used > ECL_CURVE_DIGITS(224*2)) { |
| MP_CHECKOK(mp_mod(a, &meth->irr, r)); |
| } else { |
| #ifdef ECL_THIRTY_TWO_BIT |
| /* copy out upper words of a */ |
| switch (a_used) { |
| case 14: |
| a6b = MP_DIGIT(a, 13); |
| case 13: |
| a6a = MP_DIGIT(a, 12); |
| case 12: |
| a5b = MP_DIGIT(a, 11); |
| case 11: |
| a5a = MP_DIGIT(a, 10); |
| case 10: |
| a4b = MP_DIGIT(a, 9); |
| case 9: |
| a4a = MP_DIGIT(a, 8); |
| case 8: |
| a3b = MP_DIGIT(a, 7); |
| } |
| r3a = MP_DIGIT(a, 6); |
| r2b= MP_DIGIT(a, 5); |
| r2a= MP_DIGIT(a, 4); |
| r1b = MP_DIGIT(a, 3); |
| r1a = MP_DIGIT(a, 2); |
| r0b = MP_DIGIT(a, 1); |
| r0a = MP_DIGIT(a, 0); |
| |
| |
| /* implement r = (a3a,a2,a1,a0) |
| +(a5a, a4,a3b, 0) |
| +( 0, a6,a5b, 0) |
| -( 0 0, 0|a6b, a6a|a5b ) |
| -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ |
| MP_ADD_CARRY (r1b, a3b, r1b, 0, carry); |
| MP_ADD_CARRY (r2a, a4a, r2a, carry, carry); |
| MP_ADD_CARRY (r2b, a4b, r2b, carry, carry); |
| MP_ADD_CARRY (r3a, a5a, r3a, carry, carry); |
| r3b = carry; |
| MP_ADD_CARRY (r1b, a5b, r1b, 0, carry); |
| MP_ADD_CARRY (r2a, a6a, r2a, carry, carry); |
| MP_ADD_CARRY (r2b, a6b, r2b, carry, carry); |
| MP_ADD_CARRY (r3a, 0, r3a, carry, carry); |
| r3b += carry; |
| MP_SUB_BORROW(r0a, a3b, r0a, 0, carry); |
| MP_SUB_BORROW(r0b, a4a, r0b, carry, carry); |
| MP_SUB_BORROW(r1a, a4b, r1a, carry, carry); |
| MP_SUB_BORROW(r1b, a5a, r1b, carry, carry); |
| MP_SUB_BORROW(r2a, a5b, r2a, carry, carry); |
| MP_SUB_BORROW(r2b, a6a, r2b, carry, carry); |
| MP_SUB_BORROW(r3a, a6b, r3a, carry, carry); |
| r3b -= carry; |
| MP_SUB_BORROW(r0a, a5b, r0a, 0, carry); |
| MP_SUB_BORROW(r0b, a6a, r0b, carry, carry); |
| MP_SUB_BORROW(r1a, a6b, r1a, carry, carry); |
| if (carry) { |
| MP_SUB_BORROW(r1b, 0, r1b, carry, carry); |
| MP_SUB_BORROW(r2a, 0, r2a, carry, carry); |
| MP_SUB_BORROW(r2b, 0, r2b, carry, carry); |
| MP_SUB_BORROW(r3a, 0, r3a, carry, carry); |
| r3b -= carry; |
| } |
| |
| while (r3b > 0) { |
| int tmp; |
| MP_ADD_CARRY(r1b, r3b, r1b, 0, carry); |
| if (carry) { |
| MP_ADD_CARRY(r2a, 0, r2a, carry, carry); |
| MP_ADD_CARRY(r2b, 0, r2b, carry, carry); |
| MP_ADD_CARRY(r3a, 0, r3a, carry, carry); |
| } |
| tmp = carry; |
| MP_SUB_BORROW(r0a, r3b, r0a, 0, carry); |
| if (carry) { |
| MP_SUB_BORROW(r0b, 0, r0b, carry, carry); |
| MP_SUB_BORROW(r1a, 0, r1a, carry, carry); |
| MP_SUB_BORROW(r1b, 0, r1b, carry, carry); |
| MP_SUB_BORROW(r2a, 0, r2a, carry, carry); |
| MP_SUB_BORROW(r2b, 0, r2b, carry, carry); |
| MP_SUB_BORROW(r3a, 0, r3a, carry, carry); |
| tmp -= carry; |
| } |
| r3b = tmp; |
| } |
| |
| while (r3b < 0) { |
| mp_digit maxInt = MP_DIGIT_MAX; |
| MP_ADD_CARRY (r0a, 1, r0a, 0, carry); |
| MP_ADD_CARRY (r0b, 0, r0b, carry, carry); |
| MP_ADD_CARRY (r1a, 0, r1a, carry, carry); |
| MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry); |
| MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry); |
| MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry); |
| MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry); |
| r3b += carry; |
| } |
| /* check for final reduction */ |
| /* now the only way we are over is if the top 4 words are all ones */ |
| if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX) |
| && (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) && |
| ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) { |
| /* one last subraction */ |
| MP_SUB_BORROW(r0a, 1, r0a, 0, carry); |
| MP_SUB_BORROW(r0b, 0, r0b, carry, carry); |
| MP_SUB_BORROW(r1a, 0, r1a, carry, carry); |
| r1b = r2a = r2b = r3a = 0; |
| } |
| |
| |
| if (a != r) { |
| MP_CHECKOK(s_mp_pad(r, 7)); |
| } |
| /* set the lower words of r */ |
| MP_SIGN(r) = MP_ZPOS; |
| MP_USED(r) = 7; |
| MP_DIGIT(r, 6) = r3a; |
| MP_DIGIT(r, 5) = r2b; |
| MP_DIGIT(r, 4) = r2a; |
| MP_DIGIT(r, 3) = r1b; |
| MP_DIGIT(r, 2) = r1a; |
| MP_DIGIT(r, 1) = r0b; |
| MP_DIGIT(r, 0) = r0a; |
| #else |
| /* copy out upper words of a */ |
| switch (a_used) { |
| case 7: |
| a6 = MP_DIGIT(a, 6); |
| a6b = a6 >> 32; |
| a6a_a5b = a6 << 32; |
| case 6: |
| a5 = MP_DIGIT(a, 5); |
| a5b = a5 >> 32; |
| a6a_a5b |= a5b; |
| a5b = a5b << 32; |
| a5a_a4b = a5 << 32; |
| a5a = a5 & 0xffffffff; |
| case 5: |
| a4 = MP_DIGIT(a, 4); |
| a5a_a4b |= a4 >> 32; |
| a4a_a3b = a4 << 32; |
| case 4: |
| a3b = MP_DIGIT(a, 3) >> 32; |
| a4a_a3b |= a3b; |
| a3b = a3b << 32; |
| } |
| |
| r3 = MP_DIGIT(a, 3) & 0xffffffff; |
| r2 = MP_DIGIT(a, 2); |
| r1 = MP_DIGIT(a, 1); |
| r0 = MP_DIGIT(a, 0); |
| |
| /* implement r = (a3a,a2,a1,a0) |
| +(a5a, a4,a3b, 0) |
| +( 0, a6,a5b, 0) |
| -( 0 0, 0|a6b, a6a|a5b ) |
| -( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */ |
| MP_ADD_CARRY_ZERO (r1, a3b, r1, carry); |
| MP_ADD_CARRY (r2, a4 , r2, carry, carry); |
| MP_ADD_CARRY (r3, a5a, r3, carry, carry); |
| MP_ADD_CARRY_ZERO (r1, a5b, r1, carry); |
| MP_ADD_CARRY (r2, a6 , r2, carry, carry); |
| MP_ADD_CARRY (r3, 0, r3, carry, carry); |
| |
| MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry); |
| MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry); |
| MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry); |
| MP_SUB_BORROW(r3, a6b , r3, carry, carry); |
| MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry); |
| MP_SUB_BORROW(r1, a6b , r1, carry, carry); |
| if (carry) { |
| MP_SUB_BORROW(r2, 0, r2, carry, carry); |
| MP_SUB_BORROW(r3, 0, r3, carry, carry); |
| } |
| |
| |
| /* if the value is negative, r3 has a 2's complement |
| * high value */ |
| r3b = (int)(r3 >>32); |
| while (r3b > 0) { |
| r3 &= 0xffffffff; |
| MP_ADD_CARRY_ZERO(r1,((mp_digit)r3b) << 32, r1, carry); |
| if (carry) { |
| MP_ADD_CARRY(r2, 0, r2, carry, carry); |
| MP_ADD_CARRY(r3, 0, r3, carry, carry); |
| } |
| MP_SUB_BORROW(r0, r3b, r0, 0, carry); |
| if (carry) { |
| MP_SUB_BORROW(r1, 0, r1, carry, carry); |
| MP_SUB_BORROW(r2, 0, r2, carry, carry); |
| MP_SUB_BORROW(r3, 0, r3, carry, carry); |
| } |
| r3b = (int)(r3 >>32); |
| } |
| |
| while (r3b < 0) { |
| MP_ADD_CARRY_ZERO (r0, 1, r0, carry); |
| MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry); |
| MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry); |
| MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry); |
| r3b = (int)(r3 >>32); |
| } |
| /* check for final reduction */ |
| /* now the only way we are over is if the top 4 words are all ones */ |
| if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX) |
| && ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) && |
| ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) { |
| /* one last subraction */ |
| MP_SUB_BORROW(r0, 1, r0, 0, carry); |
| MP_SUB_BORROW(r1, 0, r1, carry, carry); |
| r2 = r3 = 0; |
| } |
| |
| |
| if (a != r) { |
| MP_CHECKOK(s_mp_pad(r, 4)); |
| } |
| /* set the lower words of r */ |
| MP_SIGN(r) = MP_ZPOS; |
| MP_USED(r) = 4; |
| MP_DIGIT(r, 3) = r3; |
| MP_DIGIT(r, 2) = r2; |
| MP_DIGIT(r, 1) = r1; |
| MP_DIGIT(r, 0) = r0; |
| #endif |
| } |
| |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the square of polynomial a, reduce modulo p224. Store the |
| * result in r. r could be a. Uses optimized modular reduction for p224. |
| */ |
| mp_err |
| ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| MP_CHECKOK(mp_sqr(a, r)); |
| MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Compute the product of two polynomials a and b, reduce modulo p224. |
| * Store the result in r. r could be a or b; a could be b. Uses |
| * optimized modular reduction for p224. */ |
| mp_err |
| ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| |
| MP_CHECKOK(mp_mul(a, b, r)); |
| MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); |
| CLEANUP: |
| return res; |
| } |
| |
| /* Divides two field elements. If a is NULL, then returns the inverse of |
| * b. */ |
| mp_err |
| ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r, |
| const GFMethod *meth) |
| { |
| mp_err res = MP_OKAY; |
| mp_int t; |
| |
| /* If a is NULL, then return the inverse of b, otherwise return a/b. */ |
| if (a == NULL) { |
| return mp_invmod(b, &meth->irr, r); |
| } else { |
| /* MPI doesn't support divmod, so we implement it using invmod and |
| * mulmod. */ |
| MP_CHECKOK(mp_init(&t, FLAG(b))); |
| MP_CHECKOK(mp_invmod(b, &meth->irr, &t)); |
| MP_CHECKOK(mp_mul(a, &t, r)); |
| MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth)); |
| CLEANUP: |
| mp_clear(&t); |
| return res; |
| } |
| } |
| |
| /* Wire in fast field arithmetic and precomputation of base point for |
| * named curves. */ |
| mp_err |
| ec_group_set_gfp224(ECGroup *group, ECCurveName name) |
| { |
| if (name == ECCurve_NIST_P224) { |
| group->meth->field_mod = &ec_GFp_nistp224_mod; |
| group->meth->field_mul = &ec_GFp_nistp224_mul; |
| group->meth->field_sqr = &ec_GFp_nistp224_sqr; |
| group->meth->field_div = &ec_GFp_nistp224_div; |
| } |
| return MP_OKAY; |
| } |
