/* ********************************************************************* * * Sun elects to have this file available under and governed by the * Mozilla Public License Version 1.1 ("MPL") (see * http://www.mozilla.org/MPL/ for full license text). For the avoidance * of doubt and subject to the following, Sun also elects to allow * licensees to use this file under the MPL, the GNU General Public * License version 2 only or the Lesser General Public License version * 2.1 only. Any references to the "GNU General Public License version 2 * or later" or "GPL" in the following shall be construed to mean the * GNU General Public License version 2 only. Any references to the "GNU * Lesser General Public License version 2.1 or later" or "LGPL" in the * following shall be construed to mean the GNU Lesser General Public * License version 2.1 only. However, the following notice accompanied * the original version of this file: * * Version: MPL 1.1/GPL 2.0/LGPL 2.1 * * The contents of this file are subject to the Mozilla Public License Version * 1.1 (the "License"); you may not use this file except in compliance with * the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * Software distributed under the License is distributed on an "AS IS" basis, * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License * for the specific language governing rights and limitations under the * License. * * 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 , Sun Microsystems Laboratories * * Alternatively, the contents of this file may be used under the terms of * either the GNU General Public License Version 2 or later (the "GPL"), or * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), * in which case the provisions of the GPL or the LGPL are applicable instead * of those above. If you wish to allow use of your version of this file only * under the terms of either the GPL or the LGPL, and not to allow others to * use your version of this file under the terms of the MPL, indicate your * decision by deleting the provisions above and replace them with the notice * and other provisions required by the GPL or the LGPL. If you do not delete * the provisions above, a recipient may use your version of this file under * the terms of any one of the MPL, the GPL or the LGPL. * *********************************************************************** */ /* * Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved. * Use is subject to license terms. */ #include "ecp.h" #include "mpi.h" #include "mplogic.h" #include "mpi-priv.h" #ifndef _KERNEL #include #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; }