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* ***** BEGIN LICENSE BLOCK *****
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1
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* The contents of this file are subject to the Mozilla Public License Version
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* 1.1 (the "License"); you may not use this file except in compliance with
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* the License. You may obtain a copy of the License at
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* http://www.mozilla.org/MPL/
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* Software distributed under the License is distributed on an "AS IS" basis,
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
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* for the specific language governing rights and limitations under the
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* The Original Code is the elliptic curve math library for prime field curves.
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* The Initial Developer of the Original Code is
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* Sun Microsystems, Inc.
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* Portions created by the Initial Developer are Copyright (C) 2003
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* the Initial Developer. All Rights Reserved.
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* Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
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* Alternatively, the contents of this file may be used under the terms of
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* either the GNU General Public License Version 2 or later (the "GPL"), or
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* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
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* in which case the provisions of the GPL or the LGPL are applicable instead
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* of those above. If you wish to allow use of your version of this file only
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* under the terms of either the GPL or the LGPL, and not to allow others to
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* use your version of this file under the terms of the MPL, indicate your
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* decision by deleting the provisions above and replace them with the notice
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* and other provisions required by the GPL or the LGPL. If you do not delete
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* the provisions above, a recipient may use your version of this file under
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* the terms of any one of the MPL, the GPL or the LGPL.
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* ***** END LICENSE BLOCK ***** */
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#define ECP224_DIGITS ECL_CURVE_DIGITS(224)
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/* Fast modular reduction for p224 = 2^224 - 2^96 + 1. a can be r. Uses
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* algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
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* Implementation of the NIST Elliptic Curves over Prime Fields. */
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ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
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mp_size a_used = MP_USED(a);
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#ifdef ECL_THIRTY_TWO_BIT
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mp_digit a6a = 0, a6b = 0,
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a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
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mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
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mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
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mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
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mp_digit r0, r1, r2, r3;
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/* reduction not needed if a is not larger than field size */
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if (a_used < ECP224_DIGITS) {
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if (a == r) return MP_OKAY;
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/* for polynomials larger than twice the field size, use regular
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if (a_used > ECL_CURVE_DIGITS(224*2)) {
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MP_CHECKOK(mp_mod(a, &meth->irr, r));
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#ifdef ECL_THIRTY_TWO_BIT
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/* copy out upper words of a */
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a6b = MP_DIGIT(a, 13);
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a6a = MP_DIGIT(a, 12);
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a5b = MP_DIGIT(a, 11);
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a5a = MP_DIGIT(a, 10);
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r1a = MP_DIGIT(a, 2);
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r0b = MP_DIGIT(a, 1);
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r0a = MP_DIGIT(a, 0);
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/* implement r = (a3a,a2,a1,a0)
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-( 0 0, 0|a6b, a6a|a5b )
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-( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
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MP_ADD_CARRY (r1b, a3b, r1b, 0, carry);
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MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
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MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
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MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
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MP_ADD_CARRY (r1b, a5b, r1b, 0, carry);
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MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
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MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
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MP_ADD_CARRY (r3a, 0, r3a, carry, carry);
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MP_SUB_BORROW(r0a, a3b, r0a, 0, carry);
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MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
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MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
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MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
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MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
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MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
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MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
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MP_SUB_BORROW(r0a, a5b, r0a, 0, carry);
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MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
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MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
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MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
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MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
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MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
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MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
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MP_ADD_CARRY(r1b, r3b, r1b, 0, carry);
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MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
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MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
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MP_ADD_CARRY(r3a, 0, r3a, carry, carry);
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MP_SUB_BORROW(r0a, r3b, r0a, 0, carry);
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MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
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MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
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MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
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MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
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MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
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MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
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mp_digit maxInt = MP_DIGIT_MAX;
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MP_ADD_CARRY (r0a, 1, r0a, 0, carry);
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MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
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MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
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MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
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MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
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MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
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MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
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/* check for final reduction */
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/* now the only way we are over is if the top 4 words are all ones */
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if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
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&& (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
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((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
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/* one last subraction */
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MP_SUB_BORROW(r0a, 1, r0a, 0, carry);
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MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
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MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
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r1b = r2a = r2b = r3a = 0;
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MP_CHECKOK(s_mp_pad(r, 7));
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/* set the lower words of r */
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MP_SIGN(r) = MP_ZPOS;
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MP_DIGIT(r, 6) = r3a;
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MP_DIGIT(r, 5) = r2b;
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MP_DIGIT(r, 4) = r2a;
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MP_DIGIT(r, 3) = r1b;
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MP_DIGIT(r, 2) = r1a;
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MP_DIGIT(r, 1) = r0b;
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MP_DIGIT(r, 0) = r0a;
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/* copy out upper words of a */
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a5a = a5 & 0xffffffff;
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a3b = MP_DIGIT(a, 3) >> 32;
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r3 = MP_DIGIT(a, 3) & 0xffffffff;
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/* implement r = (a3a,a2,a1,a0)
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-( 0 0, 0|a6b, a6a|a5b )
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-( a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
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MP_ADD_CARRY (r1, a3b, r1, 0, carry);
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MP_ADD_CARRY (r2, a4 , r2, carry, carry);
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MP_ADD_CARRY (r3, a5a, r3, carry, carry);
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MP_ADD_CARRY (r1, a5b, r1, 0, carry);
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MP_ADD_CARRY (r2, a6 , r2, carry, carry);
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MP_ADD_CARRY (r3, 0, r3, carry, carry);
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MP_SUB_BORROW(r0, a4a_a3b, r0, 0, carry);
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MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
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MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
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MP_SUB_BORROW(r3, a6b , r3, carry, carry);
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MP_SUB_BORROW(r0, a6a_a5b, r0, 0, carry);
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MP_SUB_BORROW(r1, a6b , r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, 0, r3, carry, carry);
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/* if the value is negative, r3 has a 2's complement
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r3b = (int)(r3 >>32);
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MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
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MP_ADD_CARRY(r2, 0, r2, carry, carry);
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MP_ADD_CARRY(r3, 0, r3, carry, carry);
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MP_SUB_BORROW(r0, r3b, r0, 0, carry);
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MP_SUB_BORROW(r1, 0, r1, carry, carry);
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MP_SUB_BORROW(r2, 0, r2, carry, carry);
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MP_SUB_BORROW(r3, 0, r3, carry, carry);
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r3b = (int)(r3 >>32);
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MP_ADD_CARRY (r0, 1, r0, 0, carry);
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MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
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MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
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MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
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r3b = (int)(r3 >>32);
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/* check for final reduction */
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/* now the only way we are over is if the top 4 words are all ones */
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if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
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&& ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
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((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
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/* one last subraction */
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MP_SUB_BORROW(r0, 1, r0, 0, carry);
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MP_SUB_BORROW(r1, 0, r1, carry, carry);
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MP_CHECKOK(s_mp_pad(r, 4));
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/* set the lower words of r */
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MP_SIGN(r) = MP_ZPOS;
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/* Compute the square of polynomial a, reduce modulo p224. Store the
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* result in r. r could be a. Uses optimized modular reduction for p224.
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ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
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mp_err res = MP_OKAY;
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MP_CHECKOK(mp_sqr(a, r));
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MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
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/* Compute the product of two polynomials a and b, reduce modulo p224.
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* Store the result in r. r could be a or b; a could be b. Uses
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* optimized modular reduction for p224. */
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ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
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const GFMethod *meth)
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mp_err res = MP_OKAY;
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MP_CHECKOK(mp_mul(a, b, r));
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MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
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/* Divides two field elements. If a is NULL, then returns the inverse of
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ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
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const GFMethod *meth)
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mp_err res = MP_OKAY;
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/* If a is NULL, then return the inverse of b, otherwise return a/b. */
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return mp_invmod(b, &meth->irr, r);
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/* MPI doesn't support divmod, so we implement it using invmod and
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MP_CHECKOK(mp_init(&t));
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MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
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MP_CHECKOK(mp_mul(a, &t, r));
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MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
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/* Wire in fast field arithmetic and precomputation of base point for
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ec_group_set_gfp224(ECGroup *group, ECCurveName name)
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if (name == ECCurve_NIST_P224) {
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group->meth->field_mod = &ec_GFp_nistp224_mod;
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group->meth->field_mul = &ec_GFp_nistp224_mul;
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group->meth->field_sqr = &ec_GFp_nistp224_sqr;
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group->meth->field_div = &ec_GFp_nistp224_div;