X-Git-Url: https://git.openssl.org/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fec%2Fecp_nistp224.c;h=98967275addae398332159d8401166b9c632b9b1;hp=90c3589bdfc4d4d45c0b167d3447627545e26767;hb=6afed267db47a8aa604a3a9e78ac72efa02363df;hpb=30fafdebf34ba8823bc3e528e0a310fc0384b188 diff --git a/crypto/ec/ecp_nistp224.c b/crypto/ec/ecp_nistp224.c index 90c3589bdf..98967275ad 100644 --- a/crypto/ec/ecp_nistp224.c +++ b/crypto/ec/ecp_nistp224.c @@ -1,59 +1,26 @@ -/* crypto/ec/ecp_nistp224.c */ /* - * Written by Emilia Kasper (Google) for the OpenSSL project. - */ -/* ==================================================================== - * Copyright (c) 2000-2010 The OpenSSL Project. All rights reserved. - * - * Redistribution and use in source and binary forms, with or without - * modification, are permitted provided that the following conditions - * are met: - * - * 1. Redistributions of source code must retain the above copyright - * notice, this list of conditions and the following disclaimer. - * - * 2. Redistributions in binary form must reproduce the above copyright - * notice, this list of conditions and the following disclaimer in - * the documentation and/or other materials provided with the - * distribution. + * Copyright 2010-2017 The OpenSSL Project Authors. All Rights Reserved. * - * 3. All advertising materials mentioning features or use of this - * software must display the following acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" - * - * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to - * endorse or promote products derived from this software without - * prior written permission. For written permission, please contact - * licensing@OpenSSL.org. - * - * 5. Products derived from this software may not be called "OpenSSL" - * nor may "OpenSSL" appear in their names without prior written - * permission of the OpenSSL Project. + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +/* Copyright 2011 Google Inc. * - * 6. Redistributions of any form whatsoever must retain the following - * acknowledgment: - * "This product includes software developed by the OpenSSL Project - * for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" + * Licensed under the Apache License, Version 2.0 (the "License"); * - * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY - * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE - * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR - * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR - * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, - * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT - * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; - * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) - * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, - * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) - * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED - * OF THE POSSIBILITY OF SUCH DAMAGE. - * ==================================================================== + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at * - * This product includes cryptographic software written by Eric Young - * (eay@cryptsoft.com). This product includes software written by Tim - * Hudson (tjh@cryptsoft.com). + * http://www.apache.org/licenses/LICENSE-2.0 * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. */ /* @@ -62,238 +29,339 @@ * Inspired by Daniel J. Bernstein's public domain nistp224 implementation * and Adam Langley's public domain 64-bit C implementation of curve25519 */ + #include -#ifndef OPENSSL_NO_EC_NISTP224_64_GCC_128 -#include -#include -#include -#include "ec_lcl.h" +#ifdef OPENSSL_NO_EC_NISTP_64_GCC_128 +NON_EMPTY_TRANSLATION_UNIT +#else -#if defined(__GNUC__) && (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 1)) +# include +# include +# include +# include "ec_lcl.h" + +# if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__==16 /* even with gcc, the typedef won't work for 32-bit platforms */ - typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit platforms */ -#else - #error "Need GCC 3.1 or later to define type uint128_t" -#endif +typedef __uint128_t uint128_t; /* nonstandard; implemented by gcc on 64-bit + * platforms */ +# else +# error "Need GCC 4.0 or later to define type uint128_t" +# endif typedef uint8_t u8; - +typedef uint64_t u64; /******************************************************************************/ -/* INTERNAL REPRESENTATION OF FIELD ELEMENTS +/*- + * INTERNAL REPRESENTATION OF FIELD ELEMENTS * * Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 - * where each slice a_i is a 64-bit word, i.e., a field element is an fslice - * array a with 4 elements, where a[i] = a_i. - * Outputs from multiplications are represented as unreduced polynomials + * using 64-bit coefficients called 'limbs', + * and sometimes (for multiplication results) as * b_0 + 2^56*b_1 + 2^112*b_2 + 2^168*b_3 + 2^224*b_4 + 2^280*b_5 + 2^336*b_6 - * where each b_i is a 128-bit word. We ensure that inputs to each field + * using 128-bit coefficients called 'widelimbs'. + * A 4-limb representation is an 'felem'; + * a 7-widelimb representation is a 'widefelem'. + * Even within felems, bits of adjacent limbs overlap, and we don't always + * reduce the representations: we ensure that inputs to each felem * multiplication satisfy a_i < 2^60, so outputs satisfy b_i < 4*2^60*2^60, * and fit into a 128-bit word without overflow. The coefficients are then - * again partially reduced to a_i < 2^57. We only reduce to the unique minimal - * representation at the end of the computation. - * + * again partially reduced to obtain an felem satisfying a_i < 2^57. + * We only reduce to the unique minimal representation at the end of the + * computation. */ -typedef uint64_t fslice; +typedef uint64_t limb; +typedef uint128_t widelimb; + +typedef limb felem[4]; +typedef widelimb widefelem[7]; -/* Field element represented as a byte arrary. - * 28*8 = 224 bits is also the group order size for the elliptic curve. */ +/* + * Field element represented as a byte array. 28*8 = 224 bits is also the + * group order size for the elliptic curve, and we also use this type for + * scalars for point multiplication. + */ typedef u8 felem_bytearray[28]; static const felem_bytearray nistp224_curve_params[5] = { - {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* p */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0x00,0x00,0x00,0x00, - 0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x01}, - {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF, /* a */ - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFF,0xFF, - 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE}, - {0xB4,0x05,0x0A,0x85,0x0C,0x04,0xB3,0xAB,0xF5,0x41, /* b */ - 0x32,0x56,0x50,0x44,0xB0,0xB7,0xD7,0xBF,0xD8,0xBA, - 0x27,0x0B,0x39,0x43,0x23,0x55,0xFF,0xB4}, - {0xB7,0x0E,0x0C,0xBD,0x6B,0xB4,0xBF,0x7F,0x32,0x13, /* x */ - 0x90,0xB9,0x4A,0x03,0xC1,0xD3,0x56,0xC2,0x11,0x22, - 0x34,0x32,0x80,0xD6,0x11,0x5C,0x1D,0x21}, - {0xbd,0x37,0x63,0x88,0xb5,0xf7,0x23,0xfb,0x4c,0x22, /* y */ - 0xdf,0xe6,0xcd,0x43,0x75,0xa0,0x5a,0x07,0x47,0x64, - 0x44,0xd5,0x81,0x99,0x85,0x00,0x7e,0x34} + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* p */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0x00, 0x00, 0x00, 0x00, + 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}, + {0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, /* a */ + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF, + 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE}, + {0xB4, 0x05, 0x0A, 0x85, 0x0C, 0x04, 0xB3, 0xAB, 0xF5, 0x41, /* b */ + 0x32, 0x56, 0x50, 0x44, 0xB0, 0xB7, 0xD7, 0xBF, 0xD8, 0xBA, + 0x27, 0x0B, 0x39, 0x43, 0x23, 0x55, 0xFF, 0xB4}, + {0xB7, 0x0E, 0x0C, 0xBD, 0x6B, 0xB4, 0xBF, 0x7F, 0x32, 0x13, /* x */ + 0x90, 0xB9, 0x4A, 0x03, 0xC1, 0xD3, 0x56, 0xC2, 0x11, 0x22, + 0x34, 0x32, 0x80, 0xD6, 0x11, 0x5C, 0x1D, 0x21}, + {0xbd, 0x37, 0x63, 0x88, 0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, /* y */ + 0xdf, 0xe6, 0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64, + 0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34} }; -/* Precomputed multiples of the standard generator - * b_0*G + b_1*2^56*G + b_2*2^112*G + b_3*2^168*G for - * (b_3, b_2, b_1, b_0) in [0,15], i.e., gmul[0] = point_at_infinity, - * gmul[1] = G, gmul[2] = 2^56*G, gmul[3] = 2^56*G + G, etc. - * Points are given in Jacobian projective coordinates: words 0-3 represent the - * X-coordinate (slice a_0 is word 0, etc.), words 4-7 represent the - * Y-coordinate and words 8-11 represent the Z-coordinate. */ -static const fslice gmul[16][3][4] = { - {{0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, - {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}, - {0x00000000000000, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, - {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, - {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, - {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, - {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, - {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, - {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, - {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, - {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, - {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, - {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, - {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, - {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, - {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, - {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}}, - {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, - {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, - {0x00000000000001, 0x00000000000000, 0x00000000000000, 0x00000000000000}} +/*- + * Precomputed multiples of the standard generator + * Points are given in coordinates (X, Y, Z) where Z normally is 1 + * (0 for the point at infinity). + * For each field element, slice a_0 is word 0, etc. + * + * The table has 2 * 16 elements, starting with the following: + * index | bits | point + * ------+---------+------------------------------ + * 0 | 0 0 0 0 | 0G + * 1 | 0 0 0 1 | 1G + * 2 | 0 0 1 0 | 2^56G + * 3 | 0 0 1 1 | (2^56 + 1)G + * 4 | 0 1 0 0 | 2^112G + * 5 | 0 1 0 1 | (2^112 + 1)G + * 6 | 0 1 1 0 | (2^112 + 2^56)G + * 7 | 0 1 1 1 | (2^112 + 2^56 + 1)G + * 8 | 1 0 0 0 | 2^168G + * 9 | 1 0 0 1 | (2^168 + 1)G + * 10 | 1 0 1 0 | (2^168 + 2^56)G + * 11 | 1 0 1 1 | (2^168 + 2^56 + 1)G + * 12 | 1 1 0 0 | (2^168 + 2^112)G + * 13 | 1 1 0 1 | (2^168 + 2^112 + 1)G + * 14 | 1 1 1 0 | (2^168 + 2^112 + 2^56)G + * 15 | 1 1 1 1 | (2^168 + 2^112 + 2^56 + 1)G + * followed by a copy of this with each element multiplied by 2^28. + * + * The reason for this is so that we can clock bits into four different + * locations when doing simple scalar multiplies against the base point, + * and then another four locations using the second 16 elements. + */ +static const felem gmul[2][16][3] = { +{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x3280d6115c1d21, 0xc1d356c2112234, 0x7f321390b94a03, 0xb70e0cbd6bb4bf}, + {0xd5819985007e34, 0x75a05a07476444, 0xfb4c22dfe6cd43, 0xbd376388b5f723}, + {1, 0, 0, 0}}, + {{0xfd9675666ebbe9, 0xbca7664d40ce5e, 0x2242df8d8a2a43, 0x1f49bbb0f99bc5}, + {0x29e0b892dc9c43, 0xece8608436e662, 0xdc858f185310d0, 0x9812dd4eb8d321}, + {1, 0, 0, 0}}, + {{0x6d3e678d5d8eb8, 0x559eed1cb362f1, 0x16e9a3bbce8a3f, 0xeedcccd8c2a748}, + {0xf19f90ed50266d, 0xabf2b4bf65f9df, 0x313865468fafec, 0x5cb379ba910a17}, + {1, 0, 0, 0}}, + {{0x0641966cab26e3, 0x91fb2991fab0a0, 0xefec27a4e13a0b, 0x0499aa8a5f8ebe}, + {0x7510407766af5d, 0x84d929610d5450, 0x81d77aae82f706, 0x6916f6d4338c5b}, + {1, 0, 0, 0}}, + {{0xea95ac3b1f15c6, 0x086000905e82d4, 0xdd323ae4d1c8b1, 0x932b56be7685a3}, + {0x9ef93dea25dbbf, 0x41665960f390f0, 0xfdec76dbe2a8a7, 0x523e80f019062a}, + {1, 0, 0, 0}}, + {{0x822fdd26732c73, 0xa01c83531b5d0f, 0x363f37347c1ba4, 0xc391b45c84725c}, + {0xbbd5e1b2d6ad24, 0xddfbcde19dfaec, 0xc393da7e222a7f, 0x1efb7890ede244}, + {1, 0, 0, 0}}, + {{0x4c9e90ca217da1, 0xd11beca79159bb, 0xff8d33c2c98b7c, 0x2610b39409f849}, + {0x44d1352ac64da0, 0xcdbb7b2c46b4fb, 0x966c079b753c89, 0xfe67e4e820b112}, + {1, 0, 0, 0}}, + {{0xe28cae2df5312d, 0xc71b61d16f5c6e, 0x79b7619a3e7c4c, 0x05c73240899b47}, + {0x9f7f6382c73e3a, 0x18615165c56bda, 0x641fab2116fd56, 0x72855882b08394}, + {1, 0, 0, 0}}, + {{0x0469182f161c09, 0x74a98ca8d00fb5, 0xb89da93489a3e0, 0x41c98768fb0c1d}, + {0xe5ea05fb32da81, 0x3dce9ffbca6855, 0x1cfe2d3fbf59e6, 0x0e5e03408738a7}, + {1, 0, 0, 0}}, + {{0xdab22b2333e87f, 0x4430137a5dd2f6, 0xe03ab9f738beb8, 0xcb0c5d0dc34f24}, + {0x764a7df0c8fda5, 0x185ba5c3fa2044, 0x9281d688bcbe50, 0xc40331df893881}, + {1, 0, 0, 0}}, + {{0xb89530796f0f60, 0xade92bd26909a3, 0x1a0c83fb4884da, 0x1765bf22a5a984}, + {0x772a9ee75db09e, 0x23bc6c67cec16f, 0x4c1edba8b14e2f, 0xe2a215d9611369}, + {1, 0, 0, 0}}, + {{0x571e509fb5efb3, 0xade88696410552, 0xc8ae85fada74fe, 0x6c7e4be83bbde3}, + {0xff9f51160f4652, 0xb47ce2495a6539, 0xa2946c53b582f4, 0x286d2db3ee9a60}, + {1, 0, 0, 0}}, + {{0x40bbd5081a44af, 0x0995183b13926c, 0xbcefba6f47f6d0, 0x215619e9cc0057}, + {0x8bc94d3b0df45e, 0xf11c54a3694f6f, 0x8631b93cdfe8b5, 0xe7e3f4b0982db9}, + {1, 0, 0, 0}}, + {{0xb17048ab3e1c7b, 0xac38f36ff8a1d8, 0x1c29819435d2c6, 0xc813132f4c07e9}, + {0x2891425503b11f, 0x08781030579fea, 0xf5426ba5cc9674, 0x1e28ebf18562bc}, + {1, 0, 0, 0}}, + {{0x9f31997cc864eb, 0x06cd91d28b5e4c, 0xff17036691a973, 0xf1aef351497c58}, + {0xdd1f2d600564ff, 0xdead073b1402db, 0x74a684435bd693, 0xeea7471f962558}, + {1, 0, 0, 0}}}, +{{{0, 0, 0, 0}, + {0, 0, 0, 0}, + {0, 0, 0, 0}}, + {{0x9665266dddf554, 0x9613d78b60ef2d, 0xce27a34cdba417, 0xd35ab74d6afc31}, + {0x85ccdd22deb15e, 0x2137e5783a6aab, 0xa141cffd8c93c6, 0x355a1830e90f2d}, + {1, 0, 0, 0}}, + {{0x1a494eadaade65, 0xd6da4da77fe53c, 0xe7992996abec86, 0x65c3553c6090e3}, + {0xfa610b1fb09346, 0xf1c6540b8a4aaf, 0xc51a13ccd3cbab, 0x02995b1b18c28a}, + {1, 0, 0, 0}}, + {{0x7874568e7295ef, 0x86b419fbe38d04, 0xdc0690a7550d9a, 0xd3966a44beac33}, + {0x2b7280ec29132f, 0xbeaa3b6a032df3, 0xdc7dd88ae41200, 0xd25e2513e3a100}, + {1, 0, 0, 0}}, + {{0x924857eb2efafd, 0xac2bce41223190, 0x8edaa1445553fc, 0x825800fd3562d5}, + {0x8d79148ea96621, 0x23a01c3dd9ed8d, 0xaf8b219f9416b5, 0xd8db0cc277daea}, + {1, 0, 0, 0}}, + {{0x76a9c3b1a700f0, 0xe9acd29bc7e691, 0x69212d1a6b0327, 0x6322e97fe154be}, + {0x469fc5465d62aa, 0x8d41ed18883b05, 0x1f8eae66c52b88, 0xe4fcbe9325be51}, + {1, 0, 0, 0}}, + {{0x825fdf583cac16, 0x020b857c7b023a, 0x683c17744b0165, 0x14ffd0a2daf2f1}, + {0x323b36184218f9, 0x4944ec4e3b47d4, 0xc15b3080841acf, 0x0bced4b01a28bb}, + {1, 0, 0, 0}}, + {{0x92ac22230df5c4, 0x52f33b4063eda8, 0xcb3f19870c0c93, 0x40064f2ba65233}, + {0xfe16f0924f8992, 0x012da25af5b517, 0x1a57bb24f723a6, 0x06f8bc76760def}, + {1, 0, 0, 0}}, + {{0x4a7084f7817cb9, 0xbcab0738ee9a78, 0x3ec11e11d9c326, 0xdc0fe90e0f1aae}, + {0xcf639ea5f98390, 0x5c350aa22ffb74, 0x9afae98a4047b7, 0x956ec2d617fc45}, + {1, 0, 0, 0}}, + {{0x4306d648c1be6a, 0x9247cd8bc9a462, 0xf5595e377d2f2e, 0xbd1c3caff1a52e}, + {0x045e14472409d0, 0x29f3e17078f773, 0x745a602b2d4f7d, 0x191837685cdfbb}, + {1, 0, 0, 0}}, + {{0x5b6ee254a8cb79, 0x4953433f5e7026, 0xe21faeb1d1def4, 0xc4c225785c09de}, + {0x307ce7bba1e518, 0x31b125b1036db8, 0x47e91868839e8f, 0xc765866e33b9f3}, + {1, 0, 0, 0}}, + {{0x3bfece24f96906, 0x4794da641e5093, 0xde5df64f95db26, 0x297ecd89714b05}, + {0x701bd3ebb2c3aa, 0x7073b4f53cb1d5, 0x13c5665658af16, 0x9895089d66fe58}, + {1, 0, 0, 0}}, + {{0x0fef05f78c4790, 0x2d773633b05d2e, 0x94229c3a951c94, 0xbbbd70df4911bb}, + {0xb2c6963d2c1168, 0x105f47a72b0d73, 0x9fdf6111614080, 0x7b7e94b39e67b0}, + {1, 0, 0, 0}}, + {{0xad1a7d6efbe2b3, 0xf012482c0da69d, 0x6b3bdf12438345, 0x40d7558d7aa4d9}, + {0x8a09fffb5c6d3d, 0x9a356e5d9ffd38, 0x5973f15f4f9b1c, 0xdcd5f59f63c3ea}, + {1, 0, 0, 0}}, + {{0xacf39f4c5ca7ab, 0x4c8071cc5fd737, 0xc64e3602cd1184, 0x0acd4644c9abba}, + {0x6c011a36d8bf6e, 0xfecd87ba24e32a, 0x19f6f56574fad8, 0x050b204ced9405}, + {1, 0, 0, 0}}, + {{0xed4f1cae7d9a96, 0x5ceef7ad94c40a, 0x778e4a3bf3ef9b, 0x7405783dc3b55e}, + {0x32477c61b6e8c6, 0xb46a97570f018b, 0x91176d0a7e95d1, 0x3df90fbc4c7d0e}, + {1, 0, 0, 0}}} }; /* Precomputation for the group generator. */ -typedef struct { - fslice g_pre_comp[16][3][4]; - int references; -} NISTP224_PRE_COMP; +struct nistp224_pre_comp_st { + felem g_pre_comp[2][16][3]; + CRYPTO_REF_COUNT references; + CRYPTO_RWLOCK *lock; +}; const EC_METHOD *EC_GFp_nistp224_method(void) - { - static const EC_METHOD ret = { - NID_X9_62_prime_field, - ec_GFp_nistp224_group_init, - ec_GFp_simple_group_finish, - ec_GFp_simple_group_clear_finish, - ec_GFp_nist_group_copy, - ec_GFp_nistp224_group_set_curve, - ec_GFp_simple_group_get_curve, - ec_GFp_simple_group_get_degree, - ec_GFp_simple_group_check_discriminant, - ec_GFp_simple_point_init, - ec_GFp_simple_point_finish, - ec_GFp_simple_point_clear_finish, - ec_GFp_simple_point_copy, - ec_GFp_simple_point_set_to_infinity, - ec_GFp_simple_set_Jprojective_coordinates_GFp, - ec_GFp_simple_get_Jprojective_coordinates_GFp, - ec_GFp_simple_point_set_affine_coordinates, - ec_GFp_nistp224_point_get_affine_coordinates, - ec_GFp_simple_set_compressed_coordinates, - ec_GFp_simple_point2oct, - ec_GFp_simple_oct2point, - ec_GFp_simple_add, - ec_GFp_simple_dbl, - ec_GFp_simple_invert, - ec_GFp_simple_is_at_infinity, - ec_GFp_simple_is_on_curve, - ec_GFp_simple_cmp, - ec_GFp_simple_make_affine, - ec_GFp_simple_points_make_affine, - ec_GFp_nistp224_points_mul, - ec_GFp_nistp224_precompute_mult, - ec_GFp_nistp224_have_precompute_mult, - ec_GFp_nist_field_mul, - ec_GFp_nist_field_sqr, - 0 /* field_div */, - 0 /* field_encode */, - 0 /* field_decode */, - 0 /* field_set_to_one */ }; - - return &ret; - } - -/* Helper functions to convert field elements to/from internal representation */ -static void bin28_to_felem(fslice out[4], const u8 in[28]) - { - out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; - out[1] = (*((const uint64_t *)(in+7))) & 0x00ffffffffffffff; - out[2] = (*((const uint64_t *)(in+14))) & 0x00ffffffffffffff; - out[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff; - } - -static void felem_to_bin28(u8 out[28], const fslice in[4]) - { - unsigned i; - for (i = 0; i < 7; ++i) - { - out[i] = in[0]>>(8*i); - out[i+7] = in[1]>>(8*i); - out[i+14] = in[2]>>(8*i); - out[i+21] = in[3]>>(8*i); - } - } +{ + static const EC_METHOD ret = { + EC_FLAGS_DEFAULT_OCT, + NID_X9_62_prime_field, + ec_GFp_nistp224_group_init, + ec_GFp_simple_group_finish, + ec_GFp_simple_group_clear_finish, + ec_GFp_nist_group_copy, + ec_GFp_nistp224_group_set_curve, + ec_GFp_simple_group_get_curve, + ec_GFp_simple_group_get_degree, + ec_group_simple_order_bits, + ec_GFp_simple_group_check_discriminant, + ec_GFp_simple_point_init, + ec_GFp_simple_point_finish, + ec_GFp_simple_point_clear_finish, + ec_GFp_simple_point_copy, + ec_GFp_simple_point_set_to_infinity, + ec_GFp_simple_set_Jprojective_coordinates_GFp, + ec_GFp_simple_get_Jprojective_coordinates_GFp, + ec_GFp_simple_point_set_affine_coordinates, + ec_GFp_nistp224_point_get_affine_coordinates, + 0 /* point_set_compressed_coordinates */ , + 0 /* point2oct */ , + 0 /* oct2point */ , + ec_GFp_simple_add, + ec_GFp_simple_dbl, + ec_GFp_simple_invert, + ec_GFp_simple_is_at_infinity, + ec_GFp_simple_is_on_curve, + ec_GFp_simple_cmp, + ec_GFp_simple_make_affine, + ec_GFp_simple_points_make_affine, + ec_GFp_nistp224_points_mul, + ec_GFp_nistp224_precompute_mult, + ec_GFp_nistp224_have_precompute_mult, + ec_GFp_nist_field_mul, + ec_GFp_nist_field_sqr, + 0 /* field_div */ , + 0 /* field_encode */ , + 0 /* field_decode */ , + 0, /* field_set_to_one */ + ec_key_simple_priv2oct, + ec_key_simple_oct2priv, + 0, /* set private */ + ec_key_simple_generate_key, + ec_key_simple_check_key, + ec_key_simple_generate_public_key, + 0, /* keycopy */ + 0, /* keyfinish */ + ecdh_simple_compute_key + }; + + return &ret; +} + +/* + * Helper functions to convert field elements to/from internal representation + */ +static void bin28_to_felem(felem out, const u8 in[28]) +{ + out[0] = *((const uint64_t *)(in)) & 0x00ffffffffffffff; + out[1] = (*((const uint64_t *)(in + 7))) & 0x00ffffffffffffff; + out[2] = (*((const uint64_t *)(in + 14))) & 0x00ffffffffffffff; + out[3] = (*((const uint64_t *)(in+20))) >> 8; +} + +static void felem_to_bin28(u8 out[28], const felem in) +{ + unsigned i; + for (i = 0; i < 7; ++i) { + out[i] = in[0] >> (8 * i); + out[i + 7] = in[1] >> (8 * i); + out[i + 14] = in[2] >> (8 * i); + out[i + 21] = in[3] >> (8 * i); + } +} /* To preserve endianness when using BN_bn2bin and BN_bin2bn */ static void flip_endian(u8 *out, const u8 *in, unsigned len) - { - unsigned i; - for (i = 0; i < len; ++i) - out[i] = in[len-1-i]; - } +{ + unsigned i; + for (i = 0; i < len; ++i) + out[i] = in[len - 1 - i]; +} /* From OpenSSL BIGNUM to internal representation */ -static int BN_to_felem(fslice out[4], const BIGNUM *bn) - { - felem_bytearray b_in; - felem_bytearray b_out; - unsigned num_bytes; - - /* BN_bn2bin eats leading zeroes */ - memset(b_out, 0, sizeof b_out); - num_bytes = BN_num_bytes(bn); - if (num_bytes > sizeof b_out) - { - ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); - return 0; - } - if (BN_is_negative(bn)) - { - ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); - return 0; - } - num_bytes = BN_bn2bin(bn, b_in); - flip_endian(b_out, b_in, num_bytes); - bin28_to_felem(out, b_out); - return 1; - } +static int BN_to_felem(felem out, const BIGNUM *bn) +{ + felem_bytearray b_in; + felem_bytearray b_out; + unsigned num_bytes; + + /* BN_bn2bin eats leading zeroes */ + memset(b_out, 0, sizeof(b_out)); + num_bytes = BN_num_bytes(bn); + if (num_bytes > sizeof(b_out)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + if (BN_is_negative(bn)) { + ECerr(EC_F_BN_TO_FELEM, EC_R_BIGNUM_OUT_OF_RANGE); + return 0; + } + num_bytes = BN_bn2bin(bn, b_in); + flip_endian(b_out, b_in, num_bytes); + bin28_to_felem(out, b_out); + return 1; +} /* From internal representation to OpenSSL BIGNUM */ -static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4]) - { - felem_bytearray b_in, b_out; - felem_to_bin28(b_in, in); - flip_endian(b_out, b_in, sizeof b_out); - return BN_bin2bn(b_out, sizeof b_out, out); - } +static BIGNUM *felem_to_BN(BIGNUM *out, const felem in) +{ + felem_bytearray b_in, b_out; + felem_to_bin28(b_in, in); + flip_endian(b_out, b_in, sizeof(b_out)); + return BN_bin2bn(b_out, sizeof(b_out), out); +} /******************************************************************************/ -/* FIELD OPERATIONS +/*- + * FIELD OPERATIONS * * Field operations, using the internal representation of field elements. * NB! These operations are specific to our point multiplication and cannot be @@ -302,407 +370,442 @@ static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4]) * */ +static void felem_one(felem out) +{ + out[0] = 1; + out[1] = 0; + out[2] = 0; + out[3] = 0; +} + +static void felem_assign(felem out, const felem in) +{ + out[0] = in[0]; + out[1] = in[1]; + out[2] = in[2]; + out[3] = in[3]; +} + /* Sum two field elements: out += in */ -static void felem_sum64(fslice out[4], const fslice in[4]) - { - out[0] += in[0]; - out[1] += in[1]; - out[2] += in[2]; - out[3] += in[3]; - } +static void felem_sum(felem out, const felem in) +{ + out[0] += in[0]; + out[1] += in[1]; + out[2] += in[2]; + out[3] += in[3]; +} + +/* Get negative value: out = -in */ +/* Assumes in[i] < 2^57 */ +static void felem_neg(felem out, const felem in) +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Set to 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] = two58p2 - in[0]; + out[1] = two58m42m2 - in[1]; + out[2] = two58m2 - in[2]; + out[3] = two58m2 - in[3]; +} /* Subtract field elements: out -= in */ /* Assumes in[i] < 2^57 */ -static void felem_diff64(fslice out[4], const fslice in[4]) - { - static const uint64_t two58p2 = (((uint64_t) 1) << 58) + (((uint64_t) 1) << 2); - static const uint64_t two58m2 = (((uint64_t) 1) << 58) - (((uint64_t) 1) << 2); - static const uint64_t two58m42m2 = (((uint64_t) 1) << 58) - - (((uint64_t) 1) << 42) - (((uint64_t) 1) << 2); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two58p2; - out[1] += two58m42m2; - out[2] += two58m2; - out[3] += two58m2; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } - -/* Subtract in unreduced 128-bit mode: out128 -= in128 */ +static void felem_diff(felem out, const felem in) +{ + static const limb two58p2 = (((limb) 1) << 58) + (((limb) 1) << 2); + static const limb two58m2 = (((limb) 1) << 58) - (((limb) 1) << 2); + static const limb two58m42m2 = (((limb) 1) << 58) - + (((limb) 1) << 42) - (((limb) 1) << 2); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two58p2; + out[1] += two58m42m2; + out[2] += two58m2; + out[3] += two58m2; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/* Subtract in unreduced 128-bit mode: out -= in */ /* Assumes in[i] < 2^119 */ -static void felem_diff128(uint128_t out[7], const uint128_t in[4]) - { - static const uint128_t two120 = ((uint128_t) 1) << 120; - static const uint128_t two120m64 = (((uint128_t) 1) << 120) - - (((uint128_t) 1) << 64); - static const uint128_t two120m104m64 = (((uint128_t) 1) << 120) - - (((uint128_t) 1) << 104) - (((uint128_t) 1) << 64); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two120; - out[1] += two120m64; - out[2] += two120m64; - out[3] += two120; - out[4] += two120m104m64; - out[5] += two120m64; - out[6] += two120m64; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - out[4] -= in[4]; - out[5] -= in[5]; - out[6] -= in[6]; - } +static void widefelem_diff(widefelem out, const widefelem in) +{ + static const widelimb two120 = ((widelimb) 1) << 120; + static const widelimb two120m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 64); + static const widelimb two120m104m64 = (((widelimb) 1) << 120) - + (((widelimb) 1) << 104) - (((widelimb) 1) << 64); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two120; + out[1] += two120m64; + out[2] += two120m64; + out[3] += two120; + out[4] += two120m104m64; + out[5] += two120m64; + out[6] += two120m64; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; + out[4] -= in[4]; + out[5] -= in[5]; + out[6] -= in[6]; +} /* Subtract in mixed mode: out128 -= in64 */ /* in[i] < 2^63 */ -static void felem_diff_128_64(uint128_t out[7], const fslice in[4]) - { - static const uint128_t two64p8 = (((uint128_t) 1) << 64) + - (((uint128_t) 1) << 8); - static const uint128_t two64m8 = (((uint128_t) 1) << 64) - - (((uint128_t) 1) << 8); - static const uint128_t two64m48m8 = (((uint128_t) 1) << 64) - - (((uint128_t) 1) << 48) - (((uint128_t) 1) << 8); - - /* Add 0 mod 2^224-2^96+1 to ensure out > in */ - out[0] += two64p8; - out[1] += two64m48m8; - out[2] += two64m8; - out[3] += two64m8; - - out[0] -= in[0]; - out[1] -= in[1]; - out[2] -= in[2]; - out[3] -= in[3]; - } - -/* Multiply a field element by a scalar: out64 = out64 * scalar - * The scalars we actually use are small, so results fit without overflow */ -static void felem_scalar64(fslice out[4], const fslice scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - } - -/* Multiply an unreduced field element by a scalar: out128 = out128 * scalar - * The scalars we actually use are small, so results fit without overflow */ -static void felem_scalar128(uint128_t out[7], const uint128_t scalar) - { - out[0] *= scalar; - out[1] *= scalar; - out[2] *= scalar; - out[3] *= scalar; - out[4] *= scalar; - out[5] *= scalar; - out[6] *= scalar; - } +static void felem_diff_128_64(widefelem out, const felem in) +{ + static const widelimb two64p8 = (((widelimb) 1) << 64) + + (((widelimb) 1) << 8); + static const widelimb two64m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 8); + static const widelimb two64m48m8 = (((widelimb) 1) << 64) - + (((widelimb) 1) << 48) - (((widelimb) 1) << 8); + + /* Add 0 mod 2^224-2^96+1 to ensure out > in */ + out[0] += two64p8; + out[1] += two64m48m8; + out[2] += two64m8; + out[3] += two64m8; + + out[0] -= in[0]; + out[1] -= in[1]; + out[2] -= in[2]; + out[3] -= in[3]; +} + +/* + * Multiply a field element by a scalar: out = out * scalar The scalars we + * actually use are small, so results fit without overflow + */ +static void felem_scalar(felem out, const limb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; +} + +/* + * Multiply an unreduced field element by a scalar: out = out * scalar The + * scalars we actually use are small, so results fit without overflow + */ +static void widefelem_scalar(widefelem out, const widelimb scalar) +{ + out[0] *= scalar; + out[1] *= scalar; + out[2] *= scalar; + out[3] *= scalar; + out[4] *= scalar; + out[5] *= scalar; + out[6] *= scalar; +} /* Square a field element: out = in^2 */ -static void felem_square(uint128_t out[7], const fslice in[4]) - { - out[0] = ((uint128_t) in[0]) * in[0]; - out[1] = ((uint128_t) in[0]) * in[1] * 2; - out[2] = ((uint128_t) in[0]) * in[2] * 2 + ((uint128_t) in[1]) * in[1]; - out[3] = ((uint128_t) in[0]) * in[3] * 2 + - ((uint128_t) in[1]) * in[2] * 2; - out[4] = ((uint128_t) in[1]) * in[3] * 2 + ((uint128_t) in[2]) * in[2]; - out[5] = ((uint128_t) in[2]) * in[3] * 2; - out[6] = ((uint128_t) in[3]) * in[3]; - } +static void felem_square(widefelem out, const felem in) +{ + limb tmp0, tmp1, tmp2; + tmp0 = 2 * in[0]; + tmp1 = 2 * in[1]; + tmp2 = 2 * in[2]; + out[0] = ((widelimb) in[0]) * in[0]; + out[1] = ((widelimb) in[0]) * tmp1; + out[2] = ((widelimb) in[0]) * tmp2 + ((widelimb) in[1]) * in[1]; + out[3] = ((widelimb) in[3]) * tmp0 + ((widelimb) in[1]) * tmp2; + out[4] = ((widelimb) in[3]) * tmp1 + ((widelimb) in[2]) * in[2]; + out[5] = ((widelimb) in[3]) * tmp2; + out[6] = ((widelimb) in[3]) * in[3]; +} /* Multiply two field elements: out = in1 * in2 */ -static void felem_mul(uint128_t out[7], const fslice in1[4], const fslice in2[4]) - { - out[0] = ((uint128_t) in1[0]) * in2[0]; - out[1] = ((uint128_t) in1[0]) * in2[1] + ((uint128_t) in1[1]) * in2[0]; - out[2] = ((uint128_t) in1[0]) * in2[2] + ((uint128_t) in1[1]) * in2[1] + - ((uint128_t) in1[2]) * in2[0]; - out[3] = ((uint128_t) in1[0]) * in2[3] + ((uint128_t) in1[1]) * in2[2] + - ((uint128_t) in1[2]) * in2[1] + ((uint128_t) in1[3]) * in2[0]; - out[4] = ((uint128_t) in1[1]) * in2[3] + ((uint128_t) in1[2]) * in2[2] + - ((uint128_t) in1[3]) * in2[1]; - out[5] = ((uint128_t) in1[2]) * in2[3] + ((uint128_t) in1[3]) * in2[2]; - out[6] = ((uint128_t) in1[3]) * in2[3]; - } - -/* Reduce 128-bit coefficients to 64-bit coefficients. Requires in[i] < 2^126, - * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] < 2^57 */ -static void felem_reduce(fslice out[4], const uint128_t in[7]) - { - static const uint128_t two127p15 = (((uint128_t) 1) << 127) + - (((uint128_t) 1) << 15); - static const uint128_t two127m71 = (((uint128_t) 1) << 127) - - (((uint128_t) 1) << 71); - static const uint128_t two127m71m55 = (((uint128_t) 1) << 127) - - (((uint128_t) 1) << 71) - (((uint128_t) 1) << 55); - uint128_t output[5]; - - /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ - output[0] = in[0] + two127p15; - output[1] = in[1] + two127m71m55; - output[2] = in[2] + two127m71; - output[3] = in[3]; - output[4] = in[4]; - - /* Eliminate in[4], in[5], in[6] */ - output[4] += in[6] >> 16; - output[3] += (in[6]&0xffff) << 40; - output[2] -= in[6]; - - output[3] += in[5] >> 16; - output[2] += (in[5]&0xffff) << 40; - output[1] -= in[5]; - - output[2] += output[4] >> 16; - output[1] += (output[4]&0xffff) << 40; - output[0] -= output[4]; - output[4] = 0; - - /* Carry 2 -> 3 -> 4 */ - output[3] += output[2] >> 56; - output[2] &= 0x00ffffffffffffff; - - output[4] += output[3] >> 56; - output[3] &= 0x00ffffffffffffff; - - /* Now output[2] < 2^56, output[3] < 2^56 */ - - /* Eliminate output[4] */ - output[2] += output[4] >> 16; - output[1] += (output[4]&0xffff) << 40; - output[0] -= output[4]; - - /* Carry 0 -> 1 -> 2 -> 3 */ - output[1] += output[0] >> 56; - out[0] = output[0] & 0x00ffffffffffffff; - - output[2] += output[1] >> 56; - out[1] = output[1] & 0x00ffffffffffffff; - output[3] += output[2] >> 56; - out[2] = output[2] & 0x00ffffffffffffff; - - /* out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, - * out[3] < 2^57 (due to final carry) */ - out[3] = output[3]; - } - -/* Reduce to unique minimal representation */ -static void felem_contract(fslice out[4], const fslice in[4]) - { - static const int64_t two56 = ((uint64_t) 1) << 56; - /* 0 <= in < 2^225 */ - /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */ - int64_t tmp[4], a; - tmp[0] = (int64_t) in[0] - (in[3] >> 56); - tmp[1] = (int64_t) in[1] + ((in[3] >> 16) & 0x0000010000000000); - tmp[2] = (int64_t) in[2]; - tmp[3] = (int64_t) in[3] & 0x00ffffffffffffff; - - /* eliminate negative coefficients */ - a = tmp[0] >> 63; - tmp[0] += two56 & a; - tmp[1] -= 1 & a; - - a = tmp[1] >> 63; - tmp[1] += two56 & a; - tmp[2] -= 1 & a; - - a = tmp[2] >> 63; - tmp[2] += two56 & a; - tmp[3] -= 1 & a; - - a = tmp[3] >> 63; - tmp[3] += two56 & a; - tmp[0] += 1 & a; - tmp[1] -= (1 & a) << 40; - - /* carry 1 -> 2 -> 3 */ - tmp[2] += tmp[1] >> 56; - tmp[1] &= 0x00ffffffffffffff; - - tmp[3] += tmp[2] >> 56; - tmp[2] &= 0x00ffffffffffffff; - - /* 0 <= in < 2^224 + 2^96 - 1 */ - /* if in > 2^224 , reduce in = in - 2^224 + 2^96 - 1 */ - tmp[0] -= (tmp[3] >> 56); - tmp[1] += ((tmp[3] >> 16) & 0x0000010000000000); - tmp[3] &= 0x00ffffffffffffff; - - /* eliminate negative coefficients */ - a = tmp[0] >> 63; - tmp[0] += two56 & a; - tmp[1] -= 1 & a; - - a = tmp[1] >> 63; - tmp[1] += two56 & a; - tmp[2] -= 1 & a; - - a = tmp[2] >> 63; - tmp[2] += two56 & a; - tmp[3] -= 1 & a; - - a = tmp[3] >> 63; - tmp[3] += two56 & a; - tmp[0] += 1 & a; - tmp[1] -= (1 & a) << 40; - - /* carry 1 -> 2 -> 3 */ - tmp[2] += tmp[1] >> 56; - tmp[1] &= 0x00ffffffffffffff; - - tmp[3] += tmp[2] >> 56; - tmp[2] &= 0x00ffffffffffffff; - - /* Now 0 <= in < 2^224 */ - - /* if in > 2^224 - 2^96, reduce */ - /* a = 0 iff in > 2^224 - 2^96, i.e., - * the high 128 bits are all 1 and the lower part is non-zero */ - a = (tmp[3] + 1) | (tmp[2] + 1) | - ((tmp[1] | 0x000000ffffffffff) + 1) | - ((((tmp[1] & 0xffff) - 1) >> 63) & ((tmp[0] - 1) >> 63)); - /* turn a into an all-one mask (if a = 0) or an all-zero mask */ - a = ((a & 0x00ffffffffffffff) - 1) >> 63; - /* subtract 2^224 - 2^96 + 1 if a is all-one*/ - tmp[3] &= a ^ 0xffffffffffffffff; - tmp[2] &= a ^ 0xffffffffffffffff; - tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; - tmp[0] -= 1 & a; - /* eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be - * non-zero, so we only need one step */ - a = tmp[0] >> 63; - tmp[0] += two56 & a; - tmp[1] -= 1 & a; - - out[0] = tmp[0]; - out[1] = tmp[1]; - out[2] = tmp[2]; - out[3] = tmp[3]; - } - -/* Zero-check: returns 1 if input is 0, and 0 otherwise. - * We know that field elements are reduced to in < 2^225, - * so we only need to check three cases: 0, 2^224 - 2^96 + 1, - * and 2^225 - 2^97 + 2 */ -static fslice felem_is_zero(const fslice in[4]) - { - fslice zero, two224m96p1, two225m97p2; - - zero = in[0] | in[1] | in[2] | in[3]; - zero = (((int64_t)(zero) - 1) >> 63) & 1; - two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); - two224m96p1 = (((int64_t)(two224m96p1) - 1) >> 63) & 1; - two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) - | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); - two225m97p2 = (((int64_t)(two225m97p2) - 1) >> 63) & 1; - return (zero | two224m96p1 | two225m97p2); - } +static void felem_mul(widefelem out, const felem in1, const felem in2) +{ + out[0] = ((widelimb) in1[0]) * in2[0]; + out[1] = ((widelimb) in1[0]) * in2[1] + ((widelimb) in1[1]) * in2[0]; + out[2] = ((widelimb) in1[0]) * in2[2] + ((widelimb) in1[1]) * in2[1] + + ((widelimb) in1[2]) * in2[0]; + out[3] = ((widelimb) in1[0]) * in2[3] + ((widelimb) in1[1]) * in2[2] + + ((widelimb) in1[2]) * in2[1] + ((widelimb) in1[3]) * in2[0]; + out[4] = ((widelimb) in1[1]) * in2[3] + ((widelimb) in1[2]) * in2[2] + + ((widelimb) in1[3]) * in2[1]; + out[5] = ((widelimb) in1[2]) * in2[3] + ((widelimb) in1[3]) * in2[2]; + out[6] = ((widelimb) in1[3]) * in2[3]; +} + +/*- + * Reduce seven 128-bit coefficients to four 64-bit coefficients. + * Requires in[i] < 2^126, + * ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 */ +static void felem_reduce(felem out, const widefelem in) +{ + static const widelimb two127p15 = (((widelimb) 1) << 127) + + (((widelimb) 1) << 15); + static const widelimb two127m71 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71); + static const widelimb two127m71m55 = (((widelimb) 1) << 127) - + (((widelimb) 1) << 71) - (((widelimb) 1) << 55); + widelimb output[5]; + + /* Add 0 mod 2^224-2^96+1 to ensure all differences are positive */ + output[0] = in[0] + two127p15; + output[1] = in[1] + two127m71m55; + output[2] = in[2] + two127m71; + output[3] = in[3]; + output[4] = in[4]; + + /* Eliminate in[4], in[5], in[6] */ + output[4] += in[6] >> 16; + output[3] += (in[6] & 0xffff) << 40; + output[2] -= in[6]; + + output[3] += in[5] >> 16; + output[2] += (in[5] & 0xffff) << 40; + output[1] -= in[5]; + + output[2] += output[4] >> 16; + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 2 -> 3 -> 4 */ + output[3] += output[2] >> 56; + output[2] &= 0x00ffffffffffffff; + + output[4] = output[3] >> 56; + output[3] &= 0x00ffffffffffffff; + + /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */ + + /* Eliminate output[4] */ + output[2] += output[4] >> 16; + /* output[2] < 2^56 + 2^56 = 2^57 */ + output[1] += (output[4] & 0xffff) << 40; + output[0] -= output[4]; + + /* Carry 0 -> 1 -> 2 -> 3 */ + output[1] += output[0] >> 56; + out[0] = output[0] & 0x00ffffffffffffff; + + output[2] += output[1] >> 56; + /* output[2] < 2^57 + 2^72 */ + out[1] = output[1] & 0x00ffffffffffffff; + output[3] += output[2] >> 56; + /* output[3] <= 2^56 + 2^16 */ + out[2] = output[2] & 0x00ffffffffffffff; + + /*- + * out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, + * out[3] <= 2^56 + 2^16 (due to final carry), + * so out < 2*p + */ + out[3] = output[3]; +} + +static void felem_square_reduce(felem out, const felem in) +{ + widefelem tmp; + felem_square(tmp, in); + felem_reduce(out, tmp); +} + +static void felem_mul_reduce(felem out, const felem in1, const felem in2) +{ + widefelem tmp; + felem_mul(tmp, in1, in2); + felem_reduce(out, tmp); +} + +/* + * Reduce to unique minimal representation. Requires 0 <= in < 2*p (always + * call felem_reduce first) + */ +static void felem_contract(felem out, const felem in) +{ + static const int64_t two56 = ((limb) 1) << 56; + /* 0 <= in < 2*p, p = 2^224 - 2^96 + 1 */ + /* if in > p , reduce in = in - 2^224 + 2^96 - 1 */ + int64_t tmp[4], a; + tmp[0] = in[0]; + tmp[1] = in[1]; + tmp[2] = in[2]; + tmp[3] = in[3]; + /* Case 1: a = 1 iff in >= 2^224 */ + a = (in[3] >> 56); + tmp[0] -= a; + tmp[1] += a << 40; + tmp[3] &= 0x00ffffffffffffff; + /* + * Case 2: a = 0 iff p <= in < 2^224, i.e., the high 128 bits are all 1 + * and the lower part is non-zero + */ + a = ((in[3] & in[2] & (in[1] | 0x000000ffffffffff)) + 1) | + (((int64_t) (in[0] + (in[1] & 0x000000ffffffffff)) - 1) >> 63); + a &= 0x00ffffffffffffff; + /* turn a into an all-one mask (if a = 0) or an all-zero mask */ + a = (a - 1) >> 63; + /* subtract 2^224 - 2^96 + 1 if a is all-one */ + tmp[3] &= a ^ 0xffffffffffffffff; + tmp[2] &= a ^ 0xffffffffffffffff; + tmp[1] &= (a ^ 0xffffffffffffffff) | 0x000000ffffffffff; + tmp[0] -= 1 & a; + + /* + * eliminate negative coefficients: if tmp[0] is negative, tmp[1] must be + * non-zero, so we only need one step + */ + a = tmp[0] >> 63; + tmp[0] += two56 & a; + tmp[1] -= 1 & a; + + /* carry 1 -> 2 -> 3 */ + tmp[2] += tmp[1] >> 56; + tmp[1] &= 0x00ffffffffffffff; + + tmp[3] += tmp[2] >> 56; + tmp[2] &= 0x00ffffffffffffff; + + /* Now 0 <= out < p */ + out[0] = tmp[0]; + out[1] = tmp[1]; + out[2] = tmp[2]; + out[3] = tmp[3]; +} + +/* + * Zero-check: returns 1 if input is 0, and 0 otherwise. We know that field + * elements are reduced to in < 2^225, so we only need to check three cases: + * 0, 2^224 - 2^96 + 1, and 2^225 - 2^97 + 2 + */ +static limb felem_is_zero(const felem in) +{ + limb zero, two224m96p1, two225m97p2; + + zero = in[0] | in[1] | in[2] | in[3]; + zero = (((int64_t) (zero) - 1) >> 63) & 1; + two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x00ffffffffffffff); + two224m96p1 = (((int64_t) (two224m96p1) - 1) >> 63) & 1; + two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) + | (in[2] ^ 0x00ffffffffffffff) | (in[3] ^ 0x01ffffffffffffff); + two225m97p2 = (((int64_t) (two225m97p2) - 1) >> 63) & 1; + return (zero | two224m96p1 | two225m97p2); +} + +static int felem_is_zero_int(const void *in) +{ + return (int)(felem_is_zero(in) & ((limb) 1)); +} /* Invert a field element */ /* Computation chain copied from djb's code */ -static void felem_inv(fslice out[4], const fslice in[4]) - { - fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4]; - uint128_t tmp[7]; - unsigned i; - - felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^2 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 2 */ - felem_mul(tmp, in, ftmp); felem_reduce(ftmp, tmp); /* 2^3 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^6 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ - for (i = 0; i < 5; ++i) /* 2^12 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ - for (i = 0; i < 11; ++i) /* 2^24 - 2^12 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ - felem_square(tmp, ftmp2); felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ - for (i = 0; i < 23; ++i) /* 2^48 - 2^24 */ - { - felem_square(tmp, ftmp3); felem_reduce(ftmp3, tmp); - } - felem_mul(tmp, ftmp3, ftmp2); felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ - for (i = 0; i < 47; ++i) /* 2^96 - 2^48 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp3, ftmp4); felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ - felem_square(tmp, ftmp3); felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ - for (i = 0; i < 23; ++i) /* 2^120 - 2^24 */ - { - felem_square(tmp, ftmp4); felem_reduce(ftmp4, tmp); - } - felem_mul(tmp, ftmp2, ftmp4); felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ - for (i = 0; i < 6; ++i) /* 2^126 - 2^6 */ - { - felem_square(tmp, ftmp2); felem_reduce(ftmp2, tmp); - } - felem_mul(tmp, ftmp2, ftmp); felem_reduce(ftmp, tmp); /* 2^126 - 1 */ - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); /* 2^127 - 2 */ - felem_mul(tmp, ftmp, in); felem_reduce(ftmp, tmp); /* 2^127 - 1 */ - for (i = 0; i < 97; ++i) /* 2^224 - 2^97 */ - { - felem_square(tmp, ftmp); felem_reduce(ftmp, tmp); - } - felem_mul(tmp, ftmp, ftmp3); felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ - } - -/* Copy in constant time: - * if icopy == 1, copy in to out, - * if icopy == 0, copy out to itself. */ -static void -copy_conditional(fslice *out, const fslice *in, unsigned len, fslice icopy) - { - unsigned i; - /* icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one */ - const fslice copy = -icopy; - for (i = 0; i < len; ++i) - { - const fslice tmp = copy & (in[i] ^ out[i]); - out[i] ^= tmp; - } - } - -/* Copy in constant time: - * if isel == 1, copy in2 to out, - * if isel == 0, copy in1 to out. */ -static void select_conditional(fslice *out, const fslice *in1, const fslice *in2, - unsigned len, fslice isel) - { - unsigned i; - /* isel is a (64-bit) 0 or 1, so sel is either all-zero or all-one */ - const fslice sel = -isel; - for (i = 0; i < len; ++i) - { - const fslice tmp = sel & (in1[i] ^ in2[i]); - out[i] = in1[i] ^ tmp; - } +static void felem_inv(felem out, const felem in) +{ + felem ftmp, ftmp2, ftmp3, ftmp4; + widefelem tmp; + unsigned i; + + felem_square(tmp, in); + felem_reduce(ftmp, tmp); /* 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^2 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 2 */ + felem_mul(tmp, in, ftmp); + felem_reduce(ftmp, tmp); /* 2^3 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^4 - 2 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^5 - 4 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^6 - 8 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^6 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp2, tmp); /* 2^7 - 2 */ + for (i = 0; i < 5; ++i) { /* 2^12 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); /* 2^12 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^13 - 2 */ + for (i = 0; i < 11; ++i) { /* 2^24 - 2^12 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp2, tmp); /* 2^24 - 1 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^25 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^48 - 2^24 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp3, tmp); + } + felem_mul(tmp, ftmp3, ftmp2); + felem_reduce(ftmp3, tmp); /* 2^48 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^49 - 2 */ + for (i = 0; i < 47; ++i) { /* 2^96 - 2^48 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp3, ftmp4); + felem_reduce(ftmp3, tmp); /* 2^96 - 1 */ + felem_square(tmp, ftmp3); + felem_reduce(ftmp4, tmp); /* 2^97 - 2 */ + for (i = 0; i < 23; ++i) { /* 2^120 - 2^24 */ + felem_square(tmp, ftmp4); + felem_reduce(ftmp4, tmp); + } + felem_mul(tmp, ftmp2, ftmp4); + felem_reduce(ftmp2, tmp); /* 2^120 - 1 */ + for (i = 0; i < 6; ++i) { /* 2^126 - 2^6 */ + felem_square(tmp, ftmp2); + felem_reduce(ftmp2, tmp); + } + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp, tmp); /* 2^126 - 1 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); /* 2^127 - 2 */ + felem_mul(tmp, ftmp, in); + felem_reduce(ftmp, tmp); /* 2^127 - 1 */ + for (i = 0; i < 97; ++i) { /* 2^224 - 2^97 */ + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + } + felem_mul(tmp, ftmp, ftmp3); + felem_reduce(out, tmp); /* 2^224 - 2^96 - 1 */ +} + +/* + * Copy in constant time: if icopy == 1, copy in to out, if icopy == 0, copy + * out to itself. + */ +static void copy_conditional(felem out, const felem in, limb icopy) +{ + unsigned i; + /* + * icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one + */ + const limb copy = -icopy; + for (i = 0; i < 4; ++i) { + const limb tmp = copy & (in[i] ^ out[i]); + out[i] ^= tmp; + } } /******************************************************************************/ -/* ELLIPTIC CURVE POINT OPERATIONS +/*- + * ELLIPTIC CURVE POINT OPERATIONS * * Points are represented in Jacobian projective coordinates: * (X, Y, Z) corresponds to the affine point (X/Z^2, Y/Z^3), @@ -710,783 +813,907 @@ static void select_conditional(fslice *out, const fslice *in1, const fslice *in2 * */ -/* Double an elliptic curve point: +/*- + * Double an elliptic curve point: * (X', Y', Z') = 2 * (X, Y, Z), where * X' = (3 * (X - Z^2) * (X + Z^2))^2 - 8 * X * Y^2 * Y' = 3 * (X - Z^2) * (X + Z^2) * (4 * X * Y^2 - X') - 8 * Y^2 * Z' = (Y + Z)^2 - Y^2 - Z^2 = 2 * Y * Z * Outputs can equal corresponding inputs, i.e., x_out == x_in is allowed, - * while x_out == y_in is not (maybe this works, but it's not tested). */ + * while x_out == y_in is not (maybe this works, but it's not tested). + */ static void -point_double(fslice x_out[4], fslice y_out[4], fslice z_out[4], - const fslice x_in[4], const fslice y_in[4], const fslice z_in[4]) - { - uint128_t tmp[7], tmp2[7]; - fslice delta[4]; - fslice gamma[4]; - fslice beta[4]; - fslice alpha[4]; - fslice ftmp[4], ftmp2[4]; - memcpy(ftmp, x_in, 4 * sizeof(fslice)); - memcpy(ftmp2, x_in, 4 * sizeof(fslice)); - - /* delta = z^2 */ - felem_square(tmp, z_in); - felem_reduce(delta, tmp); - - /* gamma = y^2 */ - felem_square(tmp, y_in); - felem_reduce(gamma, tmp); - - /* beta = x*gamma */ - felem_mul(tmp, x_in, gamma); - felem_reduce(beta, tmp); - - /* alpha = 3*(x-delta)*(x+delta) */ - felem_diff64(ftmp, delta); - /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ - felem_sum64(ftmp2, delta); - /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ - felem_scalar64(ftmp2, 3); - /* ftmp2[i] < 3 * 2^58 < 2^60 */ - felem_mul(tmp, ftmp, ftmp2); - /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ - felem_reduce(alpha, tmp); - - /* x' = alpha^2 - 8*beta */ - felem_square(tmp, alpha); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - memcpy(ftmp, beta, 4 * sizeof(fslice)); - felem_scalar64(ftmp, 8); - /* ftmp[i] < 8 * 2^57 = 2^60 */ - felem_diff_128_64(tmp, ftmp); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(x_out, tmp); - - /* z' = (y + z)^2 - gamma - delta */ - felem_sum64(delta, gamma); - /* delta[i] < 2^57 + 2^57 = 2^58 */ - memcpy(ftmp, y_in, 4 * sizeof(fslice)); - felem_sum64(ftmp, z_in); - /* ftmp[i] < 2^57 + 2^57 = 2^58 */ - felem_square(tmp, ftmp); - /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ - felem_diff_128_64(tmp, delta); - /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ - felem_reduce(z_out, tmp); - - /* y' = alpha*(4*beta - x') - 8*gamma^2 */ - felem_scalar64(beta, 4); - /* beta[i] < 4 * 2^57 = 2^59 */ - felem_diff64(beta, x_out); - /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ - felem_mul(tmp, alpha, beta); - /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ - felem_square(tmp2, gamma); - /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ - felem_scalar128(tmp2, 8); - /* tmp2[i] < 8 * 2^116 = 2^119 */ - felem_diff128(tmp, tmp2); - /* tmp[i] < 2^119 + 2^120 < 2^121 */ - felem_reduce(y_out, tmp); - } - -/* Add two elliptic curve points: +point_double(felem x_out, felem y_out, felem z_out, + const felem x_in, const felem y_in, const felem z_in) +{ + widefelem tmp, tmp2; + felem delta, gamma, beta, alpha, ftmp, ftmp2; + + felem_assign(ftmp, x_in); + felem_assign(ftmp2, x_in); + + /* delta = z^2 */ + felem_square(tmp, z_in); + felem_reduce(delta, tmp); + + /* gamma = y^2 */ + felem_square(tmp, y_in); + felem_reduce(gamma, tmp); + + /* beta = x*gamma */ + felem_mul(tmp, x_in, gamma); + felem_reduce(beta, tmp); + + /* alpha = 3*(x-delta)*(x+delta) */ + felem_diff(ftmp, delta); + /* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */ + felem_sum(ftmp2, delta); + /* ftmp2[i] < 2^57 + 2^57 = 2^58 */ + felem_scalar(ftmp2, 3); + /* ftmp2[i] < 3 * 2^58 < 2^60 */ + felem_mul(tmp, ftmp, ftmp2); + /* tmp[i] < 2^60 * 2^59 * 4 = 2^121 */ + felem_reduce(alpha, tmp); + + /* x' = alpha^2 - 8*beta */ + felem_square(tmp, alpha); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + felem_assign(ftmp, beta); + felem_scalar(ftmp, 8); + /* ftmp[i] < 8 * 2^57 = 2^60 */ + felem_diff_128_64(tmp, ftmp); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(x_out, tmp); + + /* z' = (y + z)^2 - gamma - delta */ + felem_sum(delta, gamma); + /* delta[i] < 2^57 + 2^57 = 2^58 */ + felem_assign(ftmp, y_in); + felem_sum(ftmp, z_in); + /* ftmp[i] < 2^57 + 2^57 = 2^58 */ + felem_square(tmp, ftmp); + /* tmp[i] < 4 * 2^58 * 2^58 = 2^118 */ + felem_diff_128_64(tmp, delta); + /* tmp[i] < 2^118 + 2^64 + 8 < 2^119 */ + felem_reduce(z_out, tmp); + + /* y' = alpha*(4*beta - x') - 8*gamma^2 */ + felem_scalar(beta, 4); + /* beta[i] < 4 * 2^57 = 2^59 */ + felem_diff(beta, x_out); + /* beta[i] < 2^59 + 2^58 + 2 < 2^60 */ + felem_mul(tmp, alpha, beta); + /* tmp[i] < 4 * 2^57 * 2^60 = 2^119 */ + felem_square(tmp2, gamma); + /* tmp2[i] < 4 * 2^57 * 2^57 = 2^116 */ + widefelem_scalar(tmp2, 8); + /* tmp2[i] < 8 * 2^116 = 2^119 */ + widefelem_diff(tmp, tmp2); + /* tmp[i] < 2^119 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp); +} + +/*- + * Add two elliptic curve points: * (X_1, Y_1, Z_1) + (X_2, Y_2, Z_2) = (X_3, Y_3, Z_3), where * X_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1)^2 - (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - * 2 * Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 * Y_3 = (Z_1^3 * Y_2 - Z_2^3 * Y_1) * (Z_2^2 * X_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^2 - X_3) - * Z_2^3 * Y_1 * (Z_1^2 * X_2 - Z_2^2 * X_1)^3 - * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) */ - -/* This function is not entirely constant-time: - * it includes a branch for checking whether the two input points are equal, - * (while not equal to the point at infinity). - * This case never happens during single point multiplication, - * so there is no timing leak for ECDH or ECDSA signing. */ -static void point_add(fslice x3[4], fslice y3[4], fslice z3[4], - const fslice x1[4], const fslice y1[4], const fslice z1[4], - const fslice x2[4], const fslice y2[4], const fslice z2[4]) - { - fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4], ftmp5[4]; - uint128_t tmp[7], tmp2[7]; - fslice z1_is_zero, z2_is_zero, x_equal, y_equal; - - /* ftmp = z1^2 */ - felem_square(tmp, z1); - felem_reduce(ftmp, tmp); - - /* ftmp2 = z2^2 */ - felem_square(tmp, z2); - felem_reduce(ftmp2, tmp); - - /* ftmp3 = z1^3 */ - felem_mul(tmp, ftmp, z1); - felem_reduce(ftmp3, tmp); - - /* ftmp4 = z2^3 */ - felem_mul(tmp, ftmp2, z2); - felem_reduce(ftmp4, tmp); - - /* ftmp3 = z1^3*y2 */ - felem_mul(tmp, ftmp3, y2); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* ftmp4 = z2^3*y1 */ - felem_mul(tmp2, ftmp4, y1); - felem_reduce(ftmp4, tmp2); - - /* ftmp3 = z1^3*y2 - z2^3*y1 */ - felem_diff_128_64(tmp, ftmp4); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(ftmp3, tmp); - - /* ftmp = z1^2*x2 */ - felem_mul(tmp, ftmp, x2); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* ftmp2 =z2^2*x1 */ - felem_mul(tmp2, ftmp2, x1); - felem_reduce(ftmp2, tmp2); - - /* ftmp = z1^2*x2 - z2^2*x1 */ - felem_diff128(tmp, tmp2); - /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ - felem_reduce(ftmp, tmp); - - /* the formulae are incorrect if the points are equal - * so we check for this and do doubling if this happens */ - x_equal = felem_is_zero(ftmp); - y_equal = felem_is_zero(ftmp3); - z1_is_zero = felem_is_zero(z1); - z2_is_zero = felem_is_zero(z2); - /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ - if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) - { - point_double(x3, y3, z3, x1, y1, z1); - return; - } - - /* ftmp5 = z1*z2 */ - felem_mul(tmp, z1, z2); - felem_reduce(ftmp5, tmp); - - /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */ - felem_mul(tmp, ftmp, ftmp5); - felem_reduce(z3, tmp); - - /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ - memcpy(ftmp5, ftmp, 4 * sizeof(fslice)); - felem_square(tmp, ftmp); - felem_reduce(ftmp, tmp); - - /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ - felem_mul(tmp, ftmp, ftmp5); - felem_reduce(ftmp5, tmp); - - /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ - felem_mul(tmp, ftmp2, ftmp); - felem_reduce(ftmp2, tmp); - - /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ - felem_mul(tmp, ftmp4, ftmp5); - /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ - felem_square(tmp2, ftmp3); - /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ - felem_diff_128_64(tmp2, ftmp5); - /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ - - /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ - memcpy(ftmp5, ftmp2, 4 * sizeof(fslice)); - felem_scalar64(ftmp5, 2); - /* ftmp5[i] < 2 * 2^57 = 2^58 */ - - /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - - 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ - felem_diff_128_64(tmp2, ftmp5); - /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ - felem_reduce(x3, tmp2); - - /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */ - felem_diff64(ftmp2, x3); - /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ - - /* tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) */ - felem_mul(tmp2, ftmp3, ftmp2); - /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ - - /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) - - z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ - felem_diff128(tmp2, tmp); - /* tmp2[i] < 2^118 + 2^120 < 2^121 */ - felem_reduce(y3, tmp2); - - /* the result (x3, y3, z3) is incorrect if one of the inputs is the - * point at infinity, so we need to check for this separately */ - - /* if point 1 is at infinity, copy point 2 to output, and vice versa */ - copy_conditional(x3, x2, 4, z1_is_zero); - copy_conditional(x3, x1, 4, z2_is_zero); - copy_conditional(y3, y2, 4, z1_is_zero); - copy_conditional(y3, y1, 4, z2_is_zero); - copy_conditional(z3, z2, 4, z1_is_zero); - copy_conditional(z3, z1, 4, z2_is_zero); - } - -/* Select a point from an array of 16 precomputed point multiples, - * in constant time: for bits = {b_0, b_1, b_2, b_3}, return the point - * pre_comp[8*b_3 + 4*b_2 + 2*b_1 + b_0] */ -static void select_point(const fslice bits[4], const fslice pre_comp[16][3][4], - fslice out[12]) - { - fslice tmp[5][12]; - select_conditional(tmp[0], pre_comp[7][0], pre_comp[15][0], 12, bits[3]); - select_conditional(tmp[1], pre_comp[3][0], pre_comp[11][0], 12, bits[3]); - select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]); - select_conditional(tmp[0], pre_comp[5][0], pre_comp[13][0], 12, bits[3]); - select_conditional(tmp[1], pre_comp[1][0], pre_comp[9][0], 12, bits[3]); - select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]); - select_conditional(tmp[4], tmp[3], tmp[2], 12, bits[1]); - select_conditional(tmp[0], pre_comp[6][0], pre_comp[14][0], 12, bits[3]); - select_conditional(tmp[1], pre_comp[2][0], pre_comp[10][0], 12, bits[3]); - select_conditional(tmp[2], tmp[1], tmp[0], 12, bits[2]); - select_conditional(tmp[0], pre_comp[4][0], pre_comp[12][0], 12, bits[3]); - select_conditional(tmp[1], pre_comp[0][0], pre_comp[8][0], 12, bits[3]); - select_conditional(tmp[3], tmp[1], tmp[0], 12, bits[2]); - select_conditional(tmp[1], tmp[3], tmp[2], 12, bits[1]); - select_conditional(out, tmp[1], tmp[4], 12, bits[0]); - } - -/* Interleaved point multiplication using precomputed point multiples: - * The small point multiples 0*P, 1*P, ..., 15*P are in pre_comp[], - * the scalars in scalars[]. If g_scalar is non-NULL, we also add this multiple - * of the generator, using certain (large) precomputed multiples in g_pre_comp. - * Output point (X, Y, Z) is stored in x_out, y_out, z_out */ -static void batch_mul(fslice x_out[4], fslice y_out[4], fslice z_out[4], - const felem_bytearray scalars[], const unsigned num_points, const u8 *g_scalar, - const fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4]) - { - unsigned i, j, num; - unsigned gen_mul = (g_scalar != NULL); - fslice nq[12], nqt[12], tmp[12]; - fslice bits[4]; - u8 byte; - - /* set nq to the point at infinity */ - memset(nq, 0, 12 * sizeof(fslice)); - - /* Loop over all scalars msb-to-lsb, 4 bits at a time: for each nibble, - * double 4 times, then add the precomputed point multiples. - * If we are also adding multiples of the generator, then interleave - * these additions with the last 56 doublings. */ - for (i = (num_points ? 28 : 7); i > 0; --i) - { - for (j = 0; j < 8; ++j) - { - /* double once */ - point_double(nq, nq+4, nq+8, nq, nq+4, nq+8); - /* add multiples of the generator */ - if ((gen_mul) && (i <= 7)) - { - bits[3] = (g_scalar[i+20] >> (7-j)) & 1; - bits[2] = (g_scalar[i+13] >> (7-j)) & 1; - bits[1] = (g_scalar[i+6] >> (7-j)) & 1; - bits[0] = (g_scalar[i-1] >> (7-j)) & 1; - /* select the point to add, in constant time */ - select_point(bits, g_pre_comp, tmp); - memcpy(nqt, nq, 12 * sizeof(fslice)); - point_add(nq, nq+4, nq+8, nqt, nqt+4, nqt+8, - tmp, tmp+4, tmp+8); - } - /* do an addition after every 4 doublings */ - if (j % 4 == 3) - { - /* loop over all scalars */ - for (num = 0; num < num_points; ++num) - { - byte = scalars[num][i-1]; - bits[3] = (byte >> (10-j)) & 1; - bits[2] = (byte >> (9-j)) & 1; - bits[1] = (byte >> (8-j)) & 1; - bits[0] = (byte >> (7-j)) & 1; - /* select the point to add */ - select_point(bits, - pre_comp[num], tmp); - memcpy(nqt, nq, 12 * sizeof(fslice)); - point_add(nq, nq+4, nq+8, nqt, nqt+4, - nqt+8, tmp, tmp+4, tmp+8); - } - } - } - } - memcpy(x_out, nq, 4 * sizeof(fslice)); - memcpy(y_out, nq+4, 4 * sizeof(fslice)); - memcpy(z_out, nq+8, 4 * sizeof(fslice)); - } + * Z_3 = (Z_1^2 * X_2 - Z_2^2 * X_1) * (Z_1 * Z_2) + * + * This runs faster if 'mixed' is set, which requires Z_2 = 1 or Z_2 = 0. + */ + +/* + * This function is not entirely constant-time: it includes a branch for + * checking whether the two input points are equal, (while not equal to the + * point at infinity). This case never happens during single point + * multiplication, so there is no timing leak for ECDH or ECDSA signing. + */ +static void point_add(felem x3, felem y3, felem z3, + const felem x1, const felem y1, const felem z1, + const int mixed, const felem x2, const felem y2, + const felem z2) +{ + felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; + widefelem tmp, tmp2; + limb z1_is_zero, z2_is_zero, x_equal, y_equal; + + if (!mixed) { + /* ftmp2 = z2^2 */ + felem_square(tmp, z2); + felem_reduce(ftmp2, tmp); + + /* ftmp4 = z2^3 */ + felem_mul(tmp, ftmp2, z2); + felem_reduce(ftmp4, tmp); + + /* ftmp4 = z2^3*y1 */ + felem_mul(tmp2, ftmp4, y1); + felem_reduce(ftmp4, tmp2); + + /* ftmp2 = z2^2*x1 */ + felem_mul(tmp2, ftmp2, x1); + felem_reduce(ftmp2, tmp2); + } else { + /* + * We'll assume z2 = 1 (special case z2 = 0 is handled later) + */ + + /* ftmp4 = z2^3*y1 */ + felem_assign(ftmp4, y1); + + /* ftmp2 = z2^2*x1 */ + felem_assign(ftmp2, x1); + } + + /* ftmp = z1^2 */ + felem_square(tmp, z1); + felem_reduce(ftmp, tmp); + + /* ftmp3 = z1^3 */ + felem_mul(tmp, ftmp, z1); + felem_reduce(ftmp3, tmp); + + /* tmp = z1^3*y2 */ + felem_mul(tmp, ftmp3, y2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp3 = z1^3*y2 - z2^3*y1 */ + felem_diff_128_64(tmp, ftmp4); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp3, tmp); + + /* tmp = z1^2*x2 */ + felem_mul(tmp, ftmp, x2); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* ftmp = z1^2*x2 - z2^2*x1 */ + felem_diff_128_64(tmp, ftmp2); + /* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */ + felem_reduce(ftmp, tmp); + + /* + * the formulae are incorrect if the points are equal so we check for + * this and do doubling if this happens + */ + x_equal = felem_is_zero(ftmp); + y_equal = felem_is_zero(ftmp3); + z1_is_zero = felem_is_zero(z1); + z2_is_zero = felem_is_zero(z2); + /* In affine coordinates, (X_1, Y_1) == (X_2, Y_2) */ + if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) { + point_double(x3, y3, z3, x1, y1, z1); + return; + } + + /* ftmp5 = z1*z2 */ + if (!mixed) { + felem_mul(tmp, z1, z2); + felem_reduce(ftmp5, tmp); + } else { + /* special case z2 = 0 is handled later */ + felem_assign(ftmp5, z1); + } + + /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(z_out, tmp); + + /* ftmp = (z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp); + felem_square(tmp, ftmp); + felem_reduce(ftmp, tmp); + + /* ftmp5 = (z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp, ftmp5); + felem_reduce(ftmp5, tmp); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_mul(tmp, ftmp2, ftmp); + felem_reduce(ftmp2, tmp); + + /* tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */ + felem_mul(tmp, ftmp4, ftmp5); + /* tmp[i] < 4 * 2^57 * 2^57 = 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 */ + felem_square(tmp2, ftmp3); + /* tmp2[i] < 4 * 2^57 * 2^57 < 2^116 */ + + /* tmp2 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^116 + 2^64 + 8 < 2^117 */ + + /* ftmp5 = 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 */ + felem_assign(ftmp5, ftmp2); + felem_scalar(ftmp5, 2); + /* ftmp5[i] < 2 * 2^57 = 2^58 */ + + /*- + * x_out = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 - + * 2*z2^2*x1*(z1^2*x2 - z2^2*x1)^2 + */ + felem_diff_128_64(tmp2, ftmp5); + /* tmp2[i] < 2^117 + 2^64 + 8 < 2^118 */ + felem_reduce(x_out, tmp2); + + /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out */ + felem_diff(ftmp2, x_out); + /* ftmp2[i] < 2^57 + 2^58 + 2 < 2^59 */ + + /* + * tmp2 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) + */ + felem_mul(tmp2, ftmp3, ftmp2); + /* tmp2[i] < 4 * 2^57 * 2^59 = 2^118 */ + + /*- + * y_out = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out) - + * z2^3*y1*(z1^2*x2 - z2^2*x1)^3 + */ + widefelem_diff(tmp2, tmp); + /* tmp2[i] < 2^118 + 2^120 < 2^121 */ + felem_reduce(y_out, tmp2); + + /* + * the result (x_out, y_out, z_out) is incorrect if one of the inputs is + * the point at infinity, so we need to check for this separately + */ + + /* + * if point 1 is at infinity, copy point 2 to output, and vice versa + */ + copy_conditional(x_out, x2, z1_is_zero); + copy_conditional(x_out, x1, z2_is_zero); + copy_conditional(y_out, y2, z1_is_zero); + copy_conditional(y_out, y1, z2_is_zero); + copy_conditional(z_out, z2, z1_is_zero); + copy_conditional(z_out, z1, z2_is_zero); + felem_assign(x3, x_out); + felem_assign(y3, y_out); + felem_assign(z3, z_out); +} + +/* + * select_point selects the |idx|th point from a precomputation table and + * copies it to out. + * The pre_comp array argument should be size of |size| argument + */ +static void select_point(const u64 idx, unsigned int size, + const felem pre_comp[][3], felem out[3]) +{ + unsigned i, j; + limb *outlimbs = &out[0][0]; + + memset(out, 0, sizeof(*out) * 3); + for (i = 0; i < size; i++) { + const limb *inlimbs = &pre_comp[i][0][0]; + u64 mask = i ^ idx; + mask |= mask >> 4; + mask |= mask >> 2; + mask |= mask >> 1; + mask &= 1; + mask--; + for (j = 0; j < 4 * 3; j++) + outlimbs[j] |= inlimbs[j] & mask; + } +} + +/* get_bit returns the |i|th bit in |in| */ +static char get_bit(const felem_bytearray in, unsigned i) +{ + if (i >= 224) + return 0; + return (in[i >> 3] >> (i & 7)) & 1; +} + +/* + * Interleaved point multiplication using precomputed point multiples: The + * small point multiples 0*P, 1*P, ..., 16*P are in pre_comp[], the scalars + * in scalars[]. If g_scalar is non-NULL, we also add this multiple of the + * generator, using certain (large) precomputed multiples in g_pre_comp. + * Output point (X, Y, Z) is stored in x_out, y_out, z_out + */ +static void batch_mul(felem x_out, felem y_out, felem z_out, + const felem_bytearray scalars[], + const unsigned num_points, const u8 *g_scalar, + const int mixed, const felem pre_comp[][17][3], + const felem g_pre_comp[2][16][3]) +{ + int i, skip; + unsigned num; + unsigned gen_mul = (g_scalar != NULL); + felem nq[3], tmp[4]; + u64 bits; + u8 sign, digit; + + /* set nq to the point at infinity */ + memset(nq, 0, sizeof(nq)); + + /* + * Loop over all scalars msb-to-lsb, interleaving additions of multiples + * of the generator (two in each of the last 28 rounds) and additions of + * other points multiples (every 5th round). + */ + skip = 1; /* save two point operations in the first + * round */ + for (i = (num_points ? 220 : 27); i >= 0; --i) { + /* double */ + if (!skip) + point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); + + /* add multiples of the generator */ + if (gen_mul && (i <= 27)) { + /* first, look 28 bits upwards */ + bits = get_bit(g_scalar, i + 196) << 3; + bits |= get_bit(g_scalar, i + 140) << 2; + bits |= get_bit(g_scalar, i + 84) << 1; + bits |= get_bit(g_scalar, i + 28); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[1], tmp); + + if (!skip) { + /* value 1 below is argument for "mixed" */ + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], 1, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + + /* second, look at the current position */ + bits = get_bit(g_scalar, i + 168) << 3; + bits |= get_bit(g_scalar, i + 112) << 2; + bits |= get_bit(g_scalar, i + 56) << 1; + bits |= get_bit(g_scalar, i); + /* select the point to add, in constant time */ + select_point(bits, 16, g_pre_comp[0], tmp); + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + 1 /* mixed */ , tmp[0], tmp[1], tmp[2]); + } + + /* do other additions every 5 doublings */ + if (num_points && (i % 5 == 0)) { + /* loop over all scalars */ + for (num = 0; num < num_points; ++num) { + bits = get_bit(scalars[num], i + 4) << 5; + bits |= get_bit(scalars[num], i + 3) << 4; + bits |= get_bit(scalars[num], i + 2) << 3; + bits |= get_bit(scalars[num], i + 1) << 2; + bits |= get_bit(scalars[num], i) << 1; + bits |= get_bit(scalars[num], i - 1); + ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); + + /* select the point to add or subtract */ + select_point(digit, 17, pre_comp[num], tmp); + felem_neg(tmp[3], tmp[1]); /* (X, -Y, Z) is the negative + * point */ + copy_conditional(tmp[1], tmp[3], sign); + + if (!skip) { + point_add(nq[0], nq[1], nq[2], + nq[0], nq[1], nq[2], + mixed, tmp[0], tmp[1], tmp[2]); + } else { + memcpy(nq, tmp, 3 * sizeof(felem)); + skip = 0; + } + } + } + } + felem_assign(x_out, nq[0]); + felem_assign(y_out, nq[1]); + felem_assign(z_out, nq[2]); +} /******************************************************************************/ -/* FUNCTIONS TO MANAGE PRECOMPUTATION +/* + * FUNCTIONS TO MANAGE PRECOMPUTATION */ static NISTP224_PRE_COMP *nistp224_pre_comp_new() - { - NISTP224_PRE_COMP *ret = NULL; - ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP)); - if (!ret) - { - ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); - return ret; - } - memset(ret->g_pre_comp, 0, sizeof(ret->g_pre_comp)); - ret->references = 1; - return ret; - } - -static void *nistp224_pre_comp_dup(void *src_) - { - NISTP224_PRE_COMP *src = src_; - - /* no need to actually copy, these objects never change! */ - CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); - - return src_; - } - -static void nistp224_pre_comp_free(void *pre_) - { - int i; - NISTP224_PRE_COMP *pre = pre_; - - if (!pre) - return; - - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - return; - - OPENSSL_free(pre); - } - -static void nistp224_pre_comp_clear_free(void *pre_) - { - int i; - NISTP224_PRE_COMP *pre = pre_; - - if (!pre) - return; - - i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); - if (i > 0) - return; - - OPENSSL_cleanse(pre, sizeof *pre); - OPENSSL_free(pre); - } +{ + NISTP224_PRE_COMP *ret = OPENSSL_zalloc(sizeof(*ret)); + + if (!ret) { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + return ret; + } + + ret->references = 1; + + ret->lock = CRYPTO_THREAD_lock_new(); + if (ret->lock == NULL) { + ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); + OPENSSL_free(ret); + return NULL; + } + return ret; +} + +NISTP224_PRE_COMP *EC_nistp224_pre_comp_dup(NISTP224_PRE_COMP *p) +{ + int i; + if (p != NULL) + CRYPTO_UP_REF(&p->references, &i, p->lock); + return p; +} + +void EC_nistp224_pre_comp_free(NISTP224_PRE_COMP *p) +{ + int i; + + if (p == NULL) + return; + + CRYPTO_DOWN_REF(&p->references, &i, p->lock); + REF_PRINT_COUNT("EC_nistp224", x); + if (i > 0) + return; + REF_ASSERT_ISNT(i < 0); + + CRYPTO_THREAD_lock_free(p->lock); + OPENSSL_free(p); +} /******************************************************************************/ -/* OPENSSL EC_METHOD FUNCTIONS +/* + * OPENSSL EC_METHOD FUNCTIONS */ int ec_GFp_nistp224_group_init(EC_GROUP *group) - { - int ret; - ret = ec_GFp_simple_group_init(group); - group->a_is_minus3 = 1; - return ret; - } +{ + int ret; + ret = ec_GFp_simple_group_init(group); + group->a_is_minus3 = 1; + return ret; +} int ec_GFp_nistp224_group_set_curve(EC_GROUP *group, const BIGNUM *p, - const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) - { - int ret = 0; - BN_CTX *new_ctx = NULL; - BIGNUM *curve_p, *curve_a, *curve_b; - - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((curve_p = BN_CTX_get(ctx)) == NULL) || - ((curve_a = BN_CTX_get(ctx)) == NULL) || - ((curve_b = BN_CTX_get(ctx)) == NULL)) goto err; - BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); - BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); - BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); - if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || - (BN_cmp(curve_b, b))) - { - ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, - EC_R_WRONG_CURVE_PARAMETERS); - goto err; - } - group->field_mod_func = BN_nist_mod_224; - ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); -err: - BN_CTX_end(ctx); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - return ret; - } - -/* Takes the Jacobian coordinates (X, Y, Z) of a point and returns - * (X', Y') = (X/Z^2, Y/Z^3) */ + const BIGNUM *a, const BIGNUM *b, + BN_CTX *ctx) +{ + int ret = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *curve_p, *curve_a, *curve_b; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + curve_p = BN_CTX_get(ctx); + curve_a = BN_CTX_get(ctx); + curve_b = BN_CTX_get(ctx); + if (curve_b == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[0], sizeof(felem_bytearray), curve_p); + BN_bin2bn(nistp224_curve_params[1], sizeof(felem_bytearray), curve_a); + BN_bin2bn(nistp224_curve_params[2], sizeof(felem_bytearray), curve_b); + if ((BN_cmp(curve_p, p)) || (BN_cmp(curve_a, a)) || (BN_cmp(curve_b, b))) { + ECerr(EC_F_EC_GFP_NISTP224_GROUP_SET_CURVE, + EC_R_WRONG_CURVE_PARAMETERS); + goto err; + } + group->field_mod_func = BN_nist_mod_224; + ret = ec_GFp_simple_group_set_curve(group, p, a, b, ctx); + err: + BN_CTX_end(ctx); + BN_CTX_free(new_ctx); + return ret; +} + +/* + * Takes the Jacobian coordinates (X, Y, Z) of a point and returns (X', Y') = + * (X/Z^2, Y/Z^3) + */ int ec_GFp_nistp224_point_get_affine_coordinates(const EC_GROUP *group, - const EC_POINT *point, BIGNUM *x, BIGNUM *y, BN_CTX *ctx) - { - fslice z1[4], z2[4], x_in[4], y_in[4], x_out[4], y_out[4]; - uint128_t tmp[7]; - - if (EC_POINT_is_at_infinity(group, point)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - EC_R_POINT_AT_INFINITY); - return 0; - } - if ((!BN_to_felem(x_in, &point->X)) || (!BN_to_felem(y_in, &point->Y)) || - (!BN_to_felem(z1, &point->Z))) return 0; - felem_inv(z2, z1); - felem_square(tmp, z2); felem_reduce(z1, tmp); - felem_mul(tmp, x_in, z1); felem_reduce(x_in, tmp); - felem_contract(x_out, x_in); - if (x != NULL) - { - if (!felem_to_BN(x, x_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } - } - felem_mul(tmp, z1, z2); felem_reduce(z1, tmp); - felem_mul(tmp, y_in, z1); felem_reduce(y_in, tmp); - felem_contract(y_out, y_in); - if (y != NULL) - { - if (!felem_to_BN(y, y_out)) { - ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, - ERR_R_BN_LIB); - return 0; - } - } - return 1; - } - -/* Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL values - * Result is stored in r (r can equal one of the inputs). */ + const EC_POINT *point, + BIGNUM *x, BIGNUM *y, + BN_CTX *ctx) +{ + felem z1, z2, x_in, y_in, x_out, y_out; + widefelem tmp; + + if (EC_POINT_is_at_infinity(group, point)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + EC_R_POINT_AT_INFINITY); + return 0; + } + if ((!BN_to_felem(x_in, point->X)) || (!BN_to_felem(y_in, point->Y)) || + (!BN_to_felem(z1, point->Z))) + return 0; + felem_inv(z2, z1); + felem_square(tmp, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, x_in, z1); + felem_reduce(x_in, tmp); + felem_contract(x_out, x_in); + if (x != NULL) { + if (!felem_to_BN(x, x_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + felem_mul(tmp, z1, z2); + felem_reduce(z1, tmp); + felem_mul(tmp, y_in, z1); + felem_reduce(y_in, tmp); + felem_contract(y_out, y_in); + if (y != NULL) { + if (!felem_to_BN(y, y_out)) { + ECerr(EC_F_EC_GFP_NISTP224_POINT_GET_AFFINE_COORDINATES, + ERR_R_BN_LIB); + return 0; + } + } + return 1; +} + +static void make_points_affine(size_t num, felem points[ /* num */ ][3], + felem tmp_felems[ /* num+1 */ ]) +{ + /* + * Runs in constant time, unless an input is the point at infinity (which + * normally shouldn't happen). + */ + ec_GFp_nistp_points_make_affine_internal(num, + points, + sizeof(felem), + tmp_felems, + (void (*)(void *))felem_one, + felem_is_zero_int, + (void (*)(void *, const void *)) + felem_assign, + (void (*)(void *, const void *)) + felem_square_reduce, (void (*) + (void *, + const void + *, + const void + *)) + felem_mul_reduce, + (void (*)(void *, const void *)) + felem_inv, + (void (*)(void *, const void *)) + felem_contract); +} + +/* + * Computes scalar*generator + \sum scalars[i]*points[i], ignoring NULL + * values Result is stored in r (r can equal one of the inputs). + */ int ec_GFp_nistp224_points_mul(const EC_GROUP *group, EC_POINT *r, - const BIGNUM *scalar, size_t num, const EC_POINT *points[], - const BIGNUM *scalars[], BN_CTX *ctx) - { - int ret = 0; - int i, j; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y, *z, *tmp_scalar; - felem_bytearray g_secret; - felem_bytearray *secrets = NULL; - fslice (*pre_comp)[16][3][4] = NULL; - felem_bytearray tmp; - unsigned num_bytes; - int have_pre_comp = 0; - size_t num_points = num; - fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4]; - NISTP224_PRE_COMP *pre = NULL; - fslice (*g_pre_comp)[3][4] = NULL; - EC_POINT *generator = NULL; - const EC_POINT *p = NULL; - const BIGNUM *p_scalar = NULL; - - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL) || - ((z = BN_CTX_get(ctx)) == NULL) || - ((tmp_scalar = BN_CTX_get(ctx)) == NULL)) - goto err; - - if (scalar != NULL) - { - pre = EC_EX_DATA_get_data(group->extra_data, - nistp224_pre_comp_dup, nistp224_pre_comp_free, - nistp224_pre_comp_clear_free); - if (pre) - /* we have precomputation, try to use it */ - g_pre_comp = pre->g_pre_comp; - else - /* try to use the standard precomputation */ - g_pre_comp = (fslice (*)[3][4]) gmul; - generator = EC_POINT_new(group); - if (generator == NULL) - goto err; - /* get the generator from precomputation */ - if (!felem_to_BN(x, g_pre_comp[1][0]) || - !felem_to_BN(y, g_pre_comp[1][1]) || - !felem_to_BN(z, g_pre_comp[1][2])) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - if (!EC_POINT_set_Jprojective_coordinates_GFp(group, - generator, x, y, z, ctx)) - goto err; - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - /* precomputation matches generator */ - have_pre_comp = 1; - else - /* we don't have valid precomputation: - * treat the generator as a random point */ - num_points = num_points + 1; - } - secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray)); - pre_comp = OPENSSL_malloc(num_points * 16 * 3 * 4 * sizeof(fslice)); - - if ((num_points) && ((secrets == NULL) || (pre_comp == NULL))) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); - goto err; - } - - /* we treat NULL scalars as 0, and NULL points as points at infinity, - * i.e., they contribute nothing to the linear combination */ - memset(secrets, 0, num_points * sizeof(felem_bytearray)); - memset(pre_comp, 0, num_points * 16 * 3 * 4 * sizeof(fslice)); - for (i = 0; i < num_points; ++i) - { - if (i == num) - /* the generator */ - { - p = EC_GROUP_get0_generator(group); - p_scalar = scalar; - } - else - /* the i^th point */ - { - p = points[i]; - p_scalar = scalars[i]; - } - if ((p_scalar != NULL) && (p != NULL)) - { - num_bytes = BN_num_bytes(p_scalar); - /* reduce scalar to 0 <= scalar < 2^224 */ - if ((num_bytes > sizeof(felem_bytearray)) || (BN_is_negative(p_scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, p_scalar, &group->order, ctx)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); - } - else - BN_bn2bin(p_scalar, tmp); - flip_endian(secrets[i], tmp, num_bytes); - /* precompute multiples */ - if ((!BN_to_felem(x_out, &p->X)) || - (!BN_to_felem(y_out, &p->Y)) || - (!BN_to_felem(z_out, &p->Z))) goto err; - memcpy(pre_comp[i][1][0], x_out, 4 * sizeof(fslice)); - memcpy(pre_comp[i][1][1], y_out, 4 * sizeof(fslice)); - memcpy(pre_comp[i][1][2], z_out, 4 * sizeof(fslice)); - for (j = 1; j < 8; ++j) - { - point_double(pre_comp[i][2*j][0], - pre_comp[i][2*j][1], - pre_comp[i][2*j][2], - pre_comp[i][j][0], - pre_comp[i][j][1], - pre_comp[i][j][2]); - point_add(pre_comp[i][2*j+1][0], - pre_comp[i][2*j+1][1], - pre_comp[i][2*j+1][2], - pre_comp[i][1][0], - pre_comp[i][1][1], - pre_comp[i][1][2], - pre_comp[i][2*j][0], - pre_comp[i][2*j][1], - pre_comp[i][2*j][2]); - } - } - } - - /* the scalar for the generator */ - if ((scalar != NULL) && (have_pre_comp)) - { - memset(g_secret, 0, sizeof g_secret); - num_bytes = BN_num_bytes(scalar); - /* reduce scalar to 0 <= scalar < 2^224 */ - if ((num_bytes > sizeof(felem_bytearray)) || (BN_is_negative(scalar))) - { - /* this is an unusual input, and we don't guarantee - * constant-timeness */ - if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - num_bytes = BN_bn2bin(tmp_scalar, tmp); - } - else - BN_bn2bin(scalar, tmp); - flip_endian(g_secret, tmp, num_bytes); - /* do the multiplication with generator precomputation*/ - batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - g_secret, (const fslice (*)[16][3][4]) pre_comp, - (const fslice (*)[3][4]) g_pre_comp); - } - else - /* do the multiplication without generator precomputation */ - batch_mul(x_out, y_out, z_out, - (const felem_bytearray (*)) secrets, num_points, - NULL, (const fslice (*)[16][3][4]) pre_comp, NULL); - /* reduce the output to its unique minimal representation */ - felem_contract(x_in, x_out); - felem_contract(y_in, y_out); - felem_contract(z_in, z_out); - if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || - (!felem_to_BN(z, z_in))) - { - ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); - goto err; - } - ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); - -err: - BN_CTX_end(ctx); - if (generator != NULL) - EC_POINT_free(generator); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - if (secrets != NULL) - OPENSSL_free(secrets); - if (pre_comp != NULL) - OPENSSL_free(pre_comp); - return ret; - } + const BIGNUM *scalar, size_t num, + const EC_POINT *points[], + const BIGNUM *scalars[], BN_CTX *ctx) +{ + int ret = 0; + int j; + unsigned i; + int mixed = 0; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y, *z, *tmp_scalar; + felem_bytearray g_secret; + felem_bytearray *secrets = NULL; + felem (*pre_comp)[17][3] = NULL; + felem *tmp_felems = NULL; + felem_bytearray tmp; + unsigned num_bytes; + int have_pre_comp = 0; + size_t num_points = num; + felem x_in, y_in, z_in, x_out, y_out, z_out; + NISTP224_PRE_COMP *pre = NULL; + const felem(*g_pre_comp)[16][3] = NULL; + EC_POINT *generator = NULL; + const EC_POINT *p = NULL; + const BIGNUM *p_scalar = NULL; + + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + z = BN_CTX_get(ctx); + tmp_scalar = BN_CTX_get(ctx); + if (tmp_scalar == NULL) + goto err; + + if (scalar != NULL) { + pre = group->pre_comp.nistp224; + if (pre) + /* we have precomputation, try to use it */ + g_pre_comp = (const felem(*)[16][3])pre->g_pre_comp; + else + /* try to use the standard precomputation */ + g_pre_comp = &gmul[0]; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + /* get the generator from precomputation */ + if (!felem_to_BN(x, g_pre_comp[0][1][0]) || + !felem_to_BN(y, g_pre_comp[0][1][1]) || + !felem_to_BN(z, g_pre_comp[0][1][2])) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + if (!EC_POINT_set_Jprojective_coordinates_GFp(group, + generator, x, y, z, + ctx)) + goto err; + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) + /* precomputation matches generator */ + have_pre_comp = 1; + else + /* + * we don't have valid precomputation: treat the generator as a + * random point + */ + num_points = num_points + 1; + } + + if (num_points > 0) { + if (num_points >= 3) { + /* + * unless we precompute multiples for just one or two points, + * converting those into affine form is time well spent + */ + mixed = 1; + } + secrets = OPENSSL_zalloc(sizeof(*secrets) * num_points); + pre_comp = OPENSSL_zalloc(sizeof(*pre_comp) * num_points); + if (mixed) + tmp_felems = + OPENSSL_malloc(sizeof(felem) * (num_points * 17 + 1)); + if ((secrets == NULL) || (pre_comp == NULL) + || (mixed && (tmp_felems == NULL))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE); + goto err; + } + + /* + * we treat NULL scalars as 0, and NULL points as points at infinity, + * i.e., they contribute nothing to the linear combination + */ + for (i = 0; i < num_points; ++i) { + if (i == num) + /* the generator */ + { + p = EC_GROUP_get0_generator(group); + p_scalar = scalar; + } else + /* the i^th point */ + { + p = points[i]; + p_scalar = scalars[i]; + } + if ((p_scalar != NULL) && (p != NULL)) { + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(p_scalar) > 224) + || (BN_is_negative(p_scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, p_scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(p_scalar, tmp); + flip_endian(secrets[i], tmp, num_bytes); + /* precompute multiples */ + if ((!BN_to_felem(x_out, p->X)) || + (!BN_to_felem(y_out, p->Y)) || + (!BN_to_felem(z_out, p->Z))) + goto err; + felem_assign(pre_comp[i][1][0], x_out); + felem_assign(pre_comp[i][1][1], y_out); + felem_assign(pre_comp[i][1][2], z_out); + for (j = 2; j <= 16; ++j) { + if (j & 1) { + point_add(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][1][0], + pre_comp[i][1][1], pre_comp[i][1][2], 0, + pre_comp[i][j - 1][0], + pre_comp[i][j - 1][1], + pre_comp[i][j - 1][2]); + } else { + point_double(pre_comp[i][j][0], pre_comp[i][j][1], + pre_comp[i][j][2], pre_comp[i][j / 2][0], + pre_comp[i][j / 2][1], + pre_comp[i][j / 2][2]); + } + } + } + } + if (mixed) + make_points_affine(num_points * 17, pre_comp[0], tmp_felems); + } + + /* the scalar for the generator */ + if ((scalar != NULL) && (have_pre_comp)) { + memset(g_secret, 0, sizeof(g_secret)); + /* reduce scalar to 0 <= scalar < 2^224 */ + if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar))) { + /* + * this is an unusual input, and we don't guarantee + * constant-timeness + */ + if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + num_bytes = BN_bn2bin(tmp_scalar, tmp); + } else + num_bytes = BN_bn2bin(scalar, tmp); + flip_endian(g_secret, tmp, num_bytes); + /* do the multiplication with generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + g_secret, + mixed, (const felem(*)[17][3])pre_comp, g_pre_comp); + } else + /* do the multiplication without generator precomputation */ + batch_mul(x_out, y_out, z_out, + (const felem_bytearray(*))secrets, num_points, + NULL, mixed, (const felem(*)[17][3])pre_comp, NULL); + /* reduce the output to its unique minimal representation */ + felem_contract(x_in, x_out); + felem_contract(y_in, y_out); + felem_contract(z_in, z_out); + if ((!felem_to_BN(x, x_in)) || (!felem_to_BN(y, y_in)) || + (!felem_to_BN(z, z_in))) { + ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_BN_LIB); + goto err; + } + ret = EC_POINT_set_Jprojective_coordinates_GFp(group, r, x, y, z, ctx); + + err: + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + OPENSSL_free(secrets); + OPENSSL_free(pre_comp); + OPENSSL_free(tmp_felems); + return ret; +} int ec_GFp_nistp224_precompute_mult(EC_GROUP *group, BN_CTX *ctx) - { - int ret = 0; - NISTP224_PRE_COMP *pre = NULL; - int i, j; - BN_CTX *new_ctx = NULL; - BIGNUM *x, *y; - EC_POINT *generator = NULL; - - /* throw away old precomputation */ - EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free); - if (ctx == NULL) - if ((ctx = new_ctx = BN_CTX_new()) == NULL) return 0; - BN_CTX_start(ctx); - if (((x = BN_CTX_get(ctx)) == NULL) || - ((y = BN_CTX_get(ctx)) == NULL)) - goto err; - /* get the generator */ - if (group->generator == NULL) goto err; - generator = EC_POINT_new(group); - if (generator == NULL) - goto err; - BN_bin2bn(nistp224_curve_params[3], sizeof (felem_bytearray), x); - BN_bin2bn(nistp224_curve_params[4], sizeof (felem_bytearray), y); - if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) - goto err; - if ((pre = nistp224_pre_comp_new()) == NULL) - goto err; - /* if the generator is the standard one, use built-in precomputation */ - if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) - { - memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); - ret = 1; - goto err; - } - if ((!BN_to_felem(pre->g_pre_comp[1][0], &group->generator->X)) || - (!BN_to_felem(pre->g_pre_comp[1][1], &group->generator->Y)) || - (!BN_to_felem(pre->g_pre_comp[1][2], &group->generator->Z))) - goto err; - /* compute 2^56*G, 2^112*G, 2^168*G */ - for (i = 1; i < 5; ++i) - { - point_double(pre->g_pre_comp[2*i][0], pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], pre->g_pre_comp[i][0], - pre->g_pre_comp[i][1], pre->g_pre_comp[i][2]); - for (j = 0; j < 55; ++j) - { - point_double(pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2], - pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], - pre->g_pre_comp[2*i][2]); - } - } - /* g_pre_comp[0] is the point at infinity */ - memset(pre->g_pre_comp[0], 0, sizeof(pre->g_pre_comp[0])); - /* the remaining multiples */ - /* 2^56*G + 2^112*G */ - point_add(pre->g_pre_comp[6][0], pre->g_pre_comp[6][1], - pre->g_pre_comp[6][2], pre->g_pre_comp[4][0], - pre->g_pre_comp[4][1], pre->g_pre_comp[4][2], - pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - /* 2^56*G + 2^168*G */ - point_add(pre->g_pre_comp[10][0], pre->g_pre_comp[10][1], - pre->g_pre_comp[10][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - /* 2^112*G + 2^168*G */ - point_add(pre->g_pre_comp[12][0], pre->g_pre_comp[12][1], - pre->g_pre_comp[12][2], pre->g_pre_comp[8][0], - pre->g_pre_comp[8][1], pre->g_pre_comp[8][2], - pre->g_pre_comp[4][0], pre->g_pre_comp[4][1], - pre->g_pre_comp[4][2]); - /* 2^56*G + 2^112*G + 2^168*G */ - point_add(pre->g_pre_comp[14][0], pre->g_pre_comp[14][1], - pre->g_pre_comp[14][2], pre->g_pre_comp[12][0], - pre->g_pre_comp[12][1], pre->g_pre_comp[12][2], - pre->g_pre_comp[2][0], pre->g_pre_comp[2][1], - pre->g_pre_comp[2][2]); - for (i = 1; i < 8; ++i) - { - /* odd multiples: add G */ - point_add(pre->g_pre_comp[2*i+1][0], pre->g_pre_comp[2*i+1][1], - pre->g_pre_comp[2*i+1][2], pre->g_pre_comp[2*i][0], - pre->g_pre_comp[2*i][1], pre->g_pre_comp[2*i][2], - pre->g_pre_comp[1][0], pre->g_pre_comp[1][1], - pre->g_pre_comp[1][2]); - } - - if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free)) - goto err; - ret = 1; - pre = NULL; +{ + int ret = 0; + NISTP224_PRE_COMP *pre = NULL; + int i, j; + BN_CTX *new_ctx = NULL; + BIGNUM *x, *y; + EC_POINT *generator = NULL; + felem tmp_felems[32]; + + /* throw away old precomputation */ + EC_pre_comp_free(group); + if (ctx == NULL) + if ((ctx = new_ctx = BN_CTX_new()) == NULL) + return 0; + BN_CTX_start(ctx); + x = BN_CTX_get(ctx); + y = BN_CTX_get(ctx); + if (y == NULL) + goto err; + /* get the generator */ + if (group->generator == NULL) + goto err; + generator = EC_POINT_new(group); + if (generator == NULL) + goto err; + BN_bin2bn(nistp224_curve_params[3], sizeof(felem_bytearray), x); + BN_bin2bn(nistp224_curve_params[4], sizeof(felem_bytearray), y); + if (!EC_POINT_set_affine_coordinates_GFp(group, generator, x, y, ctx)) + goto err; + if ((pre = nistp224_pre_comp_new()) == NULL) + goto err; + /* + * if the generator is the standard one, use built-in precomputation + */ + if (0 == EC_POINT_cmp(group, generator, group->generator, ctx)) { + memcpy(pre->g_pre_comp, gmul, sizeof(pre->g_pre_comp)); + goto done; + } + if ((!BN_to_felem(pre->g_pre_comp[0][1][0], group->generator->X)) || + (!BN_to_felem(pre->g_pre_comp[0][1][1], group->generator->Y)) || + (!BN_to_felem(pre->g_pre_comp[0][1][2], group->generator->Z))) + goto err; + /* + * compute 2^56*G, 2^112*G, 2^168*G for the first table, 2^28*G, 2^84*G, + * 2^140*G, 2^196*G for the second one + */ + for (i = 1; i <= 8; i <<= 1) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[0][i][0], + pre->g_pre_comp[0][i][1], pre->g_pre_comp[0][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[1][i][0], pre->g_pre_comp[1][i][1], + pre->g_pre_comp[1][i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + } + if (i == 8) + break; + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], pre->g_pre_comp[1][i][0], + pre->g_pre_comp[1][i][1], pre->g_pre_comp[1][i][2]); + for (j = 0; j < 27; ++j) { + point_double(pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2], + pre->g_pre_comp[0][2 * i][0], + pre->g_pre_comp[0][2 * i][1], + pre->g_pre_comp[0][2 * i][2]); + } + } + for (i = 0; i < 2; i++) { + /* g_pre_comp[i][0] is the point at infinity */ + memset(pre->g_pre_comp[i][0], 0, sizeof(pre->g_pre_comp[i][0])); + /* the remaining multiples */ + /* 2^56*G + 2^112*G resp. 2^84*G + 2^140*G */ + point_add(pre->g_pre_comp[i][6][0], pre->g_pre_comp[i][6][1], + pre->g_pre_comp[i][6][2], pre->g_pre_comp[i][4][0], + pre->g_pre_comp[i][4][1], pre->g_pre_comp[i][4][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^56*G + 2^168*G resp. 2^84*G + 2^196*G */ + point_add(pre->g_pre_comp[i][10][0], pre->g_pre_comp[i][10][1], + pre->g_pre_comp[i][10][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + /* 2^112*G + 2^168*G resp. 2^140*G + 2^196*G */ + point_add(pre->g_pre_comp[i][12][0], pre->g_pre_comp[i][12][1], + pre->g_pre_comp[i][12][2], pre->g_pre_comp[i][8][0], + pre->g_pre_comp[i][8][1], pre->g_pre_comp[i][8][2], + 0, pre->g_pre_comp[i][4][0], pre->g_pre_comp[i][4][1], + pre->g_pre_comp[i][4][2]); + /* + * 2^56*G + 2^112*G + 2^168*G resp. 2^84*G + 2^140*G + 2^196*G + */ + point_add(pre->g_pre_comp[i][14][0], pre->g_pre_comp[i][14][1], + pre->g_pre_comp[i][14][2], pre->g_pre_comp[i][12][0], + pre->g_pre_comp[i][12][1], pre->g_pre_comp[i][12][2], + 0, pre->g_pre_comp[i][2][0], pre->g_pre_comp[i][2][1], + pre->g_pre_comp[i][2][2]); + for (j = 1; j < 8; ++j) { + /* odd multiples: add G resp. 2^28*G */ + point_add(pre->g_pre_comp[i][2 * j + 1][0], + pre->g_pre_comp[i][2 * j + 1][1], + pre->g_pre_comp[i][2 * j + 1][2], + pre->g_pre_comp[i][2 * j][0], + pre->g_pre_comp[i][2 * j][1], + pre->g_pre_comp[i][2 * j][2], 0, + pre->g_pre_comp[i][1][0], pre->g_pre_comp[i][1][1], + pre->g_pre_comp[i][1][2]); + } + } + make_points_affine(31, &(pre->g_pre_comp[0][1]), tmp_felems); + + done: + SETPRECOMP(group, nistp224, pre); + pre = NULL; + ret = 1; err: - BN_CTX_end(ctx); - if (generator != NULL) - EC_POINT_free(generator); - if (new_ctx != NULL) - BN_CTX_free(new_ctx); - if (pre) - nistp224_pre_comp_free(pre); - return ret; - } + BN_CTX_end(ctx); + EC_POINT_free(generator); + BN_CTX_free(new_ctx); + EC_nistp224_pre_comp_free(pre); + return ret; +} int ec_GFp_nistp224_have_precompute_mult(const EC_GROUP *group) - { - if (EC_EX_DATA_get_data(group->extra_data, nistp224_pre_comp_dup, - nistp224_pre_comp_free, nistp224_pre_comp_clear_free) - != NULL) - return 1; - else - return 0; - } +{ + return HAVEPRECOMP(group, nistp224); +} -#else -static void *dummy=&dummy; #endif