/*
* Written by Emilia Kasper (Google) for the OpenSSL project.
*/
-/* ====================================================================
- * Copyright (c) 2000-2010 The OpenSSL Project. All rights reserved.
+/* Copyright 2011 Google Inc.
*
- * Redistribution and use in source and binary forms, with or without
- * modification, are permitted provided that the following conditions
- * are met:
+ * Licensed under the Apache License, Version 2.0 (the "License");
*
- * 1. Redistributions of source code must retain the above copyright
- * notice, this list of conditions and the following disclaimer.
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
*
- * 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.
- *
- * 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.
- *
- * 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/)"
- *
- * 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.
- * ====================================================================
- *
- * 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.
*/
/*
* Inspired by Daniel J. Bernstein's public domain nistp224 implementation
* and Adam Langley's public domain 64-bit C implementation of curve25519
*/
-#ifdef EC_NISTP224_64_GCC_128
+
+#include <openssl/opensslconf.h>
+#ifndef OPENSSL_NO_EC_NISTP_64_GCC_128
+
#include <stdint.h>
#include <string.h>
#include <openssl/err.h>
#endif
typedef uint8_t u8;
+typedef uint64_t u64;
+typedef int64_t s64;
/******************************************************************************/
/* 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. */
+ * 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] = {
};
/* 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}}
-};
+ * 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];
+ felem g_pre_comp[2][16][3];
int references;
} NISTP224_PRE_COMP;
const EC_METHOD *EC_GFp_nistp224_method(void)
{
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_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,
+ 0 /* point_set_compressed_coordinates */,
+ 0 /* point2oct */,
+ 0 /* oct2point */,
ec_GFp_simple_add,
ec_GFp_simple_dbl,
ec_GFp_simple_invert,
}
/* Helper functions to convert field elements to/from internal representation */
-static void bin28_to_felem(fslice out[4], const u8 in[28])
+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[3] = (*((const uint64_t *)(in+21))) & 0x00ffffffffffffff;
}
-static void felem_to_bin28(u8 out[28], const fslice in[4])
+static void felem_to_bin28(u8 out[28], const felem in)
{
unsigned i;
for (i = 0; i < 7; ++i)
}
/* From OpenSSL BIGNUM to internal representation */
-static int BN_to_felem(fslice out[4], const BIGNUM *bn)
+static int BN_to_felem(felem out, const BIGNUM *bn)
{
- felem_bytearray b_in;
+ felem_bytearray b_in;
felem_bytearray b_out;
unsigned num_bytes;
}
/* From internal representation to OpenSSL BIGNUM */
-static BIGNUM *felem_to_BN(BIGNUM *out, const fslice in[4])
+static BIGNUM *felem_to_BN(BIGNUM *out, const felem in)
{
felem_bytearray b_in, b_out;
felem_to_bin28(b_in, in);
*
*/
+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])
+static void felem_sum(felem out, const felem in)
{
out[0] += in[0];
out[1] += in[1];
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 void felem_diff(felem out, const felem in)
{
- 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);
+ 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[3] -= in[3];
}
-/* Subtract in unreduced 128-bit mode: out128 -= in128 */
+/* 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 void widefelem_diff(widefelem out, const widefelem in)
{
- 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);
+ 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;
/* 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 void felem_diff_128_64(widefelem out, const felem in)
{
- 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);
+ 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[3] -= in[3];
}
-/* Multiply a field element by a scalar: out64 = out64 * scalar
+/* 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_scalar64(fslice out[4], const fslice scalar)
+static void felem_scalar(felem out, const limb scalar)
{
out[0] *= scalar;
out[1] *= scalar;
out[3] *= scalar;
}
-/* Multiply an unreduced field element by a scalar: out128 = out128 * 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 felem_scalar128(uint128_t out[7], const uint128_t scalar)
+static void widefelem_scalar(widefelem out, const widelimb scalar)
{
out[0] *= scalar;
out[1] *= scalar;
}
/* Square a field element: out = in^2 */
-static void felem_square(uint128_t out[7], const fslice in[4])
+static void felem_square(widefelem out, const felem in)
{
- 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];
+ 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])
+static void felem_mul(widefelem out, const felem in1, const felem in2)
{
- 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];
+ 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 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])
+/* 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 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];
+ 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;
/* Eliminate in[4], in[5], in[6] */
output[4] += in[6] >> 16;
- output[3] += (in[6]&0xffff) << 40;
+ output[3] += (in[6] & 0xffff) << 40;
output[2] -= in[6];
output[3] += in[5] >> 16;
- output[2] += (in[5]&0xffff) << 40;
+ output[2] += (in[5] & 0xffff) << 40;
output[1] -= in[5];
output[2] += output[4] >> 16;
- output[1] += (output[4]&0xffff) << 40;
+ 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[4] = output[3] >> 56;
output[3] &= 0x00ffffffffffffff;
- /* Now output[2] < 2^56, output[3] < 2^56 */
+ /* Now output[2] < 2^56, output[3] < 2^56, output[4] < 2^72 */
/* Eliminate output[4] */
output[2] += output[4] >> 16;
- output[1] += (output[4]&0xffff) << 40;
+ /* output[2] < 2^56 + 2^56 = 2^57 */
+ output[1] += (output[4] & 0xffff) << 40;
output[0] -= output[4];
/* Carry 0 -> 1 -> 2 -> 3 */
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] < 2^57 (due to final carry) */
+ * out[3] <= 2^56 + 2^16 (due to final carry),
+ * so out < 2*p */
out[3] = output[3];
}
-/* Reduce to unique minimal representation */
-static void felem_contract(fslice out[4], const fslice in[4])
+static void felem_square_reduce(felem out, const felem in)
{
- 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;
+ widefelem tmp;
+ felem_square(tmp, in);
+ felem_reduce(out, tmp);
+ }
- tmp[3] += tmp[2] >> 56;
- tmp[2] &= 0x00ffffffffffffff;
+static void felem_mul_reduce(felem out, const felem in1, const felem in2)
+ {
+ widefelem tmp;
+ felem_mul(tmp, in1, in2);
+ felem_reduce(out, tmp);
+ }
- /* 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);
+/* 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 */
+ /* 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;
- 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;
-
+ /* Now 0 <= out < p */
out[0] = tmp[0];
out[1] = tmp[1];
out[2] = tmp[2];
* 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])
+static limb felem_is_zero(const felem in)
{
- fslice zero, two224m96p1, two225m97p2;
+ limb zero, two224m96p1, two225m97p2;
zero = in[0] | in[1] | in[2] | in[3];
zero = (((int64_t)(zero) - 1) >> 63) & 1;
return (zero | two224m96p1 | two225m97p2);
}
+static limb felem_is_zero_int(const felem 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])
+static void felem_inv(felem out, const felem in)
{
- fslice ftmp[4], ftmp2[4], ftmp3[4], ftmp4[4];
- uint128_t tmp[7];
+ felem ftmp, ftmp2, ftmp3, ftmp4;
+ widefelem tmp;
unsigned i;
felem_square(tmp, in); felem_reduce(ftmp, tmp); /* 2 */
* 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)
+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 fslice copy = -icopy;
- for (i = 0; i < len; ++i)
+ const limb copy = -icopy;
+ for (i = 0; i < 4; ++i)
{
- const fslice tmp = copy & (in[i] ^ out[i]);
+ const limb 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;
- }
-}
-
/******************************************************************************/
/* ELLIPTIC CURVE POINT OPERATIONS
*
* 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). */
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])
+point_double(felem x_out, felem y_out, felem z_out,
+ const felem x_in, const felem y_in, const felem z_in)
{
- 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));
+ 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(beta, tmp);
/* alpha = 3*(x-delta)*(x+delta) */
- felem_diff64(ftmp, delta);
+ felem_diff(ftmp, delta);
/* ftmp[i] < 2^57 + 2^58 + 2 < 2^59 */
- felem_sum64(ftmp2, delta);
+ felem_sum(ftmp2, delta);
/* ftmp2[i] < 2^57 + 2^57 = 2^58 */
- felem_scalar64(ftmp2, 3);
+ 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 */
/* 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);
+ 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_sum64(delta, gamma);
+ felem_sum(delta, gamma);
/* delta[i] < 2^57 + 2^57 = 2^58 */
- memcpy(ftmp, y_in, 4 * sizeof(fslice));
- felem_sum64(ftmp, z_in);
+ 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_reduce(z_out, tmp);
/* y' = alpha*(4*beta - x') - 8*gamma^2 */
- felem_scalar64(beta, 4);
+ felem_scalar(beta, 4);
/* beta[i] < 4 * 2^57 = 2^59 */
- felem_diff64(beta, x_out);
+ 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 */
- felem_scalar128(tmp2, 8);
+ widefelem_scalar(tmp2, 8);
/* tmp2[i] < 8 * 2^116 = 2^119 */
- felem_diff128(tmp, tmp2);
+ widefelem_diff(tmp, tmp2);
/* tmp[i] < 2^119 + 2^120 < 2^121 */
felem_reduce(y_out, tmp);
}
* 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) */
+ * 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(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])
+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)
{
- 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;
+ 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);
- /* 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 */
+ /* tmp = 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 */
+ /* tmp = 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);
+ felem_diff_128_64(tmp, ftmp2);
/* tmp[i] < 2^116 + 2^64 + 8 < 2^117 */
felem_reduce(ftmp, tmp);
}
/* ftmp5 = z1*z2 */
- felem_mul(tmp, z1, z2);
- felem_reduce(ftmp5, tmp);
+ if (!mixed)
+ {
+ felem_mul(tmp, z1, z2);
+ felem_reduce(ftmp5, tmp);
+ }
+ else
+ {
+ /* special case z2 = 0 is handled later */
+ felem_assign(ftmp5, z1);
+ }
- /* z3 = (z1^2*x2 - z2^2*x1)*(z1*z2) */
+ /* z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) */
felem_mul(tmp, ftmp, ftmp5);
- felem_reduce(z3, tmp);
+ felem_reduce(z_out, tmp);
/* ftmp = (z1^2*x2 - z2^2*x1)^2 */
- memcpy(ftmp5, ftmp, 4 * sizeof(fslice));
+ felem_assign(ftmp5, ftmp);
felem_square(tmp, ftmp);
felem_reduce(ftmp, tmp);
felem_mul(tmp, ftmp2, ftmp);
felem_reduce(ftmp2, tmp);
- /* ftmp4 = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 */
+ /* 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[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);
+ felem_assign(ftmp5, ftmp2);
+ felem_scalar(ftmp5, 2);
/* ftmp5[i] < 2 * 2^57 = 2^58 */
- /* x3 = (z1^3*y2 - z2^3*y1)^2 - (z1^2*x2 - z2^2*x1)^3 -
+ /* 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(x3, tmp2);
+ felem_reduce(x_out, tmp2);
- /* ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3 */
- felem_diff64(ftmp2, x3);
+ /* 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 - x3) */
+ /* 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 */
- /* y3 = (z1^3*y2 - z2^3*y1)*(z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x3) -
+ /* 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 */
- felem_diff128(tmp2, tmp);
+ widefelem_diff(tmp2, tmp);
/* tmp2[i] < 2^118 + 2^120 < 2^121 */
- felem_reduce(y3, tmp2);
+ felem_reduce(y_out, 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 */
+ /* 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(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);
+ 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. */
+static void select_point(const u64 idx, unsigned int size, const felem pre_comp[/*size*/][3], felem out[3])
+ {
+ unsigned i, j;
+ limb *outlimbs = &out[0][0];
+ memset(outlimbs, 0, 3 * sizeof(felem));
+
+ 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;
+ }
}
-/* 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])
+/* get_bit returns the |i|th bit in |in| */
+static char get_bit(const felem_bytearray in, unsigned i)
{
- 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]);
+ 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, ..., 15*P are in pre_comp[],
+ * 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(fslice x_out[4], fslice y_out[4], fslice z_out[4],
+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 fslice pre_comp[][16][3][4], const fslice g_pre_comp[16][3][4])
+ const int mixed, const felem pre_comp[][17][3], const felem g_pre_comp[2][16][3])
{
- unsigned i, j, num;
+ int i, skip;
+ unsigned num;
unsigned gen_mul = (g_scalar != NULL);
- fslice nq[12], nqt[12], tmp[12];
- fslice bits[4];
- u8 byte;
+ felem nq[3], tmp[4];
+ u64 bits;
+ u8 sign, digit;
/* 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)
+ memset(nq, 0, 3 * sizeof(felem));
+
+ /* 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)
{
- for (j = 0; j < 8; ++j)
+ /* 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))
{
- /* double once */
- point_double(nq, nq+4, nq+8, nq, nq+4, nq+8);
- /* add multiples of the generator */
- if ((gen_mul) && (i <= 7))
+ /* 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)
{
- 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);
+ point_add(nq[0], nq[1], nq[2],
+ nq[0], nq[1], nq[2],
+ 1 /* mixed */, tmp[0], tmp[1], tmp[2]);
}
- /* do an addition after every 4 doublings */
- if (j % 4 == 3)
+ 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)
{
- /* 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
{
- 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(nq, tmp, 3 * sizeof(felem));
+ skip = 0;
}
}
}
}
- memcpy(x_out, nq, 4 * sizeof(fslice));
- memcpy(y_out, nq+4, 4 * sizeof(fslice));
- memcpy(z_out, nq+8, 4 * sizeof(fslice));
+ felem_assign(x_out, nq[0]);
+ felem_assign(y_out, nq[1]);
+ felem_assign(z_out, nq[2]);
}
/******************************************************************************/
static NISTP224_PRE_COMP *nistp224_pre_comp_new()
{
NISTP224_PRE_COMP *ret = NULL;
- ret = (NISTP224_PRE_COMP *)OPENSSL_malloc(sizeof(NISTP224_PRE_COMP));
+ ret = (NISTP224_PRE_COMP *) OPENSSL_malloc(sizeof *ret);
if (!ret)
{
ECerr(EC_F_NISTP224_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
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];
+ felem z1, z2, x_in, y_in, x_out, y_out;
+ widefelem tmp;
if (EC_POINT_is_at_infinity(group, point))
{
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,
+ (int (*)(const void *)) 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 *scalars[], BN_CTX *ctx)
{
int ret = 0;
- int i, j;
+ 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;
- fslice (*pre_comp)[16][3][4] = 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;
- fslice x_in[4], y_in[4], z_in[4], x_out[4], y_out[4], z_out[4];
+ felem x_in, y_in, z_in, x_out, y_out, z_out;
NISTP224_PRE_COMP *pre = NULL;
- fslice (*g_pre_comp)[3][4] = NULL;
+ const felem (*g_pre_comp)[16][3] = NULL;
EC_POINT *generator = NULL;
const EC_POINT *p = NULL;
const BIGNUM *p_scalar = NULL;
nistp224_pre_comp_clear_free);
if (pre)
/* we have precomputation, try to use it */
- g_pre_comp = pre->g_pre_comp;
+ g_pre_comp = (const felem (*)[16][3]) pre->g_pre_comp;
else
/* try to use the standard precomputation */
- g_pre_comp = (fslice (*)[3][4]) gmul;
+ 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[1][0]) ||
- !felem_to_BN(y, g_pre_comp[1][1]) ||
- !felem_to_BN(z, g_pre_comp[1][2]))
+ 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;
* 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 (num_points > 0)
{
- if (i == num)
- /* the generator */
+ if (num_points >= 3)
{
- p = EC_GROUP_get0_generator(group);
- p_scalar = scalar;
+ /* unless we precompute multiples for just one or two points,
+ * converting those into affine form is time well spent */
+ mixed = 1;
}
- else
- /* the i^th point */
+ secrets = OPENSSL_malloc(num_points * sizeof(felem_bytearray));
+ pre_comp = OPENSSL_malloc(num_points * 17 * 3 * sizeof(felem));
+ if (mixed)
+ tmp_felems = OPENSSL_malloc((num_points * 17 + 1) * sizeof(felem));
+ if ((secrets == NULL) || (pre_comp == NULL) || (mixed && (tmp_felems == NULL)))
{
- p = points[i];
- p_scalar = scalars[i];
+ ECerr(EC_F_EC_GFP_NISTP224_POINTS_MUL, ERR_R_MALLOC_FAILURE);
+ goto err;
}
- if ((p_scalar != NULL) && (p != NULL))
+
+ /* 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 * 17 * 3 * sizeof(felem));
+ for (i = 0; i < num_points; ++i)
{
- 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)))
+ if (i == num)
+ /* the generator */
{
- /* 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);
+ p = EC_GROUP_get0_generator(group);
+ p_scalar = scalar;
}
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)
+ /* the i^th point */
+ {
+ p = points[i];
+ p_scalar = scalars[i];
+ }
+ if ((p_scalar != NULL) && (p != NULL))
{
- 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]);
+ /* 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);
- num_bytes = BN_num_bytes(scalar);
/* reduce scalar to 0 <= scalar < 2^224 */
- if ((num_bytes > sizeof(felem_bytearray)) || (BN_is_negative(scalar)))
+ if ((BN_num_bits(scalar) > 224) || (BN_is_negative(scalar)))
{
/* this is an unusual input, and we don't guarantee
* constant-timeness */
num_bytes = BN_bn2bin(tmp_scalar, tmp);
}
else
- BN_bn2bin(scalar, tmp);
+ 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, (const fslice (*)[16][3][4]) pre_comp,
- (const fslice (*)[3][4]) g_pre_comp);
+ 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, (const fslice (*)[16][3][4]) pre_comp, NULL);
+ 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);
OPENSSL_free(secrets);
if (pre_comp != NULL)
OPENSSL_free(pre_comp);
+ if (tmp_felems != NULL)
+ OPENSSL_free(tmp_felems);
return ret;
}
BN_CTX *new_ctx = NULL;
BIGNUM *x, *y;
EC_POINT *generator = NULL;
+ felem tmp_felems[32];
/* throw away old precomputation */
EC_EX_DATA_free_data(&group->extra_data, nistp224_pre_comp_dup,
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)))
+ 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 (i = 1; i < 5; ++i)
+ /* 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[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[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[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]);
+ 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]);
}
}
- /* 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)
+ for (i = 0; i < 2; 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]);
+ /* 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);
if (!EC_EX_DATA_set_data(&group->extra_data, pre, nistp224_pre_comp_dup,
nistp224_pre_comp_free, nistp224_pre_comp_clear_free))
projects / openssl.git / blobdiff