Remove p224-64.cc.inc Instead, use the generic implementation for P-224. This is a *substantial* performance hit, but P-224 is no longer as important as it once was, and this file breaks some assumptions we'd otherwise be able to make in the EC implementation. OPENSSL_SMALL builds are not affected. This file was already not used in Chrome and Android. Benchmark Time CPU Time Old Time New CPU Old CPU New --------------------------------------------------------------------------------------------------------------------------------- BM_SpeedECDH/p224/threads:1 +3.2201 +3.2739 43679 184330 43123 184303 BM_SpeedECDSASign/p224/threads:1 +4.1784 +4.1797 19602 101506 19590 101468 BM_SpeedECDSAVerify/p224/threads:1 +1.1512 +1.1515 44381 95474 44373 95466 OVERALL_GEOMEAN +2.6091 +2.6248 0 0 0 0 Bug: 505908440 Change-Id: I809dc76b8a233f259f7cf834db022f3bb0a220f3 Reviewed-on: https://boringssl-review.googlesource.com/c/boringssl/+/93867 Commit-Queue: David Benjamin <davidben@google.com> Reviewed-by: Adam Langley <agl@google.com> Auto-Submit: David Benjamin <davidben@google.com>
diff --git a/build.json b/build.json index 65c021d..a5d57de 100644 --- a/build.json +++ b/build.json
@@ -62,7 +62,6 @@ "crypto/fipsmodule/ec/ec_montgomery.cc.inc", "crypto/fipsmodule/ec/felem.cc.inc", "crypto/fipsmodule/ec/oct.cc.inc", - "crypto/fipsmodule/ec/p224-64.cc.inc", "crypto/fipsmodule/ec/p256-nistz.cc.inc", "crypto/fipsmodule/ec/p256.cc.inc", "crypto/fipsmodule/ec/scalar.cc.inc",
diff --git a/crypto/fipsmodule/bcm.cc b/crypto/fipsmodule/bcm.cc index 86e725d..1a5a6fd 100644 --- a/crypto/fipsmodule/bcm.cc +++ b/crypto/fipsmodule/bcm.cc
@@ -87,7 +87,6 @@ #include "ec/ec_montgomery.cc.inc" #include "ec/felem.cc.inc" #include "ec/oct.cc.inc" -#include "ec/p224-64.cc.inc" #include "ec/p256-nistz.cc.inc" #include "ec/p256.cc.inc" #include "ec/scalar.cc.inc"
diff --git a/crypto/fipsmodule/ec/ec.cc.inc b/crypto/fipsmodule/ec/ec.cc.inc index 85df88d..209f101 100644 --- a/crypto/fipsmodule/ec/ec.cc.inc +++ b/crypto/fipsmodule/ec/ec.cc.inc
@@ -74,19 +74,11 @@ ec_group_init_static_mont(&out->order, std::size(kP224Order), kP224Order, kP224OrderRR, kP224OrderN0); -#if defined(BORINGSSL_HAS_UINT128) && !defined(OPENSSL_SMALL) - out->meth = EC_GFp_nistp224_method(); - OPENSSL_memcpy(out->generator.raw.X.words, kP224GX, sizeof(kP224GX)); - OPENSSL_memcpy(out->generator.raw.Y.words, kP224GY, sizeof(kP224GY)); - out->generator.raw.Z.words[0] = 1; - OPENSSL_memcpy(out->b.words, kP224B, sizeof(kP224B)); -#else out->meth = EC_GFp_mont_method(); OPENSSL_memcpy(out->generator.raw.X.words, kP224MontGX, sizeof(kP224MontGX)); OPENSSL_memcpy(out->generator.raw.Y.words, kP224MontGY, sizeof(kP224MontGY)); OPENSSL_memcpy(out->generator.raw.Z.words, kP224FieldR, sizeof(kP224FieldR)); OPENSSL_memcpy(out->b.words, kP224MontB, sizeof(kP224MontB)); -#endif out->generator.group = out; ec_group_set_a_minus3(out);
diff --git a/crypto/fipsmodule/ec/internal.h b/crypto/fipsmodule/ec/internal.h index c6043cd7..33fa29f 100644 --- a/crypto/fipsmodule/ec/internal.h +++ b/crypto/fipsmodule/ec/internal.h
@@ -491,13 +491,8 @@ // |bssl::EC_POINT_dbl| implementations can work both with // |bssl::EC_GFp_mont_method| and the tuned operations. // - // TODO(davidben): This constrains |bssl::EC_FELEM|'s internal representation, - // adds many indirect calls in the middle of the generic code, and a bunch of - // conversions. If p224-64.c were easily convertible to Montgomery form, we - // could say |bssl::EC_FELEM| is always in Montgomery form. If we routed the - // rest of simple.c to |bssl::EC_METHOD|, we could give |bssl::EC_POINT| an - // |bssl::EC_METHOD|-specific representation and say |bssl::EC_FELEM| is - // purely a |bssl::EC_GFp_mont_method| type. + // TODO(crbug.com/505908440): These are always implemented with the same + // functions, now that EC_FELEM is always in Montgomery form. Remove this. void (*felem_mul)(const EC_GROUP *, bssl::EC_FELEM *r, const bssl::EC_FELEM *a, const bssl::EC_FELEM *b); void (*felem_sqr)(const EC_GROUP *, bssl::EC_FELEM *r, @@ -698,7 +693,6 @@ void ec_GFp_nistp_recode_scalar_bits(crypto_word_t *sign, crypto_word_t *digit, crypto_word_t in); -const EC_METHOD *EC_GFp_nistp224_method(); const EC_METHOD *EC_GFp_nistp256_method(); // EC_GFp_nistz256_method is a GFp method using montgomery multiplication, with
diff --git a/crypto/fipsmodule/ec/p224-64.cc.inc b/crypto/fipsmodule/ec/p224-64.cc.inc deleted file mode 100644 index 16edaf9..0000000 --- a/crypto/fipsmodule/ec/p224-64.cc.inc +++ /dev/null
@@ -1,1169 +0,0 @@ -// Copyright 2015 The BoringSSL Authors -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// https://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. - -// A 64-bit implementation of the NIST P-224 elliptic curve point multiplication -// -// Inspired by Daniel J. Bernstein's public domain nistp224 implementation -// and Adam Langley's public domain 64-bit C implementation of curve25519. - -#include <openssl/base.h> - -#include <openssl/bn.h> -#include <openssl/ec.h> -#include <openssl/err.h> -#include <openssl/mem.h> - -#include <assert.h> -#include <string.h> - -#include "../../internal.h" -#include "../delocate.h" -#include "internal.h" - - -using namespace bssl; - -#if defined(BORINGSSL_HAS_UINT128) && !defined(OPENSSL_SMALL) - -// Field elements are represented as a_0 + 2^56*a_1 + 2^112*a_2 + 2^168*a_3 -// 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 using 128-bit coefficients called 'widelimbs'. A 4-p224_limb -// representation is an 'p224_felem'; a 7-p224_widelimb representation is a -// 'p224_widefelem'. Even within felems, bits of adjacent limbs overlap, and we -// don't always reduce the representations: we ensure that inputs to each -// p224_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 obtain an p224_felem satisfying a_i < -// 2^57. We only reduce to the unique minimal representation at the end of the -// computation. - -typedef uint64_t p224_limb; -typedef uint128_t p224_widelimb; - -typedef p224_limb p224_felem[4]; -typedef p224_widelimb p224_widefelem[7]; - -// 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 p224_felem g_p224_pre_comp[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}}}}; - - -// Helper functions to convert field elements to/from internal representation - -static void p224_generic_to_felem(p224_felem out, const EC_FELEM *in) { - // |p224_felem|'s minimal representation uses four 56-bit words. |EC_FELEM| - // uses four 64-bit words. (The top-most word only has 32 bits.) - out[0] = in->words[0] & 0x00ffffffffffffff; - out[1] = ((in->words[0] >> 56) | (in->words[1] << 8)) & 0x00ffffffffffffff; - out[2] = ((in->words[1] >> 48) | (in->words[2] << 16)) & 0x00ffffffffffffff; - out[3] = ((in->words[2] >> 40) | (in->words[3] << 24)) & 0x00ffffffffffffff; -} - -// Requires 0 <= in < 2*p (always call p224_felem_reduce first) -static void p224_felem_to_generic(EC_FELEM *out, const p224_felem in) { - // Reduce to unique minimal representation. - static const int64_t two56 = ((p224_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 <= tmp < p - p224_felem tmp2; - tmp2[0] = tmp[0]; - tmp2[1] = tmp[1]; - tmp2[2] = tmp[2]; - tmp2[3] = tmp[3]; - - // |p224_felem|'s minimal representation uses four 56-bit words. |EC_FELEM| - // uses four 64-bit words. (The top-most word only has 32 bits.) - out->words[0] = tmp2[0] | (tmp2[1] << 56); - out->words[1] = (tmp2[1] >> 8) | (tmp2[2] << 48); - out->words[2] = (tmp2[2] >> 16) | (tmp2[3] << 40); - out->words[3] = tmp2[3] >> 24; -} - - -// Field operations, using the internal representation of field elements. -// NB! These operations are specific to our point multiplication and cannot be -// expected to be correct in general - e.g., multiplication with a large scalar -// will cause an overflow. - -static void p224_felem_assign(p224_felem out, const p224_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 p224_felem_sum(p224_felem out, const p224_felem in) { - out[0] += in[0]; - out[1] += in[1]; - out[2] += in[2]; - out[3] += in[3]; -} - -// Subtract field elements: out -= in -// Assumes in[i] < 2^57 -static void p224_felem_diff(p224_felem out, const p224_felem in) { - static const p224_limb two58p2 = - (((p224_limb)1) << 58) + (((p224_limb)1) << 2); - static const p224_limb two58m2 = - (((p224_limb)1) << 58) - (((p224_limb)1) << 2); - static const p224_limb two58m42m2 = - (((p224_limb)1) << 58) - (((p224_limb)1) << 42) - (((p224_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 p224_widefelem_diff(p224_widefelem out, const p224_widefelem in) { - static const p224_widelimb two120 = ((p224_widelimb)1) << 120; - static const p224_widelimb two120m64 = - (((p224_widelimb)1) << 120) - (((p224_widelimb)1) << 64); - static const p224_widelimb two120m104m64 = (((p224_widelimb)1) << 120) - - (((p224_widelimb)1) << 104) - - (((p224_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 p224_felem_diff_128_64(p224_widefelem out, const p224_felem in) { - static const p224_widelimb two64p8 = - (((p224_widelimb)1) << 64) + (((p224_widelimb)1) << 8); - static const p224_widelimb two64m8 = - (((p224_widelimb)1) << 64) - (((p224_widelimb)1) << 8); - static const p224_widelimb two64m48m8 = (((p224_widelimb)1) << 64) - - (((p224_widelimb)1) << 48) - - (((p224_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 p224_felem_scalar(p224_felem out, const p224_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 p224_widefelem_scalar(p224_widefelem out, - const p224_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 p224_felem_square(p224_widefelem out, const p224_felem in) { - p224_limb tmp0, tmp1, tmp2; - tmp0 = 2 * in[0]; - tmp1 = 2 * in[1]; - tmp2 = 2 * in[2]; - out[0] = ((p224_widelimb)in[0]) * in[0]; - out[1] = ((p224_widelimb)in[0]) * tmp1; - out[2] = ((p224_widelimb)in[0]) * tmp2 + ((p224_widelimb)in[1]) * in[1]; - out[3] = ((p224_widelimb)in[3]) * tmp0 + ((p224_widelimb)in[1]) * tmp2; - out[4] = ((p224_widelimb)in[3]) * tmp1 + ((p224_widelimb)in[2]) * in[2]; - out[5] = ((p224_widelimb)in[3]) * tmp2; - out[6] = ((p224_widelimb)in[3]) * in[3]; -} - -// Multiply two field elements: out = in1 * in2 -static void p224_felem_mul(p224_widefelem out, const p224_felem in1, - const p224_felem in2) { - out[0] = ((p224_widelimb)in1[0]) * in2[0]; - out[1] = ((p224_widelimb)in1[0]) * in2[1] + ((p224_widelimb)in1[1]) * in2[0]; - out[2] = ((p224_widelimb)in1[0]) * in2[2] + ((p224_widelimb)in1[1]) * in2[1] + - ((p224_widelimb)in1[2]) * in2[0]; - out[3] = ((p224_widelimb)in1[0]) * in2[3] + ((p224_widelimb)in1[1]) * in2[2] + - ((p224_widelimb)in1[2]) * in2[1] + ((p224_widelimb)in1[3]) * in2[0]; - out[4] = ((p224_widelimb)in1[1]) * in2[3] + ((p224_widelimb)in1[2]) * in2[2] + - ((p224_widelimb)in1[3]) * in2[1]; - out[5] = ((p224_widelimb)in1[2]) * in2[3] + ((p224_widelimb)in1[3]) * in2[2]; - out[6] = ((p224_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 p224_felem_reduce(p224_felem out, const p224_widefelem in) { - static const p224_widelimb two127p15 = - (((p224_widelimb)1) << 127) + (((p224_widelimb)1) << 15); - static const p224_widelimb two127m71 = - (((p224_widelimb)1) << 127) - (((p224_widelimb)1) << 71); - static const p224_widelimb two127m71m55 = (((p224_widelimb)1) << 127) - - (((p224_widelimb)1) << 71) - - (((p224_widelimb)1) << 55); - p224_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]; -} - -// Get negative value: out = -in -// Requires in[i] < 2^63, -// ensures out[0] < 2^56, out[1] < 2^56, out[2] < 2^56, out[3] <= 2^56 + 2^16 -static void p224_felem_neg(p224_felem out, const p224_felem in) { - p224_widefelem tmp = {0}; - p224_felem_diff_128_64(tmp, in); - p224_felem_reduce(out, tmp); -} - -// 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 p224_limb p224_felem_is_zero(const p224_felem in) { - p224_limb zero = in[0] | in[1] | in[2] | in[3]; - zero = (((int64_t)(zero)-1) >> 63) & 1; - - p224_limb two224m96p1 = (in[0] ^ 1) | (in[1] ^ 0x00ffff0000000000) | - (in[2] ^ 0x00ffffffffffffff) | - (in[3] ^ 0x00ffffffffffffff); - two224m96p1 = (((int64_t)(two224m96p1)-1) >> 63) & 1; - p224_limb two225m97p2 = (in[0] ^ 2) | (in[1] ^ 0x00fffe0000000000) | - (in[2] ^ 0x00ffffffffffffff) | - (in[3] ^ 0x01ffffffffffffff); - two225m97p2 = (((int64_t)(two225m97p2)-1) >> 63) & 1; - return (zero | two224m96p1 | two225m97p2); -} - -// Invert a field element -// Computation chain copied from djb's code -static void p224_felem_inv(p224_felem out, const p224_felem in) { - p224_felem ftmp, ftmp2, ftmp3, ftmp4; - p224_widefelem tmp; - - p224_felem_square(tmp, in); - p224_felem_reduce(ftmp, tmp); // 2 - p224_felem_mul(tmp, in, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^2 - 1 - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^3 - 2 - p224_felem_mul(tmp, in, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^3 - 1 - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp2, tmp); // 2^4 - 2 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp2, tmp); // 2^5 - 4 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp2, tmp); // 2^6 - 8 - p224_felem_mul(tmp, ftmp2, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^6 - 1 - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp2, tmp); // 2^7 - 2 - for (size_t i = 0; i < 5; ++i) { // 2^12 - 2^6 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp2, tmp); - } - p224_felem_mul(tmp, ftmp2, ftmp); - p224_felem_reduce(ftmp2, tmp); // 2^12 - 1 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp3, tmp); // 2^13 - 2 - for (size_t i = 0; i < 11; ++i) { // 2^24 - 2^12 - p224_felem_square(tmp, ftmp3); - p224_felem_reduce(ftmp3, tmp); - } - p224_felem_mul(tmp, ftmp3, ftmp2); - p224_felem_reduce(ftmp2, tmp); // 2^24 - 1 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp3, tmp); // 2^25 - 2 - for (size_t i = 0; i < 23; ++i) { // 2^48 - 2^24 - p224_felem_square(tmp, ftmp3); - p224_felem_reduce(ftmp3, tmp); - } - p224_felem_mul(tmp, ftmp3, ftmp2); - p224_felem_reduce(ftmp3, tmp); // 2^48 - 1 - p224_felem_square(tmp, ftmp3); - p224_felem_reduce(ftmp4, tmp); // 2^49 - 2 - for (size_t i = 0; i < 47; ++i) { // 2^96 - 2^48 - p224_felem_square(tmp, ftmp4); - p224_felem_reduce(ftmp4, tmp); - } - p224_felem_mul(tmp, ftmp3, ftmp4); - p224_felem_reduce(ftmp3, tmp); // 2^96 - 1 - p224_felem_square(tmp, ftmp3); - p224_felem_reduce(ftmp4, tmp); // 2^97 - 2 - for (size_t i = 0; i < 23; ++i) { // 2^120 - 2^24 - p224_felem_square(tmp, ftmp4); - p224_felem_reduce(ftmp4, tmp); - } - p224_felem_mul(tmp, ftmp2, ftmp4); - p224_felem_reduce(ftmp2, tmp); // 2^120 - 1 - for (size_t i = 0; i < 6; ++i) { // 2^126 - 2^6 - p224_felem_square(tmp, ftmp2); - p224_felem_reduce(ftmp2, tmp); - } - p224_felem_mul(tmp, ftmp2, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^126 - 1 - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp, tmp); // 2^127 - 2 - p224_felem_mul(tmp, ftmp, in); - p224_felem_reduce(ftmp, tmp); // 2^127 - 1 - for (size_t i = 0; i < 97; ++i) { // 2^224 - 2^97 - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp, tmp); - } - p224_felem_mul(tmp, ftmp, ftmp3); - p224_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 p224_copy_conditional(p224_felem out, const p224_felem in, - p224_limb icopy) { - // icopy is a (64-bit) 0 or 1, so copy is either all-zero or all-one - const p224_limb copy = -icopy; - for (size_t i = 0; i < 4; ++i) { - const p224_limb tmp = copy & (in[i] ^ out[i]); - out[i] ^= tmp; - } -} - -// 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), -// or to the point at infinity if Z == 0. - -// 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). -static void p224_point_double(p224_felem x_out, p224_felem y_out, - p224_felem z_out, const p224_felem x_in, - const p224_felem y_in, const p224_felem z_in) { - p224_widefelem tmp, tmp2; - p224_felem delta, gamma, beta, alpha, ftmp, ftmp2; - - p224_felem_assign(ftmp, x_in); - p224_felem_assign(ftmp2, x_in); - - // delta = z^2 - p224_felem_square(tmp, z_in); - p224_felem_reduce(delta, tmp); - - // gamma = y^2 - p224_felem_square(tmp, y_in); - p224_felem_reduce(gamma, tmp); - - // beta = x*gamma - p224_felem_mul(tmp, x_in, gamma); - p224_felem_reduce(beta, tmp); - - // alpha = 3*(x-delta)*(x+delta) - p224_felem_diff(ftmp, delta); - // ftmp[i] < 2^57 + 2^58 + 2 < 2^59 - p224_felem_sum(ftmp2, delta); - // ftmp2[i] < 2^57 + 2^57 = 2^58 - p224_felem_scalar(ftmp2, 3); - // ftmp2[i] < 3 * 2^58 < 2^60 - p224_felem_mul(tmp, ftmp, ftmp2); - // tmp[i] < 2^60 * 2^59 * 4 = 2^121 - p224_felem_reduce(alpha, tmp); - - // x' = alpha^2 - 8*beta - p224_felem_square(tmp, alpha); - // tmp[i] < 4 * 2^57 * 2^57 = 2^116 - p224_felem_assign(ftmp, beta); - p224_felem_scalar(ftmp, 8); - // ftmp[i] < 8 * 2^57 = 2^60 - p224_felem_diff_128_64(tmp, ftmp); - // tmp[i] < 2^116 + 2^64 + 8 < 2^117 - p224_felem_reduce(x_out, tmp); - - // z' = (y + z)^2 - gamma - delta - p224_felem_sum(delta, gamma); - // delta[i] < 2^57 + 2^57 = 2^58 - p224_felem_assign(ftmp, y_in); - p224_felem_sum(ftmp, z_in); - // ftmp[i] < 2^57 + 2^57 = 2^58 - p224_felem_square(tmp, ftmp); - // tmp[i] < 4 * 2^58 * 2^58 = 2^118 - p224_felem_diff_128_64(tmp, delta); - // tmp[i] < 2^118 + 2^64 + 8 < 2^119 - p224_felem_reduce(z_out, tmp); - - // y' = alpha*(4*beta - x') - 8*gamma^2 - p224_felem_scalar(beta, 4); - // beta[i] < 4 * 2^57 = 2^59 - p224_felem_diff(beta, x_out); - // beta[i] < 2^59 + 2^58 + 2 < 2^60 - p224_felem_mul(tmp, alpha, beta); - // tmp[i] < 4 * 2^57 * 2^60 = 2^119 - p224_felem_square(tmp2, gamma); - // tmp2[i] < 4 * 2^57 * 2^57 = 2^116 - p224_widefelem_scalar(tmp2, 8); - // tmp2[i] < 8 * 2^116 = 2^119 - p224_widefelem_diff(tmp, tmp2); - // tmp[i] < 2^119 + 2^120 < 2^121 - p224_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 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 p224_point_add(p224_felem x3, p224_felem y3, p224_felem z3, - const p224_felem x1, const p224_felem y1, - const p224_felem z1, const int mixed, - const p224_felem x2, const p224_felem y2, - const p224_felem z2) { - p224_felem ftmp, ftmp2, ftmp3, ftmp4, ftmp5, x_out, y_out, z_out; - p224_widefelem tmp, tmp2; - p224_limb z1_is_zero, z2_is_zero, x_equal, y_equal; - - if (!mixed) { - // ftmp2 = z2^2 - p224_felem_square(tmp, z2); - p224_felem_reduce(ftmp2, tmp); - - // ftmp4 = z2^3 - p224_felem_mul(tmp, ftmp2, z2); - p224_felem_reduce(ftmp4, tmp); - - // ftmp4 = z2^3*y1 - p224_felem_mul(tmp2, ftmp4, y1); - p224_felem_reduce(ftmp4, tmp2); - - // ftmp2 = z2^2*x1 - p224_felem_mul(tmp2, ftmp2, x1); - p224_felem_reduce(ftmp2, tmp2); - } else { - // We'll assume z2 = 1 (special case z2 = 0 is handled later) - - // ftmp4 = z2^3*y1 - p224_felem_assign(ftmp4, y1); - - // ftmp2 = z2^2*x1 - p224_felem_assign(ftmp2, x1); - } - - // ftmp = z1^2 - p224_felem_square(tmp, z1); - p224_felem_reduce(ftmp, tmp); - - // ftmp3 = z1^3 - p224_felem_mul(tmp, ftmp, z1); - p224_felem_reduce(ftmp3, tmp); - - // tmp = z1^3*y2 - p224_felem_mul(tmp, ftmp3, y2); - // tmp[i] < 4 * 2^57 * 2^57 = 2^116 - - // ftmp3 = z1^3*y2 - z2^3*y1 - p224_felem_diff_128_64(tmp, ftmp4); - // tmp[i] < 2^116 + 2^64 + 8 < 2^117 - p224_felem_reduce(ftmp3, tmp); - - // tmp = z1^2*x2 - p224_felem_mul(tmp, ftmp, x2); - // tmp[i] < 4 * 2^57 * 2^57 = 2^116 - - // ftmp = z1^2*x2 - z2^2*x1 - p224_felem_diff_128_64(tmp, ftmp2); - // tmp[i] < 2^116 + 2^64 + 8 < 2^117 - p224_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 = p224_felem_is_zero(ftmp); - y_equal = p224_felem_is_zero(ftmp3); - z1_is_zero = p224_felem_is_zero(z1); - z2_is_zero = p224_felem_is_zero(z2); - // In affine coordinates, (X_1, Y_1) == (X_2, Y_2) - p224_limb is_nontrivial_double = - x_equal & y_equal & (1 - z1_is_zero) & (1 - z2_is_zero); - if (constant_time_declassify_w(is_nontrivial_double)) { - p224_point_double(x3, y3, z3, x1, y1, z1); - return; - } - - // ftmp5 = z1*z2 - if (!mixed) { - p224_felem_mul(tmp, z1, z2); - p224_felem_reduce(ftmp5, tmp); - } else { - // special case z2 = 0 is handled later - p224_felem_assign(ftmp5, z1); - } - - // z_out = (z1^2*x2 - z2^2*x1)*(z1*z2) - p224_felem_mul(tmp, ftmp, ftmp5); - p224_felem_reduce(z_out, tmp); - - // ftmp = (z1^2*x2 - z2^2*x1)^2 - p224_felem_assign(ftmp5, ftmp); - p224_felem_square(tmp, ftmp); - p224_felem_reduce(ftmp, tmp); - - // ftmp5 = (z1^2*x2 - z2^2*x1)^3 - p224_felem_mul(tmp, ftmp, ftmp5); - p224_felem_reduce(ftmp5, tmp); - - // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - p224_felem_mul(tmp, ftmp2, ftmp); - p224_felem_reduce(ftmp2, tmp); - - // tmp = z2^3*y1*(z1^2*x2 - z2^2*x1)^3 - p224_felem_mul(tmp, ftmp4, ftmp5); - // tmp[i] < 4 * 2^57 * 2^57 = 2^116 - - // tmp2 = (z1^3*y2 - z2^3*y1)^2 - p224_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 - p224_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 - p224_felem_assign(ftmp5, ftmp2); - p224_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 */ - p224_felem_diff_128_64(tmp2, ftmp5); - // tmp2[i] < 2^117 + 2^64 + 8 < 2^118 - p224_felem_reduce(x_out, tmp2); - - // ftmp2 = z2^2*x1*(z1^2*x2 - z2^2*x1)^2 - x_out - p224_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) - p224_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 */ - p224_widefelem_diff(tmp2, tmp); - // tmp2[i] < 2^118 + 2^120 < 2^121 - p224_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 - p224_copy_conditional(x_out, x2, z1_is_zero); - p224_copy_conditional(x_out, x1, z2_is_zero); - p224_copy_conditional(y_out, y2, z1_is_zero); - p224_copy_conditional(y_out, y1, z2_is_zero); - p224_copy_conditional(z_out, z2, z1_is_zero); - p224_copy_conditional(z_out, z1, z2_is_zero); - p224_felem_assign(x3, x_out); - p224_felem_assign(y3, y_out); - p224_felem_assign(z3, z_out); -} - -// p224_select_point selects the |idx|th point from a precomputation table and -// copies it to out. -static void p224_select_point(const uint64_t idx, size_t size, - const p224_felem pre_comp[/*size*/][3], - p224_felem out[3]) { - p224_limb *outlimbs = &out[0][0]; - OPENSSL_memset(outlimbs, 0, 3 * sizeof(p224_felem)); - - for (size_t i = 0; i < size; i++) { - const p224_limb *inlimbs = &pre_comp[i][0][0]; - static_assert(sizeof(uint64_t) <= sizeof(crypto_word_t), - "crypto_word_t too small"); - static_assert(sizeof(size_t) <= sizeof(crypto_word_t), - "crypto_word_t too small"); - // Without a value barrier, Clang adds a branch here. - uint64_t mask = value_barrier_w(constant_time_eq_w(i, idx)); - for (size_t j = 0; j < 4 * 3; j++) { - outlimbs[j] |= inlimbs[j] & mask; - } - } -} - -// p224_get_bit returns the |i|th bit in |in|. -static crypto_word_t p224_get_bit(const EC_SCALAR *in, size_t i) { - if (i >= 224) { - return 0; - } - static_assert(sizeof(in->words[0]) == 8, "BN_ULONG is not 64-bit"); - return (in->words[i >> 6] >> (i & 63)) & 1; -} - -// Takes the Jacobian coordinates (X, Y, Z) of a point and returns -// (X', Y') = (X/Z^2, Y/Z^3) -static int ec_GFp_nistp224_point_get_affine_coordinates( - const EC_GROUP *group, const EC_JACOBIAN *point, EC_FELEM *x, - EC_FELEM *y) { - if (constant_time_declassify_int( - ec_GFp_simple_is_at_infinity(group, point))) { - OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); - return 0; - } - - p224_felem z1, z2; - p224_widefelem tmp; - p224_generic_to_felem(z1, &point->Z); - p224_felem_inv(z2, z1); - p224_felem_square(tmp, z2); - p224_felem_reduce(z1, tmp); - - if (x != nullptr) { - p224_felem x_in, x_out; - p224_generic_to_felem(x_in, &point->X); - p224_felem_mul(tmp, x_in, z1); - p224_felem_reduce(x_out, tmp); - p224_felem_to_generic(x, x_out); - } - - if (y != nullptr) { - p224_felem y_in, y_out; - p224_generic_to_felem(y_in, &point->Y); - p224_felem_mul(tmp, z1, z2); - p224_felem_reduce(z1, tmp); - p224_felem_mul(tmp, y_in, z1); - p224_felem_reduce(y_out, tmp); - p224_felem_to_generic(y, y_out); - } - - return 1; -} - -static void ec_GFp_nistp224_add(const EC_GROUP *group, EC_JACOBIAN *r, - const EC_JACOBIAN *a, const EC_JACOBIAN *b) { - p224_felem x1, y1, z1, x2, y2, z2; - p224_generic_to_felem(x1, &a->X); - p224_generic_to_felem(y1, &a->Y); - p224_generic_to_felem(z1, &a->Z); - p224_generic_to_felem(x2, &b->X); - p224_generic_to_felem(y2, &b->Y); - p224_generic_to_felem(z2, &b->Z); - p224_point_add(x1, y1, z1, x1, y1, z1, 0 /* both Jacobian */, x2, y2, z2); - // The outputs are already reduced, but still need to be contracted. - p224_felem_to_generic(&r->X, x1); - p224_felem_to_generic(&r->Y, y1); - p224_felem_to_generic(&r->Z, z1); -} - -static void ec_GFp_nistp224_dbl(const EC_GROUP *group, EC_JACOBIAN *r, - const EC_JACOBIAN *a) { - p224_felem x, y, z; - p224_generic_to_felem(x, &a->X); - p224_generic_to_felem(y, &a->Y); - p224_generic_to_felem(z, &a->Z); - p224_point_double(x, y, z, x, y, z); - // The outputs are already reduced, but still need to be contracted. - p224_felem_to_generic(&r->X, x); - p224_felem_to_generic(&r->Y, y); - p224_felem_to_generic(&r->Z, z); -} - -static void ec_GFp_nistp224_make_precomp(p224_felem out[17][3], - const EC_JACOBIAN *p) { - OPENSSL_memset(out[0], 0, sizeof(p224_felem) * 3); - - p224_generic_to_felem(out[1][0], &p->X); - p224_generic_to_felem(out[1][1], &p->Y); - p224_generic_to_felem(out[1][2], &p->Z); - - for (size_t j = 2; j <= 16; ++j) { - if (j & 1) { - p224_point_add(out[j][0], out[j][1], out[j][2], out[1][0], out[1][1], - out[1][2], 0, out[j - 1][0], out[j - 1][1], out[j - 1][2]); - } else { - p224_point_double(out[j][0], out[j][1], out[j][2], out[j / 2][0], - out[j / 2][1], out[j / 2][2]); - } - } -} - -static void ec_GFp_nistp224_point_mul(const EC_GROUP *group, EC_JACOBIAN *r, - const EC_JACOBIAN *p, - const EC_SCALAR *scalar) { - p224_felem p_pre_comp[17][3]; - ec_GFp_nistp224_make_precomp(p_pre_comp, p); - - // Set nq to the point at infinity. - p224_felem nq[3], tmp[4]; - OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); - - int skip = 1; // Save two point operations in the first round. - for (size_t i = 220; i < 221; i--) { - if (!skip) { - p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); - } - - // Add every 5 doublings. - if (i % 5 == 0) { - crypto_word_t bits = p224_get_bit(scalar, i + 4) << 5; - bits |= p224_get_bit(scalar, i + 3) << 4; - bits |= p224_get_bit(scalar, i + 2) << 3; - bits |= p224_get_bit(scalar, i + 1) << 2; - bits |= p224_get_bit(scalar, i) << 1; - bits |= p224_get_bit(scalar, i - 1); - crypto_word_t sign, digit; - ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - - // Select the point to add or subtract. - p224_select_point(digit, 17, (const p224_felem(*)[3])p_pre_comp, tmp); - p224_felem_neg(tmp[3], tmp[1]); // (X, -Y, Z) is the negative point - p224_copy_conditional(tmp[1], tmp[3], sign); - - if (!skip) { - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, - tmp[0], tmp[1], tmp[2]); - } else { - OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); - skip = 0; - } - } - } - - // Reduce the output to its unique minimal representation. - p224_felem_to_generic(&r->X, nq[0]); - p224_felem_to_generic(&r->Y, nq[1]); - p224_felem_to_generic(&r->Z, nq[2]); -} - -static void ec_GFp_nistp224_point_mul_base(const EC_GROUP *group, - EC_JACOBIAN *r, - const EC_SCALAR *scalar) { - // Set nq to the point at infinity. - p224_felem nq[3], tmp[3]; - OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); - - int skip = 1; // Save two point operations in the first round. - for (size_t i = 27; i < 28; i--) { - // double - if (!skip) { - p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); - } - - // First, look 28 bits upwards. - crypto_word_t bits = p224_get_bit(scalar, i + 196) << 3; - bits |= p224_get_bit(scalar, i + 140) << 2; - bits |= p224_get_bit(scalar, i + 84) << 1; - bits |= p224_get_bit(scalar, i + 28); - // Select the point to add, in constant time. - p224_select_point(bits, 16, g_p224_pre_comp[1], tmp); - - if (!skip) { - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, - tmp[0], tmp[1], tmp[2]); - } else { - OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); - skip = 0; - } - - // Second, look at the current position/ - bits = p224_get_bit(scalar, i + 168) << 3; - bits |= p224_get_bit(scalar, i + 112) << 2; - bits |= p224_get_bit(scalar, i + 56) << 1; - bits |= p224_get_bit(scalar, i); - // Select the point to add, in constant time. - p224_select_point(bits, 16, g_p224_pre_comp[0], tmp); - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, - tmp[0], tmp[1], tmp[2]); - } - - // Reduce the output to its unique minimal representation. - p224_felem_to_generic(&r->X, nq[0]); - p224_felem_to_generic(&r->Y, nq[1]); - p224_felem_to_generic(&r->Z, nq[2]); -} - -static void ec_GFp_nistp224_point_mul_public(const EC_GROUP *group, - EC_JACOBIAN *r, - const EC_SCALAR *g_scalar, - const EC_JACOBIAN *p, - const EC_SCALAR *p_scalar) { - // TODO(davidben): If P-224 ECDSA verify performance ever matters, using - // |ec_compute_wNAF| for |p_scalar| would likely be an easy improvement. - p224_felem p_pre_comp[17][3]; - ec_GFp_nistp224_make_precomp(p_pre_comp, p); - - // Set nq to the point at infinity. - p224_felem nq[3], tmp[3]; - OPENSSL_memset(nq, 0, 3 * sizeof(p224_felem)); - - // Loop over both scalars msb-to-lsb, interleaving additions of multiples of - // the generator (two in each of the last 28 rounds) and additions of p (every - // 5th round). - int skip = 1; // Save two point operations in the first round. - for (size_t i = 220; i < 221; i--) { - if (!skip) { - p224_point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]); - } - - // Add multiples of the generator. - if (i <= 27) { - // First, look 28 bits upwards. - crypto_word_t bits = p224_get_bit(g_scalar, i + 196) << 3; - bits |= p224_get_bit(g_scalar, i + 140) << 2; - bits |= p224_get_bit(g_scalar, i + 84) << 1; - bits |= p224_get_bit(g_scalar, i + 28); - - size_t index = (size_t)bits; - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, - g_p224_pre_comp[1][index][0], g_p224_pre_comp[1][index][1], - g_p224_pre_comp[1][index][2]); - assert(!skip); - - // Second, look at the current position. - bits = p224_get_bit(g_scalar, i + 168) << 3; - bits |= p224_get_bit(g_scalar, i + 112) << 2; - bits |= p224_get_bit(g_scalar, i + 56) << 1; - bits |= p224_get_bit(g_scalar, i); - index = (size_t)bits; - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, - g_p224_pre_comp[0][index][0], g_p224_pre_comp[0][index][1], - g_p224_pre_comp[0][index][2]); - } - - // Incorporate |p_scalar| every 5 doublings. - if (i % 5 == 0) { - crypto_word_t bits = p224_get_bit(p_scalar, i + 4) << 5; - bits |= p224_get_bit(p_scalar, i + 3) << 4; - bits |= p224_get_bit(p_scalar, i + 2) << 3; - bits |= p224_get_bit(p_scalar, i + 1) << 2; - bits |= p224_get_bit(p_scalar, i) << 1; - bits |= p224_get_bit(p_scalar, i - 1); - crypto_word_t sign, digit; - ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits); - - // Select the point to add or subtract. - OPENSSL_memcpy(tmp, p_pre_comp[digit], 3 * sizeof(p224_felem)); - if (sign) { - p224_felem_neg(tmp[1], tmp[1]); // (X, -Y, Z) is the negative point - } - - if (!skip) { - p224_point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */, - tmp[0], tmp[1], tmp[2]); - } else { - OPENSSL_memcpy(nq, tmp, 3 * sizeof(p224_felem)); - skip = 0; - } - } - } - - // Reduce the output to its unique minimal representation. - p224_felem_to_generic(&r->X, nq[0]); - p224_felem_to_generic(&r->Y, nq[1]); - p224_felem_to_generic(&r->Z, nq[2]); -} - -static void ec_GFp_nistp224_felem_mul(const EC_GROUP *group, EC_FELEM *r, - const EC_FELEM *a, const EC_FELEM *b) { - p224_felem felem1, felem2; - p224_widefelem wide; - p224_generic_to_felem(felem1, a); - p224_generic_to_felem(felem2, b); - p224_felem_mul(wide, felem1, felem2); - p224_felem_reduce(felem1, wide); - p224_felem_to_generic(r, felem1); -} - -static void ec_GFp_nistp224_felem_sqr(const EC_GROUP *group, EC_FELEM *r, - const EC_FELEM *a) { - p224_felem felem; - p224_generic_to_felem(felem, a); - p224_widefelem wide; - p224_felem_square(wide, felem); - p224_felem_reduce(felem, wide); - p224_felem_to_generic(r, felem); -} - -BSSL_NAMESPACE_BEGIN - -DEFINE_METHOD_FUNCTION(EC_METHOD, EC_GFp_nistp224_method) { - out->point_get_affine_coordinates = - ec_GFp_nistp224_point_get_affine_coordinates; - out->add = ec_GFp_nistp224_add; - out->dbl = ec_GFp_nistp224_dbl; - out->mul = ec_GFp_nistp224_point_mul; - out->mul_base = ec_GFp_nistp224_point_mul_base; - out->mul_public = ec_GFp_nistp224_point_mul_public; - out->felem_mul = ec_GFp_nistp224_felem_mul; - out->felem_sqr = ec_GFp_nistp224_felem_sqr; - out->felem_to_bytes = ec_GFp_simple_felem_to_bytes; - out->felem_from_bytes = ec_GFp_simple_felem_from_bytes; - out->scalar_inv0_montgomery = ec_simple_scalar_inv0_montgomery; - out->scalar_to_montgomery_inv_vartime = - ec_simple_scalar_to_montgomery_inv_vartime; - out->cmp_x_coordinate = ec_GFp_simple_cmp_x_coordinate; -} - -BSSL_NAMESPACE_END - -#endif // BORINGSSL_HAS_UINT128 && !SMALL
diff --git a/crypto/fipsmodule/ec/simple.cc.inc b/crypto/fipsmodule/ec/simple.cc.inc index 4239b32..4a7e5a0 100644 --- a/crypto/fipsmodule/ec/simple.cc.inc +++ b/crypto/fipsmodule/ec/simple.cc.inc
@@ -28,8 +28,8 @@ using namespace bssl; // Most method functions in this file are designed to work with non-trivial -// representations of field elements if necessary (see ecp_mont.c): while -// standard modular addition and subtraction are used, the field_mul and +// representations of field elements if necessary (see ec_montgomery.cc.inc): +// while standard modular addition and subtraction are used, the field_mul and // field_sqr methods will be used for multiplication, and field_encode and // field_decode (if defined) will be used for converting between // representations. @@ -37,6 +37,9 @@ // Functions here specifically assume that if a non-trivial representation is // used, it is a Montgomery representation (i.e. 'encoding' means multiplying // by some factor R). +// +// TODO(crbug.com/505908440): ec_montgomery.cc.inc is now the only field element +// representation. Fold these files together. int bssl::ec_GFp_simple_group_set_curve(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b,
diff --git a/gen/sources.bzl b/gen/sources.bzl index 34d79e2..c0205a0 100644 --- a/gen/sources.bzl +++ b/gen/sources.bzl
@@ -65,7 +65,6 @@ "crypto/fipsmodule/ec/ec_montgomery.cc.inc", "crypto/fipsmodule/ec/felem.cc.inc", "crypto/fipsmodule/ec/oct.cc.inc", - "crypto/fipsmodule/ec/p224-64.cc.inc", "crypto/fipsmodule/ec/p256-nistz.cc.inc", "crypto/fipsmodule/ec/p256.cc.inc", "crypto/fipsmodule/ec/scalar.cc.inc",
diff --git a/gen/sources.cmake b/gen/sources.cmake index bc2cc27..7573a43 100644 --- a/gen/sources.cmake +++ b/gen/sources.cmake
@@ -69,7 +69,6 @@ crypto/fipsmodule/ec/ec_montgomery.cc.inc crypto/fipsmodule/ec/felem.cc.inc crypto/fipsmodule/ec/oct.cc.inc - crypto/fipsmodule/ec/p224-64.cc.inc crypto/fipsmodule/ec/p256-nistz.cc.inc crypto/fipsmodule/ec/p256.cc.inc crypto/fipsmodule/ec/scalar.cc.inc
diff --git a/gen/sources.gni b/gen/sources.gni index 2f5232a..d6aa531 100644 --- a/gen/sources.gni +++ b/gen/sources.gni
@@ -65,7 +65,6 @@ "crypto/fipsmodule/ec/ec_montgomery.cc.inc", "crypto/fipsmodule/ec/felem.cc.inc", "crypto/fipsmodule/ec/oct.cc.inc", - "crypto/fipsmodule/ec/p224-64.cc.inc", "crypto/fipsmodule/ec/p256-nistz.cc.inc", "crypto/fipsmodule/ec/p256.cc.inc", "crypto/fipsmodule/ec/scalar.cc.inc",
diff --git a/gen/sources.json b/gen/sources.json index c6f5244..2db4346 100644 --- a/gen/sources.json +++ b/gen/sources.json
@@ -50,7 +50,6 @@ "crypto/fipsmodule/ec/ec_montgomery.cc.inc", "crypto/fipsmodule/ec/felem.cc.inc", "crypto/fipsmodule/ec/oct.cc.inc", - "crypto/fipsmodule/ec/p224-64.cc.inc", "crypto/fipsmodule/ec/p256-nistz.cc.inc", "crypto/fipsmodule/ec/p256.cc.inc", "crypto/fipsmodule/ec/scalar.cc.inc",
diff --git a/gen/sources.mk b/gen/sources.mk index ac81b8f..3556653 100644 --- a/gen/sources.mk +++ b/gen/sources.mk
@@ -64,7 +64,6 @@ crypto/fipsmodule/ec/ec_montgomery.cc.inc \ crypto/fipsmodule/ec/felem.cc.inc \ crypto/fipsmodule/ec/oct.cc.inc \ - crypto/fipsmodule/ec/p224-64.cc.inc \ crypto/fipsmodule/ec/p256-nistz.cc.inc \ crypto/fipsmodule/ec/p256.cc.inc \ crypto/fipsmodule/ec/scalar.cc.inc \