diff --git a/src/crypto/shen_ed25519_ref/Makefile b/src/crypto/crypto_ops_builder/Makefile similarity index 100% rename from src/crypto/shen_ed25519_ref/Makefile rename to src/crypto/crypto_ops_builder/Makefile diff --git a/src/crypto/shen_ed25519_ref/api.h b/src/crypto/crypto_ops_builder/api.h similarity index 100% rename from src/crypto/shen_ed25519_ref/api.h rename to src/crypto/crypto_ops_builder/api.h diff --git a/src/crypto/shen_ed25519_ref/crypto-ops-data.c b/src/crypto/crypto_ops_builder/crypto-ops-data.c similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto-ops-data.c rename to src/crypto/crypto_ops_builder/crypto-ops-data.c diff --git a/src/crypto/shen_ed25519_ref/crypto-ops-old.c b/src/crypto/crypto_ops_builder/crypto-ops-old.c similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto-ops-old.c rename to src/crypto/crypto_ops_builder/crypto-ops-old.c diff --git a/src/crypto/shen_ed25519_ref/crypto-ops.h b/src/crypto/crypto_ops_builder/crypto-ops.h similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto-ops.h rename to src/crypto/crypto_ops_builder/crypto-ops.h diff --git a/src/crypto/shen_ed25519_ref/crypto_int32.h b/src/crypto/crypto_ops_builder/crypto_int32.h similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto_int32.h rename to src/crypto/crypto_ops_builder/crypto_int32.h diff --git a/src/crypto/shen_ed25519_ref/crypto_sign.h b/src/crypto/crypto_ops_builder/crypto_sign.h similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto_sign.h rename to src/crypto/crypto_ops_builder/crypto_sign.h diff --git a/src/crypto/shen_ed25519_ref/crypto_uint32.h b/src/crypto/crypto_ops_builder/crypto_uint32.h similarity index 100% rename from src/crypto/shen_ed25519_ref/crypto_uint32.h rename to src/crypto/crypto_ops_builder/crypto_uint32.h diff --git a/src/crypto/shen_ed25519_ref/crypto_verify_32.h b/src/crypto/crypto_ops_builder/crypto_verify_32.h similarity index 100% rename from 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--git a/src/crypto/shen_ed25519_ref/include/sodium/crypto_uint32.h b/src/crypto/crypto_ops_builder/include/sodium/crypto_uint32.h similarity index 100% rename from src/crypto/shen_ed25519_ref/include/sodium/crypto_uint32.h rename to src/crypto/crypto_ops_builder/include/sodium/crypto_uint32.h diff --git a/src/crypto/shen_ed25519_ref/include/sodium/crypto_uint64.h b/src/crypto/crypto_ops_builder/include/sodium/crypto_uint64.h similarity index 100% rename from src/crypto/shen_ed25519_ref/include/sodium/crypto_uint64.h rename to src/crypto/crypto_ops_builder/include/sodium/crypto_uint64.h diff --git a/src/crypto/shen_ed25519_ref/include/sodium/crypto_uint8.h b/src/crypto/crypto_ops_builder/include/sodium/crypto_uint8.h similarity index 100% rename from src/crypto/shen_ed25519_ref/include/sodium/crypto_uint8.h rename to src/crypto/crypto_ops_builder/include/sodium/crypto_uint8.h diff --git a/src/crypto/shen_ed25519_ref/include/sodium/crypto_verify_32.h b/src/crypto/crypto_ops_builder/include/sodium/crypto_verify_32.h similarity index 100% rename from src/crypto/shen_ed25519_ref/include/sodium/crypto_verify_32.h rename to src/crypto/crypto_ops_builder/include/sodium/crypto_verify_32.h diff --git a/src/crypto/shen_ed25519_ref/include/sodium/randombytes.h b/src/crypto/crypto_ops_builder/include/sodium/randombytes.h similarity index 100% rename from src/crypto/shen_ed25519_ref/include/sodium/randombytes.h rename to src/crypto/crypto_ops_builder/include/sodium/randombytes.h diff --git a/src/crypto/shen_ed25519_ref/randombytes.c b/src/crypto/crypto_ops_builder/randombytes.c similarity index 100% rename from src/crypto/shen_ed25519_ref/randombytes.c rename to src/crypto/crypto_ops_builder/randombytes.c diff --git a/src/crypto/shen_ed25519_ref/ref10/Makefile b/src/crypto/crypto_ops_builder/ref10/Makefile similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10/Makefile rename to src/crypto/crypto_ops_builder/ref10/Makefile diff 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diff --git a/src/crypto/shen_ed25519_ref/ref10/pow225521.h b/src/crypto/crypto_ops_builder/ref10/pow225521.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10/pow225521.h rename to src/crypto/crypto_ops_builder/ref10/pow225521.h diff --git a/src/crypto/shen_ed25519_ref/ref10/pow225521.q b/src/crypto/crypto_ops_builder/ref10/pow225521.q similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10/pow225521.q rename to src/crypto/crypto_ops_builder/ref10/pow225521.q diff --git a/src/crypto/shen_ed25519_ref/ref10/q2h.sh b/src/crypto/crypto_ops_builder/ref10/q2h.sh similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10/q2h.sh rename to src/crypto/crypto_ops_builder/ref10/q2h.sh diff --git a/src/crypto/shen_ed25519_ref/ref10/sc.h b/src/crypto/crypto_ops_builder/ref10/sc.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10/sc.h rename to src/crypto/crypto_ops_builder/ref10/sc.h diff --git a/src/crypto/shen_ed25519_ref/ref10/sc_muladd.c 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src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_dbl.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_to_cached.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_to_cached.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_to_cached.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_to_cached.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_to_p2.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_to_p2.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_to_p2.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_to_p2.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_tobytes.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_tobytes.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_p3_tobytes.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_p3_tobytes.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_precomp_0.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_precomp_0.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_precomp_0.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_precomp_0.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_scalarmult_base.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_scalarmult_base.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_scalarmult_base.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_scalarmult_base.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.h b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.h rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.h diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.q b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.q similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_sub.q rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_sub.q diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_tobytes.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_tobytes.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/ge_tobytes.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/ge_tobytes.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/keypair.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/keypair.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/keypair.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/keypair.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/open.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/open.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/open.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/open.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow22523.h b/src/crypto/crypto_ops_builder/ref10CommentedCombined/pow22523.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow22523.h rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/pow22523.h diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow22523.q b/src/crypto/crypto_ops_builder/ref10CommentedCombined/pow22523.q similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow22523.q rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/pow22523.q diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow225521.h b/src/crypto/crypto_ops_builder/ref10CommentedCombined/pow225521.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow225521.h rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/pow225521.h diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow225521.q b/src/crypto/crypto_ops_builder/ref10CommentedCombined/pow225521.q similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/pow225521.q rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/pow225521.q diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/q2h.sh b/src/crypto/crypto_ops_builder/ref10CommentedCombined/q2h.sh similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/q2h.sh rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/q2h.sh diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc.h b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sc.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc.h rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sc.h diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_muladd.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_muladd.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_muladd.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_muladd.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_reduce.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_reduce.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_reduce.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_reduce.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_sub.xmr.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_sub.xmr.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sc_sub.xmr.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sc_sub.xmr.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/scrap.txt b/src/crypto/crypto_ops_builder/ref10CommentedCombined/scrap.txt similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/scrap.txt rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/scrap.txt diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sign.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sign.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sign.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sign.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sqrtm1.h b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sqrtm1.h similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sqrtm1.h rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sqrtm1.h diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/sqrtm1.py b/src/crypto/crypto_ops_builder/ref10CommentedCombined/sqrtm1.py similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/sqrtm1.py rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/sqrtm1.py diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/test.py b/src/crypto/crypto_ops_builder/ref10CommentedCombined/test.py similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/test.py rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/test.py diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/xmrSpecificOld.c b/src/crypto/crypto_ops_builder/ref10CommentedCombined/xmrSpecificOld.c similarity index 100% rename from src/crypto/shen_ed25519_ref/ref10CommentedCombined/xmrSpecificOld.c rename to src/crypto/crypto_ops_builder/ref10CommentedCombined/xmrSpecificOld.c diff --git a/src/crypto/shen_ed25519_ref/sha512-blocks.c b/src/crypto/crypto_ops_builder/sha512-blocks.c similarity index 100% rename from src/crypto/shen_ed25519_ref/sha512-blocks.c rename to src/crypto/crypto_ops_builder/sha512-blocks.c diff --git a/src/crypto/shen_ed25519_ref/sha512-hash.c b/src/crypto/crypto_ops_builder/sha512-hash.c similarity index 100% rename from src/crypto/shen_ed25519_ref/sha512-hash.c rename to src/crypto/crypto_ops_builder/sha512-hash.c diff --git a/src/crypto/shen_ed25519_ref/sha512.h b/src/crypto/crypto_ops_builder/sha512.h similarity index 100% rename from src/crypto/shen_ed25519_ref/sha512.h rename to src/crypto/crypto_ops_builder/sha512.h diff --git a/src/crypto/shen_ed25519_ref/verify.c b/src/crypto/crypto_ops_builder/verify.c similarity index 100% rename from src/crypto/shen_ed25519_ref/verify.c rename to src/crypto/crypto_ops_builder/verify.c diff --git a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/crypto-ops.c b/src/crypto/shen_ed25519_ref/ref10CommentedCombined/crypto-ops.c deleted file mode 100644 index 223224f40..000000000 --- a/src/crypto/shen_ed25519_ref/ref10CommentedCombined/crypto-ops.c +++ /dev/null @@ -1,4830 +0,0 @@ -// Copyright (c) 2014-2015, The Monero Project -// -// All rights reserved. -// -// Redistribution and use in source and binary forms, with or without modification, are -// permitted provided that the following conditions are met: -// -// 1. Redistributions of source code must retain the above copyright notice, this list of -// conditions and the following disclaimer. -// -// 2. Redistributions in binary form must reproduce the above copyright notice, this list -// of conditions and the following disclaimer in the documentation and/or other -// materials provided with the distribution. -// -// 3. Neither the name of the copyright holder nor the names of its contributors may be -// used to endorse or promote products derived from this software without specific -// prior written permission. -// -// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY -// EXPRESS 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 COPYRIGHT HOLDER OR 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. -// -// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers -#include -#include - -#include "warnings.h" -#include "crypto-ops.h" - -DISABLE_VS_WARNINGS(4146 4244) -/* Predeclarations */ - -static void fe_mul(fe, const fe, const fe); -static void fe_sq(fe, const fe); -static void fe_tobytes(unsigned char *, const fe); -static int fe_isnonzero(const fe); -static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *); -static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *); -static void ge_p2_0(ge_p2 *); -static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *); -static void ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *); -static void fe_divpowm1(fe, const fe, const fe); -/* -fe means field element. -Here the field is \Z/(2^255-19). -An element t, entries t[0]...t[9], represents the integer -t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9]. -Bounds on each t[i] vary depending on context. -*/ - -/* -h = 0 -*/ - -void fe_0(fe h) -{ - h[0] = 0; - h[1] = 0; - h[2] = 0; - h[3] = 0; - h[4] = 0; - h[5] = 0; - h[6] = 0; - h[7] = 0; - h[8] = 0; - h[9] = 0; -} - -/* -h = 1 -*/ - -void fe_1(fe h) -{ - h[0] = 1; - h[1] = 0; - h[2] = 0; - h[3] = 0; - h[4] = 0; - h[5] = 0; - h[6] = 0; - h[7] = 0; - h[8] = 0; - h[9] = 0; -} - -/* -h = f + g -Can overlap h with f or g. - -Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - -Postconditions: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -*/ - -void fe_add(fe h,const fe f,const fe g) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t g0 = g[0]; - int32_t g1 = g[1]; - int32_t g2 = g[2]; - int32_t g3 = g[3]; - int32_t g4 = g[4]; - int32_t g5 = g[5]; - int32_t g6 = g[6]; - int32_t g7 = g[7]; - int32_t g8 = g[8]; - int32_t g9 = g[9]; - int32_t h0 = f0 + g0; - int32_t h1 = f1 + g1; - int32_t h2 = f2 + g2; - int32_t h3 = f3 + g3; - int32_t h4 = f4 + g4; - int32_t h5 = f5 + g5; - int32_t h6 = f6 + g6; - int32_t h7 = f7 + g7; - int32_t h8 = f8 + g8; - int32_t h9 = f9 + g9; - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* -Replace (f,g) with (g,g) if b == 1; -replace (f,g) with (f,g) if b == 0. - -Preconditions: b in {0,1}. -*/ - -void fe_cmov(fe f,const fe g,unsigned int b) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t g0 = g[0]; - int32_t g1 = g[1]; - int32_t g2 = g[2]; - int32_t g3 = g[3]; - int32_t g4 = g[4]; - int32_t g5 = g[5]; - int32_t g6 = g[6]; - int32_t g7 = g[7]; - int32_t g8 = g[8]; - int32_t g9 = g[9]; - int32_t x0 = f0 ^ g0; - int32_t x1 = f1 ^ g1; - int32_t x2 = f2 ^ g2; - int32_t x3 = f3 ^ g3; - int32_t x4 = f4 ^ g4; - int32_t x5 = f5 ^ g5; - int32_t x6 = f6 ^ g6; - int32_t x7 = f7 ^ g7; - int32_t x8 = f8 ^ g8; - int32_t x9 = f9 ^ g9; - b = -b; - x0 &= b; - x1 &= b; - x2 &= b; - x3 &= b; - x4 &= b; - x5 &= b; - x6 &= b; - x7 &= b; - x8 &= b; - x9 &= b; - f[0] = f0 ^ x0; - f[1] = f1 ^ x1; - f[2] = f2 ^ x2; - f[3] = f3 ^ x3; - f[4] = f4 ^ x4; - f[5] = f5 ^ x5; - f[6] = f6 ^ x6; - f[7] = f7 ^ x7; - f[8] = f8 ^ x8; - f[9] = f9 ^ x9; -} - -/* -h = f -*/ - -void fe_copy(fe h,const fe f) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - h[0] = f0; - h[1] = f1; - h[2] = f2; - h[3] = f3; - h[4] = f4; - h[5] = f5; - h[6] = f6; - h[7] = f7; - h[8] = f8; - h[9] = f9; -} - -static uint64_t load_3(const unsigned char *in) -{ - uint64_t result; - result = (uint64_t) in[0]; - result |= ((uint64_t) in[1]) << 8; - result |= ((uint64_t) in[2]) << 16; - return result; -} - -static uint64_t load_4(const unsigned char *in) -{ - uint64_t result; - result = (uint64_t) in[0]; - result |= ((uint64_t) in[1]) << 8; - result |= ((uint64_t) in[2]) << 16; - result |= ((uint64_t) in[3]) << 24; - return result; -} - -/* -Ignores top bit of h. -*/ - -void fe_frombytes(fe h,const unsigned char *s) -{ - int64_t h0 = load_4(s); - int64_t h1 = load_3(s + 4) << 6; - int64_t h2 = load_3(s + 7) << 5; - int64_t h3 = load_3(s + 10) << 3; - int64_t h4 = load_3(s + 13) << 2; - int64_t h5 = load_4(s + 16); - int64_t h6 = load_3(s + 20) << 7; - int64_t h7 = load_3(s + 23) << 5; - int64_t h8 = load_3(s + 26) << 4; - int64_t h9 = (load_3(s + 29) & 8388607) << 2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} -void fe_invert(fe out,const fe z) -{ - fe t0; - fe t1; - fe t2; - fe t3; - int i; -fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); -fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); -fe_mul(t1,z,t1); -fe_mul(t0,t0,t1); -fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2); -fe_mul(t1,t1,t2); -fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2); -fe_mul(t1,t2,t1); -fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2); -fe_mul(t2,t2,t1); -fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3); -fe_mul(t2,t3,t2); -fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2); -fe_mul(t1,t2,t1); -fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2); -fe_mul(t2,t2,t1); -fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3); -fe_mul(t2,t3,t2); -fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2); -fe_mul(t1,t2,t1); -fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1); -fe_mul(out,t1,t0); - return; -} - -/* -return 1 if f is in {1,3,5,...,q-2} -return 0 if f is in {0,2,4,...,q-1} - -Preconditions: - |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -*/ - -int fe_isnegative(const fe f) -{ - unsigned char s[32]; - fe_tobytes(s,f); - return s[0] & 1; -} - -/* -h = f * g -Can overlap h with f or g. - -Preconditions: - |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - -Postconditions: - |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -*/ - -/* -Notes on implementation strategy: - -Using schoolbook multiplication. -Karatsuba would save a little in some cost models. - -Most multiplications by 2 and 19 are 32-bit precomputations; -cheaper than 64-bit postcomputations. - -There is one remaining multiplication by 19 in the carry chain; -one *19 precomputation can be merged into this, -but the resulting data flow is considerably less clean. - -There are 12 carries below. -10 of them are 2-way parallelizable and vectorizable. -Can get away with 11 carries, but then data flow is much deeper. - -With tighter constraints on inputs can squeeze carries into int32. -*/ - -void fe_mul(fe h,const fe f,const fe g) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t g0 = g[0]; - int32_t g1 = g[1]; - int32_t g2 = g[2]; - int32_t g3 = g[3]; - int32_t g4 = g[4]; - int32_t g5 = g[5]; - int32_t g6 = g[6]; - int32_t g7 = g[7]; - int32_t g8 = g[8]; - int32_t g9 = g[9]; - int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ - int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ - int32_t g3_19 = 19 * g3; - int32_t g4_19 = 19 * g4; - int32_t g5_19 = 19 * g5; - int32_t g6_19 = 19 * g6; - int32_t g7_19 = 19 * g7; - int32_t g8_19 = 19 * g8; - int32_t g9_19 = 19 * g9; - int32_t f1_2 = 2 * f1; - int32_t f3_2 = 2 * f3; - int32_t f5_2 = 2 * f5; - int32_t f7_2 = 2 * f7; - int32_t f9_2 = 2 * f9; - int64_t f0g0 = f0 * (int64_t) g0; - int64_t f0g1 = f0 * (int64_t) g1; - int64_t f0g2 = f0 * (int64_t) g2; - int64_t f0g3 = f0 * (int64_t) g3; - int64_t f0g4 = f0 * (int64_t) g4; - int64_t f0g5 = f0 * (int64_t) g5; - int64_t f0g6 = f0 * (int64_t) g6; - int64_t f0g7 = f0 * (int64_t) g7; - int64_t f0g8 = f0 * (int64_t) g8; - int64_t f0g9 = f0 * (int64_t) g9; - int64_t f1g0 = f1 * (int64_t) g0; - int64_t f1g1_2 = f1_2 * (int64_t) g1; - int64_t f1g2 = f1 * (int64_t) g2; - int64_t f1g3_2 = f1_2 * (int64_t) g3; - int64_t f1g4 = f1 * (int64_t) g4; - int64_t f1g5_2 = f1_2 * (int64_t) g5; - int64_t f1g6 = f1 * (int64_t) g6; - int64_t f1g7_2 = f1_2 * (int64_t) g7; - int64_t f1g8 = f1 * (int64_t) g8; - int64_t f1g9_38 = f1_2 * (int64_t) g9_19; - int64_t f2g0 = f2 * (int64_t) g0; - int64_t f2g1 = f2 * (int64_t) g1; - int64_t f2g2 = f2 * (int64_t) g2; - int64_t f2g3 = f2 * (int64_t) g3; - int64_t f2g4 = f2 * (int64_t) g4; - int64_t f2g5 = f2 * (int64_t) g5; - int64_t f2g6 = f2 * (int64_t) g6; - int64_t f2g7 = f2 * (int64_t) g7; - int64_t f2g8_19 = f2 * (int64_t) g8_19; - int64_t f2g9_19 = f2 * (int64_t) g9_19; - int64_t f3g0 = f3 * (int64_t) g0; - int64_t f3g1_2 = f3_2 * (int64_t) g1; - int64_t f3g2 = f3 * (int64_t) g2; - int64_t f3g3_2 = f3_2 * (int64_t) g3; - int64_t f3g4 = f3 * (int64_t) g4; - int64_t f3g5_2 = f3_2 * (int64_t) g5; - int64_t f3g6 = f3 * (int64_t) g6; - int64_t f3g7_38 = f3_2 * (int64_t) g7_19; - int64_t f3g8_19 = f3 * (int64_t) g8_19; - int64_t f3g9_38 = f3_2 * (int64_t) g9_19; - int64_t f4g0 = f4 * (int64_t) g0; - int64_t f4g1 = f4 * (int64_t) g1; - int64_t f4g2 = f4 * (int64_t) g2; - int64_t f4g3 = f4 * (int64_t) g3; - int64_t f4g4 = f4 * (int64_t) g4; - int64_t f4g5 = f4 * (int64_t) g5; - int64_t f4g6_19 = f4 * (int64_t) g6_19; - int64_t f4g7_19 = f4 * (int64_t) g7_19; - int64_t f4g8_19 = f4 * (int64_t) g8_19; - int64_t f4g9_19 = f4 * (int64_t) g9_19; - int64_t f5g0 = f5 * (int64_t) g0; - int64_t f5g1_2 = f5_2 * (int64_t) g1; - int64_t f5g2 = f5 * (int64_t) g2; - int64_t f5g3_2 = f5_2 * (int64_t) g3; - int64_t f5g4 = f5 * (int64_t) g4; - int64_t f5g5_38 = f5_2 * (int64_t) g5_19; - int64_t f5g6_19 = f5 * (int64_t) g6_19; - int64_t f5g7_38 = f5_2 * (int64_t) g7_19; - int64_t f5g8_19 = f5 * (int64_t) g8_19; - int64_t f5g9_38 = f5_2 * (int64_t) g9_19; - int64_t f6g0 = f6 * (int64_t) g0; - int64_t f6g1 = f6 * (int64_t) g1; - int64_t f6g2 = f6 * (int64_t) g2; - int64_t f6g3 = f6 * (int64_t) g3; - int64_t f6g4_19 = f6 * (int64_t) g4_19; - int64_t f6g5_19 = f6 * (int64_t) g5_19; - int64_t f6g6_19 = f6 * (int64_t) g6_19; - int64_t f6g7_19 = f6 * (int64_t) g7_19; - int64_t f6g8_19 = f6 * (int64_t) g8_19; - int64_t f6g9_19 = f6 * (int64_t) g9_19; - int64_t f7g0 = f7 * (int64_t) g0; - int64_t f7g1_2 = f7_2 * (int64_t) g1; - int64_t f7g2 = f7 * (int64_t) g2; - int64_t f7g3_38 = f7_2 * (int64_t) g3_19; - int64_t f7g4_19 = f7 * (int64_t) g4_19; - int64_t f7g5_38 = f7_2 * (int64_t) g5_19; - int64_t f7g6_19 = f7 * (int64_t) g6_19; - int64_t f7g7_38 = f7_2 * (int64_t) g7_19; - int64_t f7g8_19 = f7 * (int64_t) g8_19; - int64_t f7g9_38 = f7_2 * (int64_t) g9_19; - int64_t f8g0 = f8 * (int64_t) g0; - int64_t f8g1 = f8 * (int64_t) g1; - int64_t f8g2_19 = f8 * (int64_t) g2_19; - int64_t f8g3_19 = f8 * (int64_t) g3_19; - int64_t f8g4_19 = f8 * (int64_t) g4_19; - int64_t f8g5_19 = f8 * (int64_t) g5_19; - int64_t f8g6_19 = f8 * (int64_t) g6_19; - int64_t f8g7_19 = f8 * (int64_t) g7_19; - int64_t f8g8_19 = f8 * (int64_t) g8_19; - int64_t f8g9_19 = f8 * (int64_t) g9_19; - int64_t f9g0 = f9 * (int64_t) g0; - int64_t f9g1_38 = f9_2 * (int64_t) g1_19; - int64_t f9g2_19 = f9 * (int64_t) g2_19; - int64_t f9g3_38 = f9_2 * (int64_t) g3_19; - int64_t f9g4_19 = f9 * (int64_t) g4_19; - int64_t f9g5_38 = f9_2 * (int64_t) g5_19; - int64_t f9g6_19 = f9 * (int64_t) g6_19; - int64_t f9g7_38 = f9_2 * (int64_t) g7_19; - int64_t f9g8_19 = f9 * (int64_t) g8_19; - int64_t f9g9_38 = f9_2 * (int64_t) g9_19; - int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; - int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; - int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; - int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; - int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; - int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; - int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; - int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; - int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; - int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - /* - |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) - i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 - |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) - i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 - */ - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - /* |h0| <= 2^25 */ - /* |h4| <= 2^25 */ - /* |h1| <= 1.71*2^59 */ - /* |h5| <= 1.71*2^59 */ - - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - /* |h1| <= 2^24; from now on fits into int32 */ - /* |h5| <= 2^24; from now on fits into int32 */ - /* |h2| <= 1.41*2^60 */ - /* |h6| <= 1.41*2^60 */ - - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - /* |h2| <= 2^25; from now on fits into int32 unchanged */ - /* |h6| <= 2^25; from now on fits into int32 unchanged */ - /* |h3| <= 1.71*2^59 */ - /* |h7| <= 1.71*2^59 */ - - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - /* |h3| <= 2^24; from now on fits into int32 unchanged */ - /* |h7| <= 2^24; from now on fits into int32 unchanged */ - /* |h4| <= 1.72*2^34 */ - /* |h8| <= 1.41*2^60 */ - - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - /* |h4| <= 2^25; from now on fits into int32 unchanged */ - /* |h8| <= 2^25; from now on fits into int32 unchanged */ - /* |h5| <= 1.01*2^24 */ - /* |h9| <= 1.71*2^59 */ - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - /* |h9| <= 2^24; from now on fits into int32 unchanged */ - /* |h0| <= 1.1*2^39 */ - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - /* |h0| <= 2^25; from now on fits into int32 unchanged */ - /* |h1| <= 1.01*2^24 */ - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* -h = -f - -Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - -Postconditions: - |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. -*/ - -void fe_neg(fe h,const fe f) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t h0 = -f0; - int32_t h1 = -f1; - int32_t h2 = -f2; - int32_t h3 = -f3; - int32_t h4 = -f4; - int32_t h5 = -f5; - int32_t h6 = -f6; - int32_t h7 = -f7; - int32_t h8 = -f8; - int32_t h9 = -f9; - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} -void fe_pow22523(fe out,const fe z) -{ - fe t0; - fe t1; - fe t2; - int i; -fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0); -fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1); -fe_mul(t1,z,t1); -fe_mul(t0,t0,t1); -fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0); -fe_mul(t0,t1,t0); -fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1); -fe_mul(t0,t1,t0); -fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1); -fe_mul(t1,t1,t0); -fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2); -fe_mul(t1,t2,t1); -fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1); -fe_mul(t0,t1,t0); -fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1); -fe_mul(t1,t1,t0); -fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2); -fe_mul(t1,t2,t1); -fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1); -fe_mul(t0,t1,t0); -fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0); -fe_mul(out,t0,z); - return; -} - -/* -h = f * f -Can overlap h with f. - -Preconditions: - |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - -Postconditions: - |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -*/ - -/* -See fe_mul.c for discussion of implementation strategy. -*/ - -void fe_sq(fe h,const fe f) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t f0_2 = 2 * f0; - int32_t f1_2 = 2 * f1; - int32_t f2_2 = 2 * f2; - int32_t f3_2 = 2 * f3; - int32_t f4_2 = 2 * f4; - int32_t f5_2 = 2 * f5; - int32_t f6_2 = 2 * f6; - int32_t f7_2 = 2 * f7; - int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ - int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ - int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ - int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ - int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ - int64_t f0f0 = f0 * (int64_t) f0; - int64_t f0f1_2 = f0_2 * (int64_t) f1; - int64_t f0f2_2 = f0_2 * (int64_t) f2; - int64_t f0f3_2 = f0_2 * (int64_t) f3; - int64_t f0f4_2 = f0_2 * (int64_t) f4; - int64_t f0f5_2 = f0_2 * (int64_t) f5; - int64_t f0f6_2 = f0_2 * (int64_t) f6; - int64_t f0f7_2 = f0_2 * (int64_t) f7; - int64_t f0f8_2 = f0_2 * (int64_t) f8; - int64_t f0f9_2 = f0_2 * (int64_t) f9; - int64_t f1f1_2 = f1_2 * (int64_t) f1; - int64_t f1f2_2 = f1_2 * (int64_t) f2; - int64_t f1f3_4 = f1_2 * (int64_t) f3_2; - int64_t f1f4_2 = f1_2 * (int64_t) f4; - int64_t f1f5_4 = f1_2 * (int64_t) f5_2; - int64_t f1f6_2 = f1_2 * (int64_t) f6; - int64_t f1f7_4 = f1_2 * (int64_t) f7_2; - int64_t f1f8_2 = f1_2 * (int64_t) f8; - int64_t f1f9_76 = f1_2 * (int64_t) f9_38; - int64_t f2f2 = f2 * (int64_t) f2; - int64_t f2f3_2 = f2_2 * (int64_t) f3; - int64_t f2f4_2 = f2_2 * (int64_t) f4; - int64_t f2f5_2 = f2_2 * (int64_t) f5; - int64_t f2f6_2 = f2_2 * (int64_t) f6; - int64_t f2f7_2 = f2_2 * (int64_t) f7; - int64_t f2f8_38 = f2_2 * (int64_t) f8_19; - int64_t f2f9_38 = f2 * (int64_t) f9_38; - int64_t f3f3_2 = f3_2 * (int64_t) f3; - int64_t f3f4_2 = f3_2 * (int64_t) f4; - int64_t f3f5_4 = f3_2 * (int64_t) f5_2; - int64_t f3f6_2 = f3_2 * (int64_t) f6; - int64_t f3f7_76 = f3_2 * (int64_t) f7_38; - int64_t f3f8_38 = f3_2 * (int64_t) f8_19; - int64_t f3f9_76 = f3_2 * (int64_t) f9_38; - int64_t f4f4 = f4 * (int64_t) f4; - int64_t f4f5_2 = f4_2 * (int64_t) f5; - int64_t f4f6_38 = f4_2 * (int64_t) f6_19; - int64_t f4f7_38 = f4 * (int64_t) f7_38; - int64_t f4f8_38 = f4_2 * (int64_t) f8_19; - int64_t f4f9_38 = f4 * (int64_t) f9_38; - int64_t f5f5_38 = f5 * (int64_t) f5_38; - int64_t f5f6_38 = f5_2 * (int64_t) f6_19; - int64_t f5f7_76 = f5_2 * (int64_t) f7_38; - int64_t f5f8_38 = f5_2 * (int64_t) f8_19; - int64_t f5f9_76 = f5_2 * (int64_t) f9_38; - int64_t f6f6_19 = f6 * (int64_t) f6_19; - int64_t f6f7_38 = f6 * (int64_t) f7_38; - int64_t f6f8_38 = f6_2 * (int64_t) f8_19; - int64_t f6f9_38 = f6 * (int64_t) f9_38; - int64_t f7f7_38 = f7 * (int64_t) f7_38; - int64_t f7f8_38 = f7_2 * (int64_t) f8_19; - int64_t f7f9_76 = f7_2 * (int64_t) f9_38; - int64_t f8f8_19 = f8 * (int64_t) f8_19; - int64_t f8f9_38 = f8 * (int64_t) f9_38; - int64_t f9f9_38 = f9 * (int64_t) f9_38; - int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; - int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; - int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; - int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; - int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; - int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; - int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; - int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; - int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; - int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* -h = 2 * f * f -Can overlap h with f. - -Preconditions: - |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. - -Postconditions: - |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. -*/ - -/* -See fe_mul.c for discussion of implementation strategy. -*/ - -void fe_sq2(fe h,const fe f) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t f0_2 = 2 * f0; - int32_t f1_2 = 2 * f1; - int32_t f2_2 = 2 * f2; - int32_t f3_2 = 2 * f3; - int32_t f4_2 = 2 * f4; - int32_t f5_2 = 2 * f5; - int32_t f6_2 = 2 * f6; - int32_t f7_2 = 2 * f7; - int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ - int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ - int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ - int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ - int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ - int64_t f0f0 = f0 * (int64_t) f0; - int64_t f0f1_2 = f0_2 * (int64_t) f1; - int64_t f0f2_2 = f0_2 * (int64_t) f2; - int64_t f0f3_2 = f0_2 * (int64_t) f3; - int64_t f0f4_2 = f0_2 * (int64_t) f4; - int64_t f0f5_2 = f0_2 * (int64_t) f5; - int64_t f0f6_2 = f0_2 * (int64_t) f6; - int64_t f0f7_2 = f0_2 * (int64_t) f7; - int64_t f0f8_2 = f0_2 * (int64_t) f8; - int64_t f0f9_2 = f0_2 * (int64_t) f9; - int64_t f1f1_2 = f1_2 * (int64_t) f1; - int64_t f1f2_2 = f1_2 * (int64_t) f2; - int64_t f1f3_4 = f1_2 * (int64_t) f3_2; - int64_t f1f4_2 = f1_2 * (int64_t) f4; - int64_t f1f5_4 = f1_2 * (int64_t) f5_2; - int64_t f1f6_2 = f1_2 * (int64_t) f6; - int64_t f1f7_4 = f1_2 * (int64_t) f7_2; - int64_t f1f8_2 = f1_2 * (int64_t) f8; - int64_t f1f9_76 = f1_2 * (int64_t) f9_38; - int64_t f2f2 = f2 * (int64_t) f2; - int64_t f2f3_2 = f2_2 * (int64_t) f3; - int64_t f2f4_2 = f2_2 * (int64_t) f4; - int64_t f2f5_2 = f2_2 * (int64_t) f5; - int64_t f2f6_2 = f2_2 * (int64_t) f6; - int64_t f2f7_2 = f2_2 * (int64_t) f7; - int64_t f2f8_38 = f2_2 * (int64_t) f8_19; - int64_t f2f9_38 = f2 * (int64_t) f9_38; - int64_t f3f3_2 = f3_2 * (int64_t) f3; - int64_t f3f4_2 = f3_2 * (int64_t) f4; - int64_t f3f5_4 = f3_2 * (int64_t) f5_2; - int64_t f3f6_2 = f3_2 * (int64_t) f6; - int64_t f3f7_76 = f3_2 * (int64_t) f7_38; - int64_t f3f8_38 = f3_2 * (int64_t) f8_19; - int64_t f3f9_76 = f3_2 * (int64_t) f9_38; - int64_t f4f4 = f4 * (int64_t) f4; - int64_t f4f5_2 = f4_2 * (int64_t) f5; - int64_t f4f6_38 = f4_2 * (int64_t) f6_19; - int64_t f4f7_38 = f4 * (int64_t) f7_38; - int64_t f4f8_38 = f4_2 * (int64_t) f8_19; - int64_t f4f9_38 = f4 * (int64_t) f9_38; - int64_t f5f5_38 = f5 * (int64_t) f5_38; - int64_t f5f6_38 = f5_2 * (int64_t) f6_19; - int64_t f5f7_76 = f5_2 * (int64_t) f7_38; - int64_t f5f8_38 = f5_2 * (int64_t) f8_19; - int64_t f5f9_76 = f5_2 * (int64_t) f9_38; - int64_t f6f6_19 = f6 * (int64_t) f6_19; - int64_t f6f7_38 = f6 * (int64_t) f7_38; - int64_t f6f8_38 = f6_2 * (int64_t) f8_19; - int64_t f6f9_38 = f6 * (int64_t) f9_38; - int64_t f7f7_38 = f7 * (int64_t) f7_38; - int64_t f7f8_38 = f7_2 * (int64_t) f8_19; - int64_t f7f9_76 = f7_2 * (int64_t) f9_38; - int64_t f8f8_19 = f8 * (int64_t) f8_19; - int64_t f8f9_38 = f8 * (int64_t) f9_38; - int64_t f9f9_38 = f9 * (int64_t) f9_38; - int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; - int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; - int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; - int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; - int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; - int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; - int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; - int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; - int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; - int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - h0 += h0; - h1 += h1; - h2 += h2; - h3 += h3; - h4 += h4; - h5 += h5; - h6 += h6; - h7 += h7; - h8 += h8; - h9 += h9; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* -h = f - g -Can overlap h with f or g. - -Preconditions: - |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. - -Postconditions: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. -*/ - -void fe_sub(fe h,const fe f,const fe g) -{ - int32_t f0 = f[0]; - int32_t f1 = f[1]; - int32_t f2 = f[2]; - int32_t f3 = f[3]; - int32_t f4 = f[4]; - int32_t f5 = f[5]; - int32_t f6 = f[6]; - int32_t f7 = f[7]; - int32_t f8 = f[8]; - int32_t f9 = f[9]; - int32_t g0 = g[0]; - int32_t g1 = g[1]; - int32_t g2 = g[2]; - int32_t g3 = g[3]; - int32_t g4 = g[4]; - int32_t g5 = g[5]; - int32_t g6 = g[6]; - int32_t g7 = g[7]; - int32_t g8 = g[8]; - int32_t g9 = g[9]; - int32_t h0 = f0 - g0; - int32_t h1 = f1 - g1; - int32_t h2 = f2 - g2; - int32_t h3 = f3 - g3; - int32_t h4 = f4 - g4; - int32_t h5 = f5 - g5; - int32_t h6 = f6 - g6; - int32_t h7 = f7 - g7; - int32_t h8 = f8 - g8; - int32_t h9 = f9 - g9; - h[0] = h0; - h[1] = h1; - h[2] = h2; - h[3] = h3; - h[4] = h4; - h[5] = h5; - h[6] = h6; - h[7] = h7; - h[8] = h8; - h[9] = h9; -} - -/* -Preconditions: - |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. - -Write p=2^255-19; q=floor(h/p). -Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). - -Proof: - Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. - Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. - - Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). - Then 0> 25; - q = (h0 + q) >> 26; - q = (h1 + q) >> 25; - q = (h2 + q) >> 26; - q = (h3 + q) >> 25; - q = (h4 + q) >> 26; - q = (h5 + q) >> 25; - q = (h6 + q) >> 26; - q = (h7 + q) >> 25; - q = (h8 + q) >> 26; - q = (h9 + q) >> 25; - - /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ - h0 += 19 * q; - /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ - - carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; - carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; - carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; - carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; - carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; - carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; - carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; - carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; - carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; - carry9 = h9 >> 25; h9 -= carry9 << 25; - /* h10 = carry9 */ - - /* - Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. - Have h0+...+2^230 h9 between 0 and 2^255-1; - evidently 2^255 h10-2^255 q = 0. - Goal: Output h0+...+2^230 h9. - */ - - s[0] = h0 >> 0; - s[1] = h0 >> 8; - s[2] = h0 >> 16; - s[3] = (h0 >> 24) | (h1 << 2); - s[4] = h1 >> 6; - s[5] = h1 >> 14; - s[6] = (h1 >> 22) | (h2 << 3); - s[7] = h2 >> 5; - s[8] = h2 >> 13; - s[9] = (h2 >> 21) | (h3 << 5); - s[10] = h3 >> 3; - s[11] = h3 >> 11; - s[12] = (h3 >> 19) | (h4 << 6); - s[13] = h4 >> 2; - s[14] = h4 >> 10; - s[15] = h4 >> 18; - s[16] = h5 >> 0; - s[17] = h5 >> 8; - s[18] = h5 >> 16; - s[19] = (h5 >> 24) | (h6 << 1); - s[20] = h6 >> 7; - s[21] = h6 >> 15; - s[22] = (h6 >> 23) | (h7 << 3); - s[23] = h7 >> 5; - s[24] = h7 >> 13; - s[25] = (h7 >> 21) | (h8 << 4); - s[26] = h8 >> 4; - s[27] = h8 >> 12; - s[28] = (h8 >> 20) | (h9 << 6); - s[29] = h9 >> 2; - s[30] = h9 >> 10; - s[31] = h9 >> 18; -} -/* - * - * sc code - * - * -The set of scalars is \Z/l -where l = 2^252 + 27742317777372353535851937790883648493. - -This is the order of the curve ed25519. -The point is that if a is a scalar and P is a point, -and b is congruent to a mod l, then aP = bP. -Thus, reducing mod l can possibly give you a smaller scalar, -so your elliptic curve operations take less time -*/ - -/* -Input: - a[0]+256*a[1]+...+256^31*a[31] = a - b[0]+256*b[1]+...+256^31*b[31] = b - c[0]+256*c[1]+...+256^31*c[31] = c - -Output: - s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l - where l = 2^252 + 27742317777372353535851937790883648493. -*/ - -void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c) -{ - int64_t a0 = 2097151 & load_3(a); - int64_t a1 = 2097151 & (load_4(a + 2) >> 5); - int64_t a2 = 2097151 & (load_3(a + 5) >> 2); - int64_t a3 = 2097151 & (load_4(a + 7) >> 7); - int64_t a4 = 2097151 & (load_4(a + 10) >> 4); - int64_t a5 = 2097151 & (load_3(a + 13) >> 1); - int64_t a6 = 2097151 & (load_4(a + 15) >> 6); - int64_t a7 = 2097151 & (load_3(a + 18) >> 3); - int64_t a8 = 2097151 & load_3(a + 21); - int64_t a9 = 2097151 & (load_4(a + 23) >> 5); - int64_t a10 = 2097151 & (load_3(a + 26) >> 2); - int64_t a11 = (load_4(a + 28) >> 7); - int64_t b0 = 2097151 & load_3(b); - int64_t b1 = 2097151 & (load_4(b + 2) >> 5); - int64_t b2 = 2097151 & (load_3(b + 5) >> 2); - int64_t b3 = 2097151 & (load_4(b + 7) >> 7); - int64_t b4 = 2097151 & (load_4(b + 10) >> 4); - int64_t b5 = 2097151 & (load_3(b + 13) >> 1); - int64_t b6 = 2097151 & (load_4(b + 15) >> 6); - int64_t b7 = 2097151 & (load_3(b + 18) >> 3); - int64_t b8 = 2097151 & load_3(b + 21); - int64_t b9 = 2097151 & (load_4(b + 23) >> 5); - int64_t b10 = 2097151 & (load_3(b + 26) >> 2); - int64_t b11 = (load_4(b + 28) >> 7); - int64_t c0 = 2097151 & load_3(c); - int64_t c1 = 2097151 & (load_4(c + 2) >> 5); - int64_t c2 = 2097151 & (load_3(c + 5) >> 2); - int64_t c3 = 2097151 & (load_4(c + 7) >> 7); - int64_t c4 = 2097151 & (load_4(c + 10) >> 4); - int64_t c5 = 2097151 & (load_3(c + 13) >> 1); - int64_t c6 = 2097151 & (load_4(c + 15) >> 6); - int64_t c7 = 2097151 & (load_3(c + 18) >> 3); - int64_t c8 = 2097151 & load_3(c + 21); - int64_t c9 = 2097151 & (load_4(c + 23) >> 5); - int64_t c10 = 2097151 & (load_3(c + 26) >> 2); - int64_t c11 = (load_4(c + 28) >> 7); - int64_t s0; - int64_t s1; - int64_t s2; - int64_t s3; - int64_t s4; - int64_t s5; - int64_t s6; - int64_t s7; - int64_t s8; - int64_t s9; - int64_t s10; - int64_t s11; - int64_t s12; - int64_t s13; - int64_t s14; - int64_t s15; - int64_t s16; - int64_t s17; - int64_t s18; - int64_t s19; - int64_t s20; - int64_t s21; - int64_t s22; - int64_t s23; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - int64_t carry12; - int64_t carry13; - int64_t carry14; - int64_t carry15; - int64_t carry16; - int64_t carry17; - int64_t carry18; - int64_t carry19; - int64_t carry20; - int64_t carry21; - int64_t carry22; - - s0 = c0 + a0*b0; - s1 = c1 + a0*b1 + a1*b0; - s2 = c2 + a0*b2 + a1*b1 + a2*b0; - s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0; - s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0; - s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0; - s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0; - s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0; - s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0; - s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0; - s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0; - s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0; - s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1; - s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2; - s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3; - s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4; - s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5; - s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6; - s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7; - s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8; - s20 = a9*b11 + a10*b10 + a11*b9; - s21 = a10*b11 + a11*b10; - s22 = a11*b11; - s23 = 0; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; - carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; - carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; - carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; - carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; - carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; - carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; - carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; - carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; - carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - s23 = 0; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - s22 = 0; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - s21 = 0; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - s20 = 0; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - s19 = 0; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - s18 = 0; - - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; - carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; - carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; - - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; - carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - s17 = 0; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - s16 = 0; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - s15 = 0; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - s14 = 0; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - s13 = 0; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - -/* -Input: - s[0]+256*s[1]+...+256^63*s[63] = s - -Output: - s[0]+256*s[1]+...+256^31*s[31] = s mod l - where l = 2^252 + 27742317777372353535851937790883648493. - Overwrites s in place. -*/ - -void sc_reduce(unsigned char *s) -{ - int64_t s0 = 2097151 & load_3(s); - int64_t s1 = 2097151 & (load_4(s + 2) >> 5); - int64_t s2 = 2097151 & (load_3(s + 5) >> 2); - int64_t s3 = 2097151 & (load_4(s + 7) >> 7); - int64_t s4 = 2097151 & (load_4(s + 10) >> 4); - int64_t s5 = 2097151 & (load_3(s + 13) >> 1); - int64_t s6 = 2097151 & (load_4(s + 15) >> 6); - int64_t s7 = 2097151 & (load_3(s + 18) >> 3); - int64_t s8 = 2097151 & load_3(s + 21); - int64_t s9 = 2097151 & (load_4(s + 23) >> 5); - int64_t s10 = 2097151 & (load_3(s + 26) >> 2); - int64_t s11 = 2097151 & (load_4(s + 28) >> 7); - int64_t s12 = 2097151 & (load_4(s + 31) >> 4); - int64_t s13 = 2097151 & (load_3(s + 34) >> 1); - int64_t s14 = 2097151 & (load_4(s + 36) >> 6); - int64_t s15 = 2097151 & (load_3(s + 39) >> 3); - int64_t s16 = 2097151 & load_3(s + 42); - int64_t s17 = 2097151 & (load_4(s + 44) >> 5); - int64_t s18 = 2097151 & (load_3(s + 47) >> 2); - int64_t s19 = 2097151 & (load_4(s + 49) >> 7); - int64_t s20 = 2097151 & (load_4(s + 52) >> 4); - int64_t s21 = 2097151 & (load_3(s + 55) >> 1); - int64_t s22 = 2097151 & (load_4(s + 57) >> 6); - int64_t s23 = (load_4(s + 60) >> 3); - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - int64_t carry12; - int64_t carry13; - int64_t carry14; - int64_t carry15; - int64_t carry16; - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - s23 = 0; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - s22 = 0; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - s21 = 0; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - s20 = 0; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - s19 = 0; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - s18 = 0; - - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; - carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; - carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; - - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; - carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - s17 = 0; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - s16 = 0; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - s15 = 0; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - s14 = 0; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - s13 = 0; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - -void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) { - int64_t a0 = 2097151 & load_3(a); - int64_t a1 = 2097151 & (load_4(a + 2) >> 5); - int64_t a2 = 2097151 & (load_3(a + 5) >> 2); - int64_t a3 = 2097151 & (load_4(a + 7) >> 7); - int64_t a4 = 2097151 & (load_4(a + 10) >> 4); - int64_t a5 = 2097151 & (load_3(a + 13) >> 1); - int64_t a6 = 2097151 & (load_4(a + 15) >> 6); - int64_t a7 = 2097151 & (load_3(a + 18) >> 3); - int64_t a8 = 2097151 & load_3(a + 21); - int64_t a9 = 2097151 & (load_4(a + 23) >> 5); - int64_t a10 = 2097151 & (load_3(a + 26) >> 2); - int64_t a11 = (load_4(a + 28) >> 7); - int64_t b0 = 2097151 & load_3(b); - int64_t b1 = 2097151 & (load_4(b + 2) >> 5); - int64_t b2 = 2097151 & (load_3(b + 5) >> 2); - int64_t b3 = 2097151 & (load_4(b + 7) >> 7); - int64_t b4 = 2097151 & (load_4(b + 10) >> 4); - int64_t b5 = 2097151 & (load_3(b + 13) >> 1); - int64_t b6 = 2097151 & (load_4(b + 15) >> 6); - int64_t b7 = 2097151 & (load_3(b + 18) >> 3); - int64_t b8 = 2097151 & load_3(b + 21); - int64_t b9 = 2097151 & (load_4(b + 23) >> 5); - int64_t b10 = 2097151 & (load_3(b + 26) >> 2); - int64_t b11 = (load_4(b + 28) >> 7); - int64_t s0 = a0 - b0; - int64_t s1 = a1 - b1; - int64_t s2 = a2 - b2; - int64_t s3 = a3 - b3; - int64_t s4 = a4 - b4; - int64_t s5 = a5 - b5; - int64_t s6 = a6 - b6; - int64_t s7 = a7 - b7; - int64_t s8 = a8 - b8; - int64_t s9 = a9 - b9; - int64_t s10 = a10 - b10; - int64_t s11 = a11 - b11; - int64_t s12 = 0; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - -/* -Input: - a[0]+256*a[1]+...+256^31*a[31] = a - b[0]+256*b[1]+...+256^31*b[31] = b - c[0]+256*c[1]+...+256^31*c[31] = c - -Output: - s[0]+256*s[1]+...+256^31*s[31] = (c-ab) mod l - where l = 2^252 + 27742317777372353535851937790883648493. -*/ - -//x -void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { - int64_t a0 = 2097151 & load_3(a); - int64_t a1 = 2097151 & (load_4(a + 2) >> 5); - int64_t a2 = 2097151 & (load_3(a + 5) >> 2); - int64_t a3 = 2097151 & (load_4(a + 7) >> 7); - int64_t a4 = 2097151 & (load_4(a + 10) >> 4); - int64_t a5 = 2097151 & (load_3(a + 13) >> 1); - int64_t a6 = 2097151 & (load_4(a + 15) >> 6); - int64_t a7 = 2097151 & (load_3(a + 18) >> 3); - int64_t a8 = 2097151 & load_3(a + 21); - int64_t a9 = 2097151 & (load_4(a + 23) >> 5); - int64_t a10 = 2097151 & (load_3(a + 26) >> 2); - int64_t a11 = (load_4(a + 28) >> 7); - int64_t b0 = 2097151 & load_3(b); - int64_t b1 = 2097151 & (load_4(b + 2) >> 5); - int64_t b2 = 2097151 & (load_3(b + 5) >> 2); - int64_t b3 = 2097151 & (load_4(b + 7) >> 7); - int64_t b4 = 2097151 & (load_4(b + 10) >> 4); - int64_t b5 = 2097151 & (load_3(b + 13) >> 1); - int64_t b6 = 2097151 & (load_4(b + 15) >> 6); - int64_t b7 = 2097151 & (load_3(b + 18) >> 3); - int64_t b8 = 2097151 & load_3(b + 21); - int64_t b9 = 2097151 & (load_4(b + 23) >> 5); - int64_t b10 = 2097151 & (load_3(b + 26) >> 2); - int64_t b11 = (load_4(b + 28) >> 7); - int64_t c0 = 2097151 & load_3(c); - int64_t c1 = 2097151 & (load_4(c + 2) >> 5); - int64_t c2 = 2097151 & (load_3(c + 5) >> 2); - int64_t c3 = 2097151 & (load_4(c + 7) >> 7); - int64_t c4 = 2097151 & (load_4(c + 10) >> 4); - int64_t c5 = 2097151 & (load_3(c + 13) >> 1); - int64_t c6 = 2097151 & (load_4(c + 15) >> 6); - int64_t c7 = 2097151 & (load_3(c + 18) >> 3); - int64_t c8 = 2097151 & load_3(c + 21); - int64_t c9 = 2097151 & (load_4(c + 23) >> 5); - int64_t c10 = 2097151 & (load_3(c + 26) >> 2); - int64_t c11 = (load_4(c + 28) >> 7); - int64_t s0; - int64_t s1; - int64_t s2; - int64_t s3; - int64_t s4; - int64_t s5; - int64_t s6; - int64_t s7; - int64_t s8; - int64_t s9; - int64_t s10; - int64_t s11; - int64_t s12; - int64_t s13; - int64_t s14; - int64_t s15; - int64_t s16; - int64_t s17; - int64_t s18; - int64_t s19; - int64_t s20; - int64_t s21; - int64_t s22; - int64_t s23; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - int64_t carry12; - int64_t carry13; - int64_t carry14; - int64_t carry15; - int64_t carry16; - int64_t carry17; - int64_t carry18; - int64_t carry19; - int64_t carry20; - int64_t carry21; - int64_t carry22; - - s0 = c0 - a0*b0; - s1 = c1 - (a0*b1 + a1*b0); - s2 = c2 - (a0*b2 + a1*b1 + a2*b0); - s3 = c3 - (a0*b3 + a1*b2 + a2*b1 + a3*b0); - s4 = c4 - (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0); - s5 = c5 - (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0); - s6 = c6 - (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0); - s7 = c7 - (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0); - s8 = c8 - (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0); - s9 = c9 - (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0); - s10 = c10 - (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0); - s11 = c11 - (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0); - s12 = -(a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1); - s13 = -(a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2); - s14 = -(a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3); - s15 = -(a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4); - s16 = -(a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5); - s17 = -(a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6); - s18 = -(a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7); - s19 = -(a8*b11 + a9*b10 + a10*b9 + a11*b8); - s20 = -(a9*b11 + a10*b10 + a11*b9); - s21 = -(a10*b11 + a11*b10); - s22 = -a11*b11; - s23 = 0; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; - carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; - carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; - carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; - carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; - carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; - carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; - carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; - carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; - carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; - - s11 += s23 * 666643; - s12 += s23 * 470296; - s13 += s23 * 654183; - s14 -= s23 * 997805; - s15 += s23 * 136657; - s16 -= s23 * 683901; - - s10 += s22 * 666643; - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - - s9 += s21 * 666643; - s10 += s21 * 470296; - s11 += s21 * 654183; - s12 -= s21 * 997805; - s13 += s21 * 136657; - s14 -= s21 * 683901; - - s8 += s20 * 666643; - s9 += s20 * 470296; - s10 += s20 * 654183; - s11 -= s20 * 997805; - s12 += s20 * 136657; - s13 -= s20 * 683901; - - s7 += s19 * 666643; - s8 += s19 * 470296; - s9 += s19 * 654183; - s10 -= s19 * 997805; - s11 += s19 * 136657; - s12 -= s19 * 683901; - - s6 += s18 * 666643; - s7 += s18 * 470296; - s8 += s18 * 654183; - s9 -= s18 * 997805; - s10 += s18 * 136657; - s11 -= s18 * 683901; - - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; - carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; - carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; - - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; - carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; - - s5 += s17 * 666643; - s6 += s17 * 470296; - s7 += s17 * 654183; - s8 -= s17 * 997805; - s9 += s17 * 136657; - s10 -= s17 * 683901; - - s4 += s16 * 666643; - s5 += s16 * 470296; - s6 += s16 * 654183; - s7 -= s16 * 997805; - s8 += s16 * 136657; - s9 -= s16 * 683901; - - s3 += s15 * 666643; - s4 += s15 * 470296; - s5 += s15 * 654183; - s6 -= s15 * 997805; - s7 += s15 * 136657; - s8 -= s15 * 683901; - - s2 += s14 * 666643; - s3 += s14 * 470296; - s4 += s14 * 654183; - s5 -= s14 * 997805; - s6 += s14 * 136657; - s7 -= s14 * 683901; - - s1 += s13 * 666643; - s2 += s13 * 470296; - s3 += s13 * 654183; - s4 -= s13 * 997805; - s5 += s13 * 136657; - s6 -= s13 * 683901; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - - -/* - * - * ge code - * - * -ge means group element. - -Here the group is the set of pairs (x,y) of field elements (see fe.h) -satisfying -x^2 + y^2 = 1 + d x^2y^2 -where d = -121665/121666. - -Representations: - ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z - ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT - ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T - ge_precomp (Duif): (y+x,y-x,2dxy) -*/ -/* -r = p + q -*/ -void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) -{ - fe t0; -fe_add(r->X,p->Y,p->X); -fe_sub(r->Y,p->Y,p->X); -fe_mul(r->Z,r->X,q->YplusX); -fe_mul(r->Y,r->Y,q->YminusX); -fe_mul(r->T,q->T2d,p->T); -fe_mul(r->X,p->Z,q->Z); -fe_add(t0,r->X,r->X); -fe_sub(r->X,r->Z,r->Y); -fe_add(r->Y,r->Z,r->Y); -fe_add(r->Z,t0,r->T); -fe_sub(r->T,t0,r->T); -} -static void slide(signed char *r,const unsigned char *a) -{ - int i; - int b; - int k; - for (i = 0;i < 256;++i) - r[i] = 1 & (a[i >> 3] >> (i & 7)); - for (i = 0;i < 256;++i) - if (r[i]) { - for (b = 1;b <= 6 && i + b < 256;++b) { - if (r[i + b]) { - if (r[i] + (r[i + b] << b) <= 15) { - r[i] += r[i + b] << b; r[i + b] = 0; - } else if (r[i] - (r[i + b] << b) >= -15) { - r[i] -= r[i + b] << b; - for (k = i + b;k < 256;++k) { - if (!r[k]) { - r[k] = 1; - break; - } - r[k] = 0; - } - } else - break; - } - } - } -} -static ge_precomp Bi[8] = { - { - { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, - { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, - { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, - }, - { - { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, - { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, - { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, - }, - { - { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, - { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, - { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, - }, - { - { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, - { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, - { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, - }, - { - { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 }, - { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 }, - { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 }, - }, - { - { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 }, - { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 }, - { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 }, - }, - { - { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 }, - { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 }, - { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 }, - }, - { - { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 }, - { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 }, - { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 }, - }, -} ; -/* -r = a * A + b * B -where a = a[0]+256*a[1]+...+256^31 a[31]. -and b = b[0]+256*b[1]+...+256^31 b[31]. -B is the Ed25519 base point (x,4/5) with x positive. -*/ -void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b) -{ - signed char aslide[256]; - signed char bslide[256]; - ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ - ge_p1p1 t; - ge_p3 u; - ge_p3 A2; - int i; - slide(aslide,a); - slide(bslide,b); - ge_p3_to_cached(&Ai[0],A); - ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); - ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); - ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); - ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); - ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); - ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); - ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); - ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); - ge_p2_0(r); - for (i = 255;i >= 0;--i) { - if (aslide[i] || bslide[i]) break; - } - for (;i >= 0;--i) { - ge_p2_dbl(&t,r); - if (aslide[i] > 0) { - ge_p1p1_to_p3(&u,&t); - ge_add(&t,&u,&Ai[aslide[i]/2]); - } else if (aslide[i] < 0) { - ge_p1p1_to_p3(&u,&t); - ge_sub(&t,&u,&Ai[(-aslide[i])/2]); - } - if (bslide[i] > 0) { - ge_p1p1_to_p3(&u,&t); - ge_madd(&t,&u,&Bi[bslide[i]/2]); - } else if (bslide[i] < 0) { - ge_p1p1_to_p3(&u,&t); - ge_msub(&t,&u,&Bi[(-bslide[i])/2]); - } - ge_p1p1_to_p2(r,&t); - } -} -static const fe d = { --10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116 -} ; -static const fe sqrtm1 = { --32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482 -} ; -int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s) -{ - fe u; - fe v; - fe v3; - fe vxx; - fe check; - fe_frombytes(h->Y,s); - fe_1(h->Z); - fe_sq(u,h->Y); - fe_mul(v,u,d); - fe_sub(u,u,h->Z); /* u = y^2-1 */ - fe_add(v,v,h->Z); /* v = dy^2+1 */ - fe_sq(v3,v); - fe_mul(v3,v3,v); /* v3 = v^3 */ - fe_sq(h->X,v3); - fe_mul(h->X,h->X,v); - fe_mul(h->X,h->X,u); /* x = uv^7 */ - fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */ - fe_mul(h->X,h->X,v3); - fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */ - fe_sq(vxx,h->X); - fe_mul(vxx,vxx,v); - fe_sub(check,vxx,u); /* vx^2-u */ - if (fe_isnonzero(check)) { - fe_add(check,vxx,u); /* vx^2+u */ - if (fe_isnonzero(check)) return -1; - fe_mul(h->X,h->X,sqrtm1); - } - if (fe_isnegative(h->X) == (s[31] >> 7)) - fe_neg(h->X,h->X); - fe_mul(h->T,h->X,h->Y); - return 0; -} -/* -r = p + q -*/ -void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) -{ - fe t0; -fe_add(r->X,p->Y,p->X); -fe_sub(r->Y,p->Y,p->X); -fe_mul(r->Z,r->X,q->yplusx); -fe_mul(r->Y,r->Y,q->yminusx); -fe_mul(r->T,q->xy2d,p->T); -fe_add(t0,p->Z,p->Z); -fe_sub(r->X,r->Z,r->Y); -fe_add(r->Y,r->Z,r->Y); -fe_add(r->Z,t0,r->T); -fe_sub(r->T,t0,r->T); -} -/* -r = p - q -*/ -void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q) -{ - fe t0; -fe_add(r->X,p->Y,p->X); -fe_sub(r->Y,p->Y,p->X); -fe_mul(r->Z,r->X,q->yminusx); -fe_mul(r->Y,r->Y,q->yplusx); -fe_mul(r->T,q->xy2d,p->T); -fe_add(t0,p->Z,p->Z); -fe_sub(r->X,r->Z,r->Y); -fe_add(r->Y,r->Z,r->Y); -fe_sub(r->Z,t0,r->T); -fe_add(r->T,t0,r->T); -} - -/* -r = p -*/ - -extern void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p) -{ - fe_mul(r->X,p->X,p->T); - fe_mul(r->Y,p->Y,p->Z); - fe_mul(r->Z,p->Z,p->T); -} - -/* -r = p -*/ - -extern void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p) -{ - fe_mul(r->X,p->X,p->T); - fe_mul(r->Y,p->Y,p->Z); - fe_mul(r->Z,p->Z,p->T); - fe_mul(r->T,p->X,p->Y); -} - -void ge_p2_0(ge_p2 *h) -{ - fe_0(h->X); - fe_1(h->Y); - fe_1(h->Z); -} -/* -r = 2 * p -*/ -void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) -{ - fe t0; -fe_sq(r->X,p->X); -fe_sq(r->Z,p->Y); -fe_sq2(r->T,p->Z); -fe_add(r->Y,p->X,p->Y); -fe_sq(t0,r->Y); -fe_add(r->Y,r->Z,r->X); -fe_sub(r->Z,r->Z,r->X); -fe_sub(r->X,t0,r->Y); -fe_sub(r->T,r->T,r->Z); -} - -void ge_p3_0(ge_p3 *h) -{ - fe_0(h->X); - fe_1(h->Y); - fe_1(h->Z); - fe_0(h->T); -} - -/* -r = 2 * p -*/ - -void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p) -{ - ge_p2 q; - ge_p3_to_p2(&q,p); - ge_p2_dbl(r,&q); -} -/* -r = p -*/ -static const fe d2 = { --21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199 -} ; -extern void ge_p3_to_cached(ge_cached *r,const ge_p3 *p) -{ - fe_add(r->YplusX,p->Y,p->X); - fe_sub(r->YminusX,p->Y,p->X); - fe_copy(r->Z,p->Z); - fe_mul(r->T2d,p->T,d2); -} - -/* -r = p -*/ - -extern void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p) -{ - fe_copy(r->X,p->X); - fe_copy(r->Y,p->Y); - fe_copy(r->Z,p->Z); -} - -void ge_p3_tobytes(unsigned char *s,const ge_p3 *h) -{ - fe recip; - fe x; - fe y; - - fe_invert(recip,h->Z); - fe_mul(x,h->X,recip); - fe_mul(y,h->Y,recip); - fe_tobytes(s,y); - s[31] ^= fe_isnegative(x) << 7; -} - -void ge_precomp_0(ge_precomp *h) -{ - fe_1(h->yplusx); - fe_1(h->yminusx); - fe_0(h->xy2d); -} -static unsigned char equal(signed char b,signed char c) -{ - unsigned char ub = b; - unsigned char uc = c; - unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ - uint32_t y = x; /* 0: yes; 1..255: no */ - y -= 1; /* 4294967295: yes; 0..254: no */ - y >>= 31; /* 1: yes; 0: no */ - return y; -} -static unsigned char negative(signed char b) -{ - unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ - x >>= 63; /* 1: yes; 0: no */ - return x; -} -static void ge_precomp_cmov(ge_precomp *t,ge_precomp *u,unsigned char b) -{ - fe_cmov(t->yplusx,u->yplusx,b); - fe_cmov(t->yminusx,u->yminusx,b); - fe_cmov(t->xy2d,u->xy2d,b); -} -/* base[i][j] = (j+1)*256^i*B */ -static ge_precomp base[32][8] = { -{ - { - { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 }, - { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 }, - { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 }, - }, - { - { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 }, - { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 }, - { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 }, - }, - { - { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 }, - { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 }, - { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 }, - }, - { - { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 }, - { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 }, - { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 }, - }, - { - { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 }, - { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 }, - { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 }, - }, - { - { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 }, - { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 }, - { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 }, - }, - { - { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 }, - { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 }, - { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 }, - }, - { - { 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 }, - { -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 }, - { 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 }, - }, -}, -{ - { - { -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 }, - { 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 }, - { 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 }, - }, - { - { -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 }, - { 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 }, - { 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 }, - }, - { - { -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 }, - { 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 }, - { 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 }, - }, - { - { -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 }, - { -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 }, - { -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 }, - }, - { - { 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 }, - { 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 }, - { 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 }, - }, - { - { -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 }, - { -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 }, - { -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 }, - }, - { - { 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 }, - { -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 }, - { -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 }, - }, - { - { 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 }, - { 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 }, - { 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 }, - }, -}, -{ - { - { 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 }, - { 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 }, - { -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 }, - }, - { - { 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 }, - { -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 }, - { -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 }, - }, - { - { -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 }, - { 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 }, - { 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 }, - }, - { - { -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 }, - { 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 }, - { 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 }, - 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{ -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 }, - }, -}, -} ; -static void select(ge_precomp *t,int pos,signed char b) -{ - ge_precomp minust; - unsigned char bnegative = negative(b); - unsigned char babs = b - (((-bnegative) & b) << 1); - ge_precomp_0(t); - ge_precomp_cmov(t,&base[pos][0],equal(babs,1)); - ge_precomp_cmov(t,&base[pos][1],equal(babs,2)); - ge_precomp_cmov(t,&base[pos][2],equal(babs,3)); - ge_precomp_cmov(t,&base[pos][3],equal(babs,4)); - ge_precomp_cmov(t,&base[pos][4],equal(babs,5)); - ge_precomp_cmov(t,&base[pos][5],equal(babs,6)); - ge_precomp_cmov(t,&base[pos][6],equal(babs,7)); - ge_precomp_cmov(t,&base[pos][7],equal(babs,8)); - fe_copy(minust.yplusx,t->yminusx); - fe_copy(minust.yminusx,t->yplusx); - fe_neg(minust.xy2d,t->xy2d); - ge_precomp_cmov(t,&minust,bnegative); -} -/* -h = a * B -where a = a[0]+256*a[1]+...+256^31 a[31] -B is the Ed25519 base point (x,4/5) with x positive. -Preconditions: - a[31] <= 127 -*/ -void ge_scalarmult_base(ge_p3 *h,const unsigned char *a) -{ - signed char e[64]; - signed char carry; - ge_p1p1 r; - ge_p2 s; - ge_precomp t; - int i; - for (i = 0;i < 32;++i) { - e[2 * i + 0] = (a[i] >> 0) & 15; - e[2 * i + 1] = (a[i] >> 4) & 15; - } - /* each e[i] is between 0 and 15 */ - /* e[63] is between 0 and 7 */ - carry = 0; - for (i = 0;i < 63;++i) { - e[i] += carry; - carry = e[i] + 8; - carry >>= 4; - e[i] -= carry << 4; - } - e[63] += carry; - /* each e[i] is between -8 and 8 */ - ge_p3_0(h); - for (i = 1;i < 64;i += 2) { - select(&t,i / 2,e[i]); - ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); - } - ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r); - ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); - ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); - ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r); - for (i = 0;i < 64;i += 2) { - select(&t,i / 2,e[i]); - ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); - } -} -/* -r = p - q -*/ -void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q) -{ - fe t0; -fe_add(r->X,p->Y,p->X); -fe_sub(r->Y,p->Y,p->X); -fe_mul(r->Z,r->X,q->YminusX); -fe_mul(r->Y,r->Y,q->YplusX); -fe_mul(r->T,q->T2d,p->T); -fe_mul(r->X,p->Z,q->Z); -fe_add(t0,r->X,r->X); -fe_sub(r->X,r->Z,r->Y); -fe_add(r->Y,r->Z,r->Y); -fe_sub(r->Z,t0,r->T); -fe_add(r->T,t0,r->T); -} - -void ge_tobytes(unsigned char *s,const ge_p2 *h) -{ - fe recip; - fe x; - fe y; - - fe_invert(recip,h->Z); - fe_mul(x,h->X,recip); - fe_mul(y,h->Y,recip); - fe_tobytes(s,y); - s[31] ^= fe_isnegative(x) << 7; -} -/* - * - * xmr specific code - * - * -This code is from the original CryptoNote. -Some additional functions were needed to compute ring signatures -which are not needed for signing. -Note that sc_sub and sc_mulsub have been given their own file -since these have been rewritten - -*/ -/*Code inherited from the original cryptonote (I didn't write these) */ -/*These functions either don't exist in, or are modified from ref10*/ - - -/* From fe_isnonzero.c, modified */ - -//x -static int fe_isnonzero(const fe f) { - unsigned char s[32]; - fe_tobytes(s, f); - return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | - s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | - s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | - s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; -} - -//double scalar mult precomp -void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) { - ge_p1p1 t; - ge_p3 s2, u; - ge_p3_to_cached(&r[0], s); - ge_p3_dbl(&t, s); ge_p1p1_to_p3(&s2, &t); - ge_add(&t, &s2, &r[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[1], &u); - ge_add(&t, &s2, &r[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[2], &u); - ge_add(&t, &s2, &r[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[3], &u); - ge_add(&t, &s2, &r[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[4], &u); - ge_add(&t, &s2, &r[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[5], &u); - ge_add(&t, &s2, &r[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[6], &u); - ge_add(&t, &s2, &r[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[7], &u); -} - -/* -r = a * A + b * B -where a = a[0]+256*a[1]+...+256^31 a[31]. -and b = b[0]+256*b[1]+...+256^31 b[31]. -B is the Ed25519 base point (x,4/5) with x positive. -*/ - -void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { - signed char aslide[256]; - signed char bslide[256]; - ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ - ge_p1p1 t; - ge_p3 u; - int i; - - slide(aslide, a); - slide(bslide, b); - ge_dsm_precomp(Ai, A);/* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ - - ge_p2_0(r); - - for (i = 255; i >= 0; --i) { - //so this gets us to the highest i such that both have a nonzero - if (aslide[i] || bslide[i]) break; - } - - for (; i >= 0; --i) { - ge_p2_dbl(&t, r);//simple double and add - - if (aslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_add(&t, &u, &Ai[aslide[i]/2]); - } else if (aslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_sub(&t, &u, &Ai[(-aslide[i])/2]); - } - - if (bslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_madd(&t, &u, &ge_Bi[bslide[i]/2]); - } else if (bslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]); - } - - ge_p1p1_to_p2(r, &t); - } -} - - -/* From ge_frombytes.c, modified */ -//this is like xrecover .. -//x -int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) { - fe u; - fe v; - fe vxx; - fe check; - - /* From fe_frombytes.c */ - - int64_t h0 = load_4(s); - int64_t h1 = load_3(s + 4) << 6; - int64_t h2 = load_3(s + 7) << 5; - int64_t h3 = load_3(s + 10) << 3; - int64_t h4 = load_3(s + 13) << 2; - int64_t h5 = load_4(s + 16); - int64_t h6 = load_3(s + 20) << 7; - int64_t h7 = load_3(s + 23) << 5; - int64_t h8 = load_3(s + 26) << 4; - int64_t h9 = (load_3(s + 29) & 8388607) << 2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - /* Validate the number to be canonical */ - if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 && - h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 && - h1 == 1073741760 && h0 >= 4294967277) { - return -1; - } - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - - h->Y[0] = h0; - h->Y[1] = h1; - h->Y[2] = h2; - h->Y[3] = h3; - h->Y[4] = h4; - h->Y[5] = h5; - h->Y[6] = h6; - h->Y[7] = h7; - h->Y[8] = h8; - h->Y[9] = h9; - - /* End fe_frombytes.c */ - - fe_1(h->Z); - fe_sq(u, h->Y); - fe_mul(v, u, fe_d); - fe_sub(u, u, h->Z); /* u = y^2-1 */ - fe_add(v, v, h->Z); /* v = dy^2+1 */ - - fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */ - - fe_sq(vxx, h->X); - fe_mul(vxx, vxx, v); - fe_sub(check, vxx, u); /* vx^2-u */ - if (fe_isnonzero(check)) { - fe_add(check, vxx, u); /* vx^2+u */ - if (fe_isnonzero(check)) { - return -1; - } - fe_mul(h->X, h->X, fe_sqrtm1); //this is mapping X to X * sqrt(-1) c.f. 3.1 in hisil, dong, etc. - } - - if (fe_isnegative(h->X) != (s[31] >> 7)) { - /* If x = 0, the sign must be positive */ - if (!fe_isnonzero(h->X)) { - return -1; - } - fe_neg(h->X, h->X); - } - - fe_mul(h->T, h->X, h->Y); - return 0; -} - -/* New code */ -/* (u / v)^(m + 1) */ -static void fe_divpowm1(fe r, const fe u, const fe v) { - fe v3, uv7, t0, t1, t2; - int i; - - fe_sq(v3, v); - fe_mul(v3, v3, v); /* v3 = v^3 */ - fe_sq(uv7, v3); - fe_mul(uv7, uv7, v); - fe_mul(uv7, uv7, u); /* uv7 = uv^7 */ - - /*fe_pow22523(uv7, uv7);*/ - - /* From fe_pow22523.c */ - - fe_sq(t0, uv7); - fe_sq(t1, t0); - fe_sq(t1, t1); - fe_mul(t1, uv7, t1); - fe_mul(t0, t0, t1); - fe_sq(t0, t0); - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 0; i < 4; ++i) { - fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 0; i < 9; ++i) { - fe_sq(t1, t1); - } - fe_mul(t1, t1, t0); - fe_sq(t2, t1); - for (i = 0; i < 19; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - for (i = 0; i < 10; ++i) { - fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t1, t0); - for (i = 0; i < 49; ++i) { - fe_sq(t1, t1); - } - fe_mul(t1, t1, t0); - fe_sq(t2, t1); - for (i = 0; i < 99; ++i) { - fe_sq(t2, t2); - } - fe_mul(t1, t2, t1); - for (i = 0; i < 50; ++i) { - fe_sq(t1, t1); - } - fe_mul(t0, t1, t0); - fe_sq(t0, t0); - fe_sq(t0, t0); - fe_mul(t0, t0, uv7); - - /* End fe_pow22523.c */ - /* t0 = (uv^7)^((q-5)/8) */ - fe_mul(t0, t0, v3); - fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */ -} - -static void ge_cached_0(ge_cached *r) { - fe_1(r->YplusX); - fe_1(r->YminusX); - fe_1(r->Z); - fe_0(r->T2d); -} - -static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char b) { - fe_cmov(t->YplusX, u->YplusX, b); - fe_cmov(t->YminusX, u->YminusX, b); - fe_cmov(t->Z, u->Z, b); - fe_cmov(t->T2d, u->T2d, b); -} - -/* Assumes that a[31] <= 127 */ -void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) { - signed char e[64]; - int carry, carry2, i; - ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */ - ge_p1p1 t; - ge_p3 u; - - carry = 0; /* 0..1 */ - for (i = 0; i < 31; i++) { - carry += a[i]; /* 0..256 */ - carry2 = (carry + 8) >> 4; /* 0..16 */ - e[2 * i] = carry - (carry2 << 4); /* -8..7 */ - carry = (carry2 + 8) >> 4; /* 0..1 */ - e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */ - } - carry += a[31]; /* 0..128 */ - carry2 = (carry + 8) >> 4; /* 0..8 */ - e[62] = carry - (carry2 << 4); /* -8..7 */ - e[63] = carry2; /* 0..8 */ - - ge_p3_to_cached(&Ai[0], A); - for (i = 0; i < 7; i++) { - ge_add(&t, A, &Ai[i]); - ge_p1p1_to_p3(&u, &t); - ge_p3_to_cached(&Ai[i + 1], &u); - } - - ge_p2_0(r); - for (i = 63; i >= 0; i--) { - signed char b = e[i]; - unsigned char bnegative = negative(b); - unsigned char babs = b - (((-bnegative) & b) << 1); - ge_cached cur, minuscur; - ge_p2_dbl(&t, r); - ge_p1p1_to_p2(r, &t); - ge_p2_dbl(&t, r); - ge_p1p1_to_p2(r, &t); - ge_p2_dbl(&t, r); - ge_p1p1_to_p2(r, &t); - ge_p2_dbl(&t, r); - ge_p1p1_to_p3(&u, &t); - ge_cached_0(&cur); - ge_cached_cmov(&cur, &Ai[0], equal(babs, 1)); - ge_cached_cmov(&cur, &Ai[1], equal(babs, 2)); - ge_cached_cmov(&cur, &Ai[2], equal(babs, 3)); - ge_cached_cmov(&cur, &Ai[3], equal(babs, 4)); - ge_cached_cmov(&cur, &Ai[4], equal(babs, 5)); - ge_cached_cmov(&cur, &Ai[5], equal(babs, 6)); - ge_cached_cmov(&cur, &Ai[6], equal(babs, 7)); - ge_cached_cmov(&cur, &Ai[7], equal(babs, 8)); - fe_copy(minuscur.YplusX, cur.YminusX); - fe_copy(minuscur.YminusX, cur.YplusX); - fe_copy(minuscur.Z, cur.Z); - fe_neg(minuscur.T2d, cur.T2d); - ge_cached_cmov(&cur, &minuscur, bnegative); - ge_add(&t, &u, &cur); - ge_p1p1_to_p2(r, &t); - } -} - -//assume Bi has precomputed multiples -void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bii) { - signed char aslide[256]; - signed char bslide[256]; - ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ //precomps - ge_p1p1 t; - ge_p3 u; - int i; - - slide(aslide, a); - slide(bslide, b); - ge_dsm_precomp(Ai, A); - - ge_p2_0(r); - - for (i = 255; i >= 0; --i) { - if (aslide[i] || bslide[i]) break; - } - - for (; i >= 0; --i) { - ge_p2_dbl(&t, r); - - if (aslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_add(&t, &u, &Ai[aslide[i]/2]); - } else if (aslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_sub(&t, &u, &Ai[(-aslide[i])/2]); - } - - if (bslide[i] > 0) { - ge_p1p1_to_p3(&u, &t); - ge_add(&t, &u, &Bii[bslide[i]/2]); - } else if (bslide[i] < 0) { - ge_p1p1_to_p3(&u, &t); - ge_sub(&t, &u, &Bii[(-bslide[i])/2]); - } - - ge_p1p1_to_p2(r, &t); - } -} - -//x -void ge_mul8(ge_p1p1 *r, const ge_p2 *t) { - ge_p2 u; - ge_p2_dbl(r, t); - ge_p1p1_to_p2(&u, r); - ge_p2_dbl(r, &u); - ge_p1p1_to_p2(&u, r); - ge_p2_dbl(r, &u); -} - -//x -void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) { - fe u, v, w, x, y, z; - unsigned char sign; - - /* From fe_frombytes.c */ - - int64_t h0 = load_4(s); - int64_t h1 = load_3(s + 4) << 6; - int64_t h2 = load_3(s + 7) << 5; - int64_t h3 = load_3(s + 10) << 3; - int64_t h4 = load_3(s + 13) << 2; - int64_t h5 = load_4(s + 16); - int64_t h6 = load_3(s + 20) << 7; - int64_t h7 = load_3(s + 23) << 5; - int64_t h8 = load_3(s + 26) << 4; - int64_t h9 = load_3(s + 29) << 2; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - - carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; - carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; - carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; - carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; - carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; - - carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; - carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; - carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; - carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; - carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; - - u[0] = h0; - u[1] = h1; - u[2] = h2; - u[3] = h3; - u[4] = h4; - u[5] = h5; - u[6] = h6; - u[7] = h7; - u[8] = h8; - u[9] = h9; - - /* End fe_frombytes.c */ - - fe_sq2(v, u); /* 2 * u^2 */ - fe_1(w); - fe_add(w, v, w); /* w = 2 * u^2 + 1 */ - fe_sq(x, w); /* w^2 */ - fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */ - fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */ - fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */ - fe_sq(y, r->X); - fe_mul(x, y, x); - fe_sub(y, w, x); - fe_copy(z, fe_ma); - if (fe_isnonzero(y)) { - fe_add(y, w, x); - if (fe_isnonzero(y)) { - goto negative; - } else { - fe_mul(r->X, r->X, fe_fffb1); - } - } else { - fe_mul(r->X, r->X, fe_fffb2); - } - fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */ - fe_mul(z, z, v); /* -2 * A * u^2 */ - sign = 0; - goto setsign; -negative: - fe_mul(x, x, fe_sqrtm1); - fe_sub(y, w, x); - if (fe_isnonzero(y)) { - assert((fe_add(y, w, x), !fe_isnonzero(y))); - fe_mul(r->X, r->X, fe_fffb3); - } else { - fe_mul(r->X, r->X, fe_fffb4); - } - /* r->X = sqrt(A * (A + 2) * w / x) */ - /* z = -A */ - sign = 1; -setsign: - if (fe_isnegative(r->X) != sign) { - assert(fe_isnonzero(r->X)); - fe_neg(r->X, r->X); - } - fe_add(r->Z, z, w); - fe_sub(r->Y, z, w); - fe_mul(r->X, r->X, r->Z); -#if !defined(NDEBUG) - { - fe check_x, check_y, check_iz, check_v; - fe_invert(check_iz, r->Z); - fe_mul(check_x, r->X, check_iz); - fe_mul(check_y, r->Y, check_iz); - fe_sq(check_x, check_x); - fe_sq(check_y, check_y); - fe_mul(check_v, check_x, check_y); - fe_mul(check_v, fe_d, check_v); - fe_add(check_v, check_v, check_x); - fe_sub(check_v, check_v, check_y); - fe_1(check_x); - fe_add(check_v, check_v, check_x); - assert(!fe_isnonzero(check_v)); - } -#endif -} - -//x -void sc_0(unsigned char *s) { - int i; - for (i = 0; i < 32; i++) { - s[i] = 0; - } -} - -//x -void sc_reduce32(unsigned char *s) { - int64_t s0 = 2097151 & load_3(s); - int64_t s1 = 2097151 & (load_4(s + 2) >> 5); - int64_t s2 = 2097151 & (load_3(s + 5) >> 2); - int64_t s3 = 2097151 & (load_4(s + 7) >> 7); - int64_t s4 = 2097151 & (load_4(s + 10) >> 4); - int64_t s5 = 2097151 & (load_3(s + 13) >> 1); - int64_t s6 = 2097151 & (load_4(s + 15) >> 6); - int64_t s7 = 2097151 & (load_3(s + 18) >> 3); - int64_t s8 = 2097151 & load_3(s + 21); - int64_t s9 = 2097151 & (load_4(s + 23) >> 5); - int64_t s10 = 2097151 & (load_3(s + 26) >> 2); - int64_t s11 = (load_4(s + 28) >> 7); - int64_t s12 = 0; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - -//x -void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) { - int64_t a0 = 2097151 & load_3(a); - int64_t a1 = 2097151 & (load_4(a + 2) >> 5); - int64_t a2 = 2097151 & (load_3(a + 5) >> 2); - int64_t a3 = 2097151 & (load_4(a + 7) >> 7); - int64_t a4 = 2097151 & (load_4(a + 10) >> 4); - int64_t a5 = 2097151 & (load_3(a + 13) >> 1); - int64_t a6 = 2097151 & (load_4(a + 15) >> 6); - int64_t a7 = 2097151 & (load_3(a + 18) >> 3); - int64_t a8 = 2097151 & load_3(a + 21); - int64_t a9 = 2097151 & (load_4(a + 23) >> 5); - int64_t a10 = 2097151 & (load_3(a + 26) >> 2); - int64_t a11 = (load_4(a + 28) >> 7); - int64_t b0 = 2097151 & load_3(b); - int64_t b1 = 2097151 & (load_4(b + 2) >> 5); - int64_t b2 = 2097151 & (load_3(b + 5) >> 2); - int64_t b3 = 2097151 & (load_4(b + 7) >> 7); - int64_t b4 = 2097151 & (load_4(b + 10) >> 4); - int64_t b5 = 2097151 & (load_3(b + 13) >> 1); - int64_t b6 = 2097151 & (load_4(b + 15) >> 6); - int64_t b7 = 2097151 & (load_3(b + 18) >> 3); - int64_t b8 = 2097151 & load_3(b + 21); - int64_t b9 = 2097151 & (load_4(b + 23) >> 5); - int64_t b10 = 2097151 & (load_3(b + 26) >> 2); - int64_t b11 = (load_4(b + 28) >> 7); - int64_t s0 = a0 + b0; - int64_t s1 = a1 + b1; - int64_t s2 = a2 + b2; - int64_t s3 = a3 + b3; - int64_t s4 = a4 + b4; - int64_t s5 = a5 + b5; - int64_t s6 = a6 + b6; - int64_t s7 = a7 + b7; - int64_t s8 = a8 + b8; - int64_t s9 = a9 + b9; - int64_t s10 = a10 + b10; - int64_t s11 = a11 + b11; - int64_t s12 = 0; - int64_t carry0; - int64_t carry1; - int64_t carry2; - int64_t carry3; - int64_t carry4; - int64_t carry5; - int64_t carry6; - int64_t carry7; - int64_t carry8; - int64_t carry9; - int64_t carry10; - int64_t carry11; - - carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; - carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; - carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; - carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; - carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; - - carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; - carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; - carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; - carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; - carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; - carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; - - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; - carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; - carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; - carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; - carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; - carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; - carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; - carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; - carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; - carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; - carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; - - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); - s[3] = s1 >> 3; - s[4] = s1 >> 11; - s[5] = (s1 >> 19) | (s2 << 2); - s[6] = s2 >> 6; - s[7] = (s2 >> 14) | (s3 << 7); - s[8] = s3 >> 1; - s[9] = s3 >> 9; - s[10] = (s3 >> 17) | (s4 << 4); - s[11] = s4 >> 4; - s[12] = s4 >> 12; - s[13] = (s4 >> 20) | (s5 << 1); - s[14] = s5 >> 7; - s[15] = (s5 >> 15) | (s6 << 6); - s[16] = s6 >> 2; - s[17] = s6 >> 10; - s[18] = (s6 >> 18) | (s7 << 3); - s[19] = s7 >> 5; - s[20] = s7 >> 13; - s[21] = s8 >> 0; - s[22] = s8 >> 8; - s[23] = (s8 >> 16) | (s9 << 5); - s[24] = s9 >> 3; - s[25] = s9 >> 11; - s[26] = (s9 >> 19) | (s10 << 2); - s[27] = s10 >> 6; - s[28] = (s10 >> 14) | (s11 << 7); - s[29] = s11 >> 1; - s[30] = s11 >> 9; - s[31] = s11 >> 17; -} - -/* Assumes that a != INT64_MIN */ -//x c.f. lt in 32 bit ref -static int64_t signum(int64_t a) { - return (a >> 63) - ((-a) >> 63); -} - -//x -int sc_check(const unsigned char *s) { - int64_t s0 = load_4(s); - int64_t s1 = load_4(s + 4); - int64_t s2 = load_4(s + 8); - int64_t s3 = load_4(s + 12); - int64_t s4 = load_4(s + 16); - int64_t s5 = load_4(s + 20); - int64_t s6 = load_4(s + 24); - int64_t s7 = load_4(s + 28); - return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8; -} - -//x -int sc_isnonzero(const unsigned char *s) { - return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | - s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | - s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | - s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; -}