From 559aa2a62b84c8bcde8b74a6b96d915615aa8385 Mon Sep 17 00:00:00 2001 From: Russell O'Connor Date: Mon, 28 Jun 2021 16:33:03 -0400 Subject: [PATCH] Generate ecmult_static_pre_g.h This header contains a static array that replaces the ecmult_context pre_g and pre_g_128 tables. The gen_ecmult_static_pre_g program generates this header file. --- .gitattributes | 1 + .gitignore | 1 + Makefile.am | 11 +- src/ecmult.h | 18 + src/ecmult_impl.h | 18 +- src/ecmult_static_pre_g.h | 16608 ++++++++++++++++++++++++++++++++ src/gen_ecmult_static_pre_g.c | 246 + src/group_impl.h | 47 +- 8 files changed, 16911 insertions(+), 39 deletions(-) create mode 100644 .gitattributes create mode 100644 src/ecmult_static_pre_g.h create mode 100644 src/gen_ecmult_static_pre_g.c diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000000..9cf2163c39 --- /dev/null +++ b/.gitattributes @@ -0,0 +1 @@ +src/ecmult_static_pre_g.h linguist-generated diff --git a/.gitignore b/.gitignore index 79b740db8a..9e187a34a9 100644 --- a/.gitignore +++ b/.gitignore @@ -9,6 +9,7 @@ bench_internal tests exhaustive_tests gen_context +gen_ecmult_static_pre_g valgrind_ctime_test *.exe *.so diff --git a/Makefile.am b/Makefile.am index 1e03560884..d8b21de4fb 100644 --- a/Makefile.am +++ b/Makefile.am @@ -127,12 +127,19 @@ exhaustive_tests_LDFLAGS = -static TESTS += exhaustive_tests endif +EXTRA_PROGRAMS = gen_ecmult_static_pre_g +gen_ecmult_static_pre_g_SOURCES = src/gen_ecmult_static_pre_g.c +# See Automake manual, Section "Errors with distclean" +src/ecmult_static_pre_g.h: + $(MAKE) $(AM_MAKEFLAGS) gen_ecmult_static_pre_g$(EXEEXT) + ./gen_ecmult_static_pre_g$(EXEEXT) + if USE_ECMULT_STATIC_PRECOMPUTATION CPPFLAGS_FOR_BUILD +=-I$(top_srcdir) -I$(builddir)/src gen_context_OBJECTS = gen_context.o gen_context_BIN = gen_context$(BUILD_EXEEXT) -gen_%.o: src/gen_%.c src/libsecp256k1-config.h +$(gen_context_OBJECTS): src/gen_context.c src/libsecp256k1-config.h $(CC_FOR_BUILD) $(DEFS) $(CPPFLAGS_FOR_BUILD) $(SECP_CFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@ $(gen_context_BIN): $(gen_context_OBJECTS) @@ -149,7 +156,7 @@ src/ecmult_static_context.h: $(gen_context_BIN) CLEANFILES = $(gen_context_BIN) src/ecmult_static_context.h endif -EXTRA_DIST = autogen.sh src/gen_context.c src/basic-config.h +EXTRA_DIST = autogen.sh src/gen_context.c src/ecmult_static_pre_g.h src/basic-config.h if ENABLE_MODULE_ECDH include src/modules/ecdh/Makefile.am.include diff --git a/src/ecmult.h b/src/ecmult.h index 7ab617e20e..54257c900f 100644 --- a/src/ecmult.h +++ b/src/ecmult.h @@ -11,6 +11,24 @@ #include "scalar.h" #include "scratch.h" +/* Noone will ever need more than a window size of 24. The code might + * be correct for larger values of ECMULT_WINDOW_SIZE but this is not + * not tested. + * + * The following limitations are known, and there are probably more: + * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect + * because the size of the memory object that we allocate (in bytes) + * will not fit in a size_t. + * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect + * because certain expressions will overflow. + */ +#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24 +# error Set ECMULT_WINDOW_SIZE to an integer in range [2..24]. +#endif + +/** The number of entries a table with precomputed multiples needs to have. */ +#define ECMULT_TABLE_SIZE(w) (1L << ((w)-2)) + typedef struct { /* For accelerating the computation of a*P + b*G: */ secp256k1_ge_storage (*pre_g)[]; /* odd multiples of the generator */ diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index 5c2edac68f..ca15a14381 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -44,28 +44,14 @@ # define WINDOW_G ECMULT_WINDOW_SIZE #endif -/* Noone will ever need more than a window size of 24. The code might - * be correct for larger values of ECMULT_WINDOW_SIZE but this is not - * not tested. - * - * The following limitations are known, and there are probably more: - * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect - * because the size of the memory object that we allocate (in bytes) - * will not fit in a size_t. - * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect - * because certain expressions will overflow. - */ -#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24 -# error Set ECMULT_WINDOW_SIZE to an integer in range [2..24]. +#if ECMULT_WINDOW_SIZE < WINDOW_G +# error ECMULT_WINDOW_SIZE to small for WINDOW_G. #endif #define WNAF_BITS 128 #define WNAF_SIZE_BITS(bits, w) (((bits) + (w) - 1) / (w)) #define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w) -/** The number of entries a table with precomputed multiples needs to have. */ -#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2)) - /* The number of objects allocated on the scratch space for ecmult_multi algorithms */ #define PIPPENGER_SCRATCH_OBJECTS 6 #define STRAUSS_SCRATCH_OBJECTS 6 diff --git a/src/ecmult_static_pre_g.h b/src/ecmult_static_pre_g.h new file mode 100644 index 0000000000..f6e993a573 --- /dev/null +++ b/src/ecmult_static_pre_g.h @@ -0,0 +1,16608 @@ +/* This file was automatically generated by gen_ecmult_static_pre_g. */ +#ifndef SECP256K1_ECMULT_STATIC_PRE_G_H +#define SECP256K1_ECMULT_STATIC_PRE_G_H +#include "src/group.h" +#ifdef S + #error macro identifier S already in use. +#endif +#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) +#if ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE) > 8192 + #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting ecmult_static_pre_g.h before the build. +#endif +#if defined(EXHAUSTIVE_TEST_ORDER) +#if EXHAUSTIVE_TEST_ORDER == 13 +#define WINDOW_G 4 +static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(c3459c3d,35326167,cd86cce8,7a2417f,5b8bd567,de8538ee,d507b0c,d128f5bb,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) +,S(ae64a1bd,38872f22,f637b457,125cc859,e4c7a31b,cf553cf5,b96e7096,cc61cc10,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) +,S(851695d4,9a83f8ef,919bb861,53cbcb16,630fb68a,ed0a766a,3ec693d6,8e6afa40,3c915051,a5fb60b4,fec49de6,e4385101,59f30035,b6502bc0,f5edba86,9753a96c) +,S(0,0,0,0,0,0,0,1,c36eafae,5a049f4b,13b6219,1bc7aefe,a60cffca,49afd43f,a124578,68ac52c3) +}; +static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(8e55c205,92466f75,3c417ec0,e600f626,bfac877c,52258a1c,3941145a,62753693,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) +,S(c3459c3d,35326167,cd86cce8,7a2417f,5b8bd567,de8538ee,d507b0c,d128f5bb,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) +,S(0,0,0,0,0,0,0,1,3c915051,a5fb60b4,fec49de6,e4385101,59f30035,b6502bc0,f5edba86,9753a96c) +,S(7ae96a2b,657c0710,6e64479e,ac3434e9,9cf04975,12f58995,c1396c28,719501ee,c36eafae,5a049f4b,13b6219,1bc7aefe,a60cffca,49afd43f,a124578,68ac52c3) +}; +#elif EXHAUSTIVE_TEST_ORDER == 199 +#define WINDOW_G 8 +static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(226e653f,c8df7744,9bacbf12,7d1dcbf9,87f05b2a,e7edbd28,1f564575,c48dcf18,a13872c2,e933bb17,5d9ffd5b,b5b6e10c,57fe3c00,baaaa15a,e003ec3e,9c269bae) +,S(ff1755e,623c8369,f55edda4,2a5deef0,b32c57f4,80c5884f,d2a2dde1,b1c078c4,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) 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+,S(318f2c1f,3dc109ad,ed9d8958,e2e6eb8c,e26eec32,f2725ad1,68e116c7,497e7044,75b3371,ac71e480,9d8398ec,8376914e,3aab7ea6,bcb96a5,15c6b39b,a6d2ba60) +,S(bcea96e9,4ff1b11e,6e8a09d6,ec594b00,597e2b0a,37b0e581,50a58d59,33220419,7f0c4863,45a07ba8,c0d55b8c,fe2ef3e0,649abc1e,47313a1f,1763291f,79733985) +,S(4ed9d2a,7f32fa30,fd059de5,ee512073,47d68d12,b77df5b8,6a83a814,3fcdd5c0,5ec78d3d,16cc44e8,a26002a4,4a491ef3,a801c3ff,45555ea5,1ffc13c0,63d96081) +,S(875c93a1,8ac5a86e,9e85e4aa,3c5ad0ac,3d697192,6384b05b,568604b3,8fee8fb6,3738dc95,97add4e5,c0a39af1,b98ccba2,7bb43333,e35ab481,54c52779,9191144b) +,S(47a7cc2e,1cbd64c8,301443ed,be1ab328,85dce80e,a6d8c847,4eb9be09,6db5fecf,d160b834,5807531a,327a7269,3627dab6,f9770a12,14eb182d,fa73ad15,41b57ff0) +,S(3e8a6608,17f28243,f363d67e,b874856f,1fc9810a,9da6c3f3,a72dd23f,ec45513e,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) +,S(9556e393,974bcd02,c6356a53,fce819d4,887b188c,99b8de16,1e5d3697,d595cdce,23575727,9da3d12b,c0004d12,e06a9cda,8405c91e,b8118260,2793e62f,16c2a29e) +,S(5245e215,52c6f785,2cccef32,e9f54774,cfb6bb9b,c363ae72,71174df4,6d77fdcc,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) +,S(5d6f8ab3,ca0a5fca,611b7738,16adb4f8,df73ad68,5ce45286,75101d00,54ff3eca,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) +,S(a4465b18,b7f702e2,a8165184,834ce490,68fb0a51,6658734b,6229eda0,605911a2,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) +,S(d49b0640,1e240c43,21b2b173,3b640c6a,e2c4b389,2d3f4f73,8faac78b,9995cf2e,75b3371,ac71e480,9d8398ec,8376914e,3aab7ea6,bcb96a5,15c6b39b,a6d2ba60) +,S(599db82f,8229ad47,7a662726,d2d351a6,f76cefd7,8fc376b1,ef6e344e,4e4dae3a,284268b5,4bf5e42c,5ca5e116,e92cd897,b7184303,418f7ae2,7458a745,6692db96) +,S(a0627644,ebc6a423,1f3e113b,eedbf9d8,21d9374a,af2e7c55,14ee7395,aa9992b7,859f03d8,1b54f459,158e3fc9,ad47c3a3,a54a2537,15bc213d,7b8e6072,9283bfae) +}; +static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(ec823227,1d0e875a,8e1cf7e6,f9a35a15,749be650,1cc885c4,f383060b,46bd3d33,aa140b83,97ca0dcd,a15dcd4c,7509bb87,9a34231e,d0d3a586,543bba01,ae7545b8) +,S(66abbf18,f58dd1c9,4b6072c,eb182abe,c31d3af9,6d91060b,d233f462,5716f289,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) +,S(4d756b2,e61d9806,e02ec830,f1fd44f8,46438689,c528346,15a1addf,ac864bcd,36f8fb36,708d2741,9c75c923,178976f6,5386de3,23ab2ceb,f76044c0,9256faa5) +,S(875c93a1,8ac5a86e,9e85e4aa,3c5ad0ac,3d697192,6384b05b,568604b3,8fee8fb6,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) +,S(f3a864ac,edc7852f,f4dfae93,5f8588a6,96ff17bf,7233134e,6704ceb,16f3b74c,39cfeb15,665f371f,535d56c1,317a8d62,29ea2827,943a98f1,cee7f685,86e47eec) +,S(3e8a6608,17f28243,f363d67e,b874856f,1fc9810a,9da6c3f3,a72dd23f,ec45513e,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) +,S(47bbafcd,f612ca3e,703f7721,623bde14,926fc00d,a6bf9e9,41ddb2d5,587626e3,d160b834,5807531a,327a7269,3627dab6,f9770a12,14eb182d,fa73ad15,41b57ff0) +,S(709c8403,ed2fd0f9,5fac44f0,dfa96ec2,e7b357e4,4ebb3dcf,6f688f20,39d3d67d,2e9f47cb,a7f8ace5,cd858d96,c9d82549,688f5ed,eb14e7d2,58c52e9,be4a7c3f) +,S(66fd0ada,7159c2df,fdd925e7,2eb70772,743e39e3,4c10d5cf,f58eac4e,a30e4157,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) +,S(60d5d771,4e1e7589,e0b1e68c,ed7f881,73fca809,eae35685,65334942,79962dc2,99bb92f2,4fe59864,a6504cb5,d4407301,f5bb78f,f1f8b31,875ae5c8,644408f3) +,S(3d98fe85,5d42f661,e35d8ce3,cfee5f17,57bc3de9,ecec02fa,11a2d90,378ac0e8,bdc6dc52,8a55814e,da6bcb58,e2a73b96,9d975c7,a3270483,b419b29b,5263f45) +,S(2f63a396,4d14ca73,2167e033,306863d8,f75605c7,4ea6c917,890dd50d,fc20f53b,1dd6a38e,deb870ad,f2b2e755,8d327d51,e66a2c81,910d1fa5,b215911c,9c8e004c) +,S(bcea96e9,4ff1b11e,6e8a09d6,ec594b00,597e2b0a,37b0e581,50a58d59,33220419,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) +,S(ae3796a4,823f3eb4,ea4bd677,110dc3fb,45537c3c,4d10d2e8,e758a3be,4875db83,ef2b477b,a9c921df,5ff65b6e,7c6f96a8,627743ff,a53e3858,cd9d7673,f7435ac4) +,S(5245e215,52c6f785,2cccef32,e9f54774,cfb6bb9b,c363ae72,71174df4,6d77fdcc,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) +,S(26e2e75b,aeb04a72,8b893f67,d27ebfc6,b8984a88,6fbd8eee,5719107d,5a413f0f,61b51308,ac8643f0,7c18eda7,ef9a4196,aa66221,1b809acc,2b2cb538,23010ef8) +,S(e0089ec9,4b25ac6,ff44b5da,2dfedb37,9fdaedf1,6bc8cecd,b1a95fa0,32431c73,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) +,S(f8f16642,266d8dc6,abfdbbc6,f6c47711,a192c051,7f00a633,b78076a7,a7884e72,4f6d0e5,148ce7e1,772f84c,b08903b8,71d2beb5,d0934488,8ab1c75d,42232790) +,S(23082df9,a86b80fc,5185ee3c,6493763b,14a6e237,baf686aa,f589b649,8573d04c,bdc6dc52,8a55814e,da6bcb58,e2a73b96,9d975c7,a3270483,b419b29b,5263f45) +,S(76dac07e,bc240289,791e6a9a,56abdc7,bdf2fac1,e7a0100b,5a0ee09e,3455cc33,8b4502cd,420d4202,39a5ad3c,fa10b0b2,6ccd084d,5faed560,7de07a6,fb7b4093) +,S(8735fb32,6950ae71,31cd03f7,cc1511d8,65c87e84,748c9824,8ccc576e,5480ed8,c63014ea,99a0c8e0,aca2a93e,ce85729d,d615d7d8,6bc5670e,31180979,791b7d43) +,S(969360d2,54e2dba9,e79d0789,c339250d,c438330a,a66addf9,f27e2ee8,fc9036ac,66446d0d,b01a679b,59afb34a,2bbf8cfe,f0a44870,f0e074ce,78a51a36,9bbbf33c) +,S(74f5ba33,89d075d3,eebaa54d,73e9f038,881b7329,5623e833,b5e87beb,29ba3246,74bafd32,bdf2bdfd,c65a52c3,5ef4f4d,9332f7b2,a0512a9f,f821f858,484bb9c) +,S(a4465b18,b7f702e2,a8165184,834ce490,68fb0a51,6658734b,6229eda0,605911a2,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) +,S(eac612b0,84cb452a,35d49c60,c0d0c0bd,359eb909,68a80186,92a028f,ece4c331,23575727,9da3d12b,c0004d12,e06a9cda,8405c91e,b8118260,2793e62f,16c2a29e) +,S(f31a7dfe,4d2e4a98,aaf3dd70,25441c7a,2da056b0,db6795e8,3a39d76f,b316bd92,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) +,S(470ce05d,53f77ff0,c5ab8770,a4c11a3e,23f7d4fe,f5c0ab36,1b940a8a,6b8cf7b9,57d6adb1,5f0b1daa,1fce91d7,ccf75d45,9480b056,6f81ff8a,85612173,1cd8f2b8) +,S(d9fbce92,515652cf,3714f87b,e16e505,91a28eb4,1bf7053,2ab42ebd,be900212,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) +,S(1ea4ff3b,5a0a78a9,fda9d73a,ea5f0629,886b083a,6d3beea4,d6bc96e1,b50da944,9edf1300,7f2b7fb2,92301e8c,77ddb63e,5f2d23c4,315118c1,8b1b6273,86bba11a) +,S(3d303d12,f8eb67d0,ecaee514,bdd90e57,b58b6d6a,c896a26f,78c06103,52225b04,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) +,S(9fa3c7bd,6b8544f2,df48309,596ea267,8f8537e1,dc406ec7,cf2c67d1,ae5f1e8a,37d97203,d25d9c14,53827e27,9474afb2,92943df0,8ba1108a,43644c86,ee6c87e4) +,S(92906a31,52682000,a59736ed,ef48a7b0,c78d6a49,8727b3b,893d3478,de04ada5,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) +,S(599db82f,8229ad47,7a662726,d2d351a6,f76cefd7,8fc376b1,ef6e344e,4e4dae3a,284268b5,4bf5e42c,5ca5e116,e92cd897,b7184303,418f7ae2,7458a745,6692db96) +,S(ee534645,42ff07e2,8cf783ee,1da96e00,b81f531,9b9a4885,27f92302,acd12cac,c90704c9,8f72d8be,638a36dc,e8768909,fac7921c,dc54d314,89fbb3e,6da9018a) +,S(7fe309bb,e3e8edd3,3f5f94b,4247256e,41e62e69,fd9f2063,d878c6d6,3d85675f,dca8a8d8,625c2ed4,3fffb2ed,1f956325,7bfa36e1,47ee7d9f,d86c19cf,e93d5991) +,S(64eaaad1,9c7e9d01,5cc997ff,c2f23022,c59805d,48a48e1,970b8847,10211659,fb092f1a,eb73181e,f88d07b3,4f76fc47,8e2d414a,2f6cbb77,754e38a1,bddcd49f) +,S(59e10f43,eb4b2fb0,94f2f66d,1404dd08,ab9c2442,50bd16e0,21feb78f,e0380d01,e2295c71,21478f52,d4d18aa,72cd82ae,1995d37e,6ef2e05a,4dea6ee2,6371fbe3) +,S(c979de1c,1318f60f,a9929ff3,a6621b9,d15226e8,2883556e,36a5f77b,28e3b585,d7bd974a,b40a1bd3,a35a1ee9,16d32768,48e7bcfc,be70851d,8ba758b9,996d2099) +,S(64dd1439,5d19a544,a7a1e81b,b9d079b3,593e7022,6bcd444e,6dc8197a,1a6dc3e6,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) +,S(d8a3fd95,b7ed8e8a,674da307,94911393,303917c2,60944d1f,76261274,fba45757,a13872c2,e933bb17,5d9ffd5b,b5b6e10c,57fe3c00,baaaa15a,e003ec3e,9c269bae) +,S(acee4285,57fc32a1,d3d14199,30cadaf0,613a630a,7a7e8c14,d08d05df,19143c3a,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) +,S(5d771e5d,6dc6c87,5ede8bae,4b27a9d4,3c5f8da2,8e84f5c3,501299c8,db16484c,859f03d8,1b54f459,158e3fc9,ad47c3a3,a54a2537,15bc213d,7b8e6072,9283bfae) +,S(e8d3f45a,b5be455f,dc3c2270,34100ca2,b8d203e1,35a9ed3d,5c8b703c,ef4d9b48,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) +,S(9963e528,754cbba8,29622664,1aec11b0,3fba2739,40f61cbd,5d4c0478,5429f40,298f1c0e,f903dc7d,b940cdc0,ed8183eb,a891c59b,a2a3be25,bf0dd4d5,b03574c3) +,S(cbdb65,553cd5d8,ff61cf33,e53fdd9a,cf0ee159,c21dc578,be5bac2b,7973c229,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) +,S(5029bff6,d4c80347,738230c8,cb252906,471b5bc1,3d26a533,304f5f0d,808f756c,97682462,a5c276b7,1568f961,f218a99e,4e528b1b,d4e255b0,acc27744,98ec84fe) +,S(80c5672b,3f773975,b5829101,6fa9de9b,33863263,8a978db,934f04c1,3a909b85,55ebf47c,6835f232,5ea232b3,8af64478,65cbdce1,2f2c5a79,abc445fd,518ab677) +,S(226e653f,c8df7744,9bacbf12,7d1dcbf9,87f05b2a,e7edbd28,1f564575,c48dcf18,5ec78d3d,16cc44e8,a26002a4,4a491ef3,a801c3ff,45555ea5,1ffc13c0,63d96081) +,S(521e20fc,9c7c0514,47f31e74,5bb81662,dac66374,9b891a6f,d9681cb6,21e3155c,9e4aecf7,5379bc0f,83e71258,1065be69,f5599dde,e47f6533,d4d34ac6,dcfeed37) +,S(5472b5d0,4ba1ca80,236183b1,46e596e5,4b20b83b,248988c8,bbe8460e,3666f262,a829524e,a0f4e255,e0316e28,3308a2ba,6b7f4fa9,907e0075,7a9ede8b,e3270977) +,S(2ecd421e,47399e76,60d10143,1789a437,89b54d23,31d1cb78,49cabda2,bc5174f9,c8268dfc,2da263eb,ac7d81d8,6b8b504d,6d6bc20f,745eef75,bc9bb378,1193744b) +,S(4097892c,5478baea,62e8da20,6d17fcd8,b8eed45f,24fb7648,fe742508,8da60a4e,10d4b884,5636de20,a009a491,83906957,9d88bc00,5ac1c7a7,3262898b,8bca16b) +,S(eb5c4120,4917d176,6fea883b,e680dfd9,233d9654,97fac48b,76f5d0d4,7f6dbf73,6897db9d,5a3d8948,ea97069e,de75661,b1ad74e4,2b1daa4f,533d88ba,67137731) +,S(92b866ad,a37a3f2f,bc607717,96b2c74f,57dde74c,da8e015f,792df531,7eb21fa6,55ebf47c,6835f232,5ea232b3,8af64478,65cbdce1,2f2c5a79,abc445fd,518ab677) +,S(a78dab,f2f2ef7f,4d424752,aa1aeaf5,50bec241,bf9ad129,3b9fe680,32b6141b,9de02272,226d60c0,97e5907c,407f9e07,d4bc6959,a2079419,139a9578,4e48cb7f) +,S(b084fee5,5da62ee0,ebdebf3b,245e0d4e,def46aac,bfdc9f43,261d3e2b,eed946a0,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) +,S(ff1755e,623c8369,f55edda4,2a5deef0,b32c57f4,80c5884f,d2a2dde1,b1c078c4,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) +,S(2cdce338,ae1f5aa0,55c76cb5,acbd084e,3284bb5d,b8cf9b4a,141cc8ee,1aa61e59,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) +,S(3faf6744,2aebb675,c6b75911,e3d34f4c,a8f5b669,a4c438f2,2c163659,3e36c1ea,fc0b579e,cbaf2c74,7b5c792d,7b66abf2,dfb1a44d,2ed6a417,7e1fc6bd,a989b623) +,S(34772cad,ad5888f2,53a810b7,5b175b8d,e3a454e4,26a1b5a5,c003f222,8e7b45c0,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) +,S(853cffd4,4cb0a29e,390ad886,455566cc,2776ab74,55210e57,9bf1fcc0,c8d767ed,621fdd8d,dd929f3f,681a6f83,bf8061f8,2b4396a6,5df86be6,ec656a86,b1b730b0) +,S(1130e02f,29480660,b2cb4f68,81da3f2c,1bdaf64,8df3b6ce,1a333738,29e4165e,10d4b884,5636de20,a009a491,83906957,9d88bc00,5ac1c7a7,3262898b,8bca16b) +,S(a0627644,ebc6a423,1f3e113b,eedbf9d8,21d9374a,af2e7c55,14ee7395,aa9992b7,7a60fc27,e4ab0ba6,ea71c036,52b83c5c,5ab5dac8,ea43dec2,84719f8c,6d7c3c81) +,S(1e864d74,9e96a16a,c4299b88,226aaff9,9a45ab9c,203853ac,ea0378ef,5715ded6,6120ecff,80d4804d,6dcfe173,882249c1,a0d2dc3b,ceaee73e,74e49d8b,79445b15) +}; +#else + #error No known generator for the specified exhaustive test group order. +#endif +#else +#define WINDOW_G ECMULT_WINDOW_SIZE +static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(79be667e,f9dcbbac,55a06295,ce870b07,29bfcdb,2dce28d9,59f2815b,16f81798,483ada77,26a3c465,5da4fbfc,e1108a8,fd17b448,a6855419,9c47d08f,fb10d4b8) +#if ECMULT_TABLE_SIZE(WINDOW_G) > 1 +,S(f9308a01,9258c310,49344f85,f89d5229,b531c845,836f99b0,8601f113,bce036f9,388f7b0f,632de814,fe337e6,2a37f356,6500a999,34c2231b,6cb9fd75,84b8e672) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 2 +,S(2f8bde4d,1a072093,55b4a725,a5c5128,e88b84bd,dc619ab7,cba8d569,b240efe4,d8ac2226,36e5e3d6,d4dba9dd,a6c9c426,f788271b,ab0d6840,dca87d3a,a6ac62d6) +,S(5cbdf064,6e5db4ea,a398f365,f2ea7a0e,3d419b7e,330e39c,e92bdded,cac4f9bc,6aebca40,ba255960,a3178d6d,861a54db,a813d0b8,13fde7b5,a5082628,87264da) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 4 +,S(acd484e2,f0c7f653,9ad178a,9f559abd,e0979697,4c57e714,c35f110d,fc27ccbe,cc338921,b0a7d9fd,64380971,763b61e9,add888a4,375f8e0f,5cc262a,c64f9c37) +,S(774ae7f8,58a9411e,5ef4246b,70c65aac,5649980b,e5c17891,bbec1789,5da008cb,d984a032,eb6b5e19,243dd56,d7b7b365,372db1e2,dff9d6a8,301d74c9,c953c61b) +,S(f28773c2,d975288b,c7d1d205,c3748651,b075fbc6,610e58cd,deeddf8f,19405aa8,ab0902e,8d880a89,758212eb,65cdaf47,3a1a06da,521fa91f,29b5cb52,db03ed81) +,S(d7924d4f,7d43ea96,5a465ae3,95ff411,31e5946f,3c85f79e,44adbcf8,e27e080e,581e2872,a86c72a6,83842ec2,28cc6def,ea40af2b,d896d3a5,c504dc9f,f6a26b58) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 8 +,S(defdea4c,db677750,a420fee8,7eacf21,eb9898ae,79b97687,66e4faa0,4a2d4a34,4211ab06,94635168,e997b0ea,d2a93dae,ced1f4a0,4a95c0f6,cfb199f6,9e56eb77) +,S(2b4ea0a7,97a443d2,93ef5cff,444f4979,f06acfeb,d7e86d27,74756561,38385b6c,85e89bc0,37945d93,b343083b,5a1c8613,1a01f60c,50269763,b570c854,e5c09b7a) +,S(352bbf4a,4cdd1256,4f93fa33,2ce33330,1d9ad402,71f81071,81340aef,25be59d5,321eb407,5348f534,d59c1825,9dda3e1f,4a1b3b2e,71b1039c,67bd3d8b,cf81998c) +,S(2fa2104d,6b38d11b,2300105,59879124,e42ab8df,eff5ff29,dc9cdadd,4ecacc3f,2de1068,295dd865,b6456933,5bd5dd80,181d70ec,fc882648,423ba76b,532b7d67) +,S(9248279b,9b4d68d,ab21a9b0,66edda83,263c3d84,e09572e2,69ca0cd7,f5453714,73016f7b,f234aade,5d1aa71b,dea2b1ff,3fc0de2a,887912ff,e54a32ce,97cb3402) +,S(daed4f2b,e3a8bf27,8e70132f,b0beb752,2f570e14,4bf615c0,7e996d44,3dee8729,a69dce4a,7d6c98e8,d4a1aca8,7ef8d700,3f83c230,f3afa726,ab40e522,90be1c55) +,S(c44d12c7,65d812e,8acf28d7,cbb19f90,11ecd9e9,fdf281b0,e6a3b5e8,7d22e7db,2119a460,ce326cdc,76c45926,c982fdac,e106e86,1edf61c5,a039063f,e0e6482) +,S(6a245bf6,dc698504,c89a20cf,ded60853,152b6953,36c28063,b61c65cb,d269e6b4,e022cf42,c2bd4a70,8b3f5126,f16a24ad,8b33ba48,d0423b6e,fd5e6348,100d8a82) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 16 +,S(1697ffa6,fd9de627,c077e3d2,fe541084,ce13300b,bec1146,f95ae57f,d0bd6a5,b9c398f1,86806f5d,27561506,e4557433,a2cf1500,9e498ae7,adee9d63,d01b2396) +,S(605bdb01,9981718b,986d0f07,e834cb0d,9deb8360,ffb7f61d,f982345e,f27a7479,2972d2d,e4f8d206,81a78d93,ec96fe23,c26bfae8,4fb14db4,3b01e1e9,56b8c49) +,S(62d14dab,4150bf49,7402fdc4,5a215e10,dcb01c35,4959b10c,fe31c7e9,d87ff33d,80fc06bd,8cc5b010,98088a19,50eed0db,1aa1329,67ab4722,35f56424,83b25eaf) +,S(80c60ad0,40f27da,de5b4b06,c408e56b,2c50e9f5,6b9b8b42,5e555c2f,86308b6f,1c38303f,1cc5c30f,26e66bad,7fe72f70,a65eed4c,be7024eb,1aa01f56,430bd57a) +,S(7a9375ad,6167ad54,aa74c634,8cc54d34,4cc5dc94,87d84704,9d5eabb0,fa03c8fb,d0e3fa9,eca87269,9559e0d,79269046,bdc59ea1,c70ce2b,2d499ec,224dc7f7) +,S(d528ecd9,b696b54c,907a9ed0,45447a79,bb408ec3,9b68df50,4bb51f45,9bc3ffc9,eecf4125,3136e5f9,9966f218,81fd656e,bc434540,5c520dbc,63465b5,21409933) +,S(49370a4,b5f43412,ea25f514,e8ecdad0,5266115e,4a7ecb13,87231808,f8b45963,758f3f41,afd6ed42,8b3081b0,512fd62a,54c3f3af,bb5b6764,b653052a,12949c9a) +,S(77f23093,6ee88cbb,d73df930,d64702ef,881d811e,e1498e2,f1c13eb1,fc345d74,958ef42a,7886b640,a08266e,9ba1b378,96c95330,d97077cb,be8eb3c7,671c60d6) +,S(f2dac991,cc4ce4b9,ea44887e,5c7c0bce,58c80074,ab9d4dba,eb28531b,7739f530,e0dedc9b,3b2f8dad,4da1f32d,ec2531df,9eb5fbeb,598e4fd,1a117dba,703a3c37) +,S(463b3d9f,662621fb,1b4be8fb,be252012,5a216cdf,c9dae3de,bcba4850,c690d45b,5ed430d7,8c296c35,43114306,dd8622d7,c622e27c,970a1de3,1cb377b0,1af7307e) +,S(f16f8042,44e46e2a,9232d4a,ff3b5997,6b98fac1,4328a2d1,a32496b4,9998f247,cedabd9b,82203f7e,13d206fc,df4e33d9,2a6c53c2,6e5cce26,d6579962,c4e31df6) +,S(caf75427,2dc84563,b0352b7a,14311af5,5d245315,ace27c65,369e15f7,151d41d1,cb474660,ef35f5f2,a41b643f,a5e46057,5f4fa9b7,962232a5,c32f9083,18a04476) +,S(2600ca4b,282cb986,f85d0f17,9979d8b,44a09c07,cb86d7c1,24497bc8,6f082120,4119b887,53c15bd6,a693b03f,cddbb45d,5ac6be74,ab5f0ef4,4b0be947,5a7e4b40) +,S(7635ca72,d7e8432c,338ec53c,d12220bc,1c48685,e24f7dc8,c602a774,6998e435,91b6496,9489d61,3d1d5e59,f78e6d7,4ecfc061,d57048ba,d9e76f30,2c5b9c61) +,S(754e3239,f325570c,dbbf4a87,deee8a66,b7f2b334,79d468fb,c1a50743,bf56cc18,673fb86,e5bda30f,b3cd0ed3,4ea49a0,23ee33d0,197a695d,c5d9809,3c536683) +,S(e3e6bd10,71a1e96a,ff57859c,82d570f0,33080066,1d1c952f,9fe26946,91d9b9e8,59c9e0bb,a394e76f,40c0aa58,379a3cb6,a5a22839,93e90c41,67002af4,920e37f5) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 32 +,S(186b483d,56a0338,26ae73d8,8f732985,c4ccb1f3,2ba35f4b,4cc47fdc,f04aa6eb,3b952d32,c67cf77e,2e17446e,204180ab,21fb8090,895138b4,a4a797f8,6e80888b) +,S(df9d70a6,b9876ce5,44c98561,f4be4f72,5442e6d2,b737d9c9,1a832172,4ce0963f,55eb2daf,d84d6ccd,5f862b78,5dc39d4a,b1572227,20ef9da2,17b8c45c,f2ba2417) +,S(5edd5cc2,3c51e87a,497ca815,d5dce0f8,ab52554f,849ed899,5de64c5f,34ce7143,efae9c8d,bc141306,61e8cec0,30c89ad0,c13c66c0,d17a2905,cdc706ab,7399a868) +,S(290798c2,b6476830,da12fe02,287e9e77,7aa3fba1,c355b17a,722d362f,84614fba,e38da76d,cd440621,988d00bc,f79af25d,5b29c094,db2a2314,6d003afd,41943e7a) +,S(af3c423a,95d9f5b3,54754ef,a150ac39,cd29552f,e3602573,62dfdece,f4053b45,f98a3fd8,31eb2b74,9a93b0e6,f35cfb40,c8cd5aa6,67a15581,bc2feded,498fd9c6) +,S(766dbb24,d134e745,cccaa28c,99bf2749,6bb66b2,6dcf98df,8d2fed50,d884249a,744b1152,eacbe5e3,8dcc8879,80da38b8,97584a65,fa06cedd,2c924f97,cbac5996) +,S(59dbf46f,8c94759b,a21277c3,3784f416,45f7b44f,6c596a58,ce92e666,191abe3e,c534ad44,175fbc30,f4ea6ce,648309a0,42ce739a,7919798c,d85e216c,4a307f6e) +,S(f13ada95,103c4537,305e691e,74e9a4a8,dd647e71,1a95e73c,b62dc601,8cfd87b8,e13817b4,4ee14de6,63bf4bc8,8341f32,6949e21a,6a75c257,778419b,daf5733d) +,S(7754b4fa,e8aced0,6d4167a2,c59cca4c,da1869c0,6ebadfb6,48855001,5a88522c,30e93e86,4e669d82,224b967c,3020b8fa,8d1e4e35,b6cbcc5,37a48b57,841163a2) 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+,S(15d94412,54945064,cf1a1c33,bbd3b49f,8966c509,2171e699,ef258dfa,b81c045c,d56eb30b,69463e72,34f5137b,73b84177,434800ba,cebfc685,fc37bbe9,efe4070d) +,S(a1d0fcf2,ec9de675,b612136e,5ce70d27,1c21417c,9d2b8aaa,ac138599,d0717940,edd77f50,bcb5a3ca,b2e90737,309667f2,641462a5,4070f3d5,19212d39,c197a629) +,S(e22fbe15,c0af8ccc,5780c073,5f84dbe9,a790bade,e8245c06,c7ca3733,1cb36980,a855bab,ad5cd60c,88b430a6,9f53a1a7,a3828915,4964799b,e43d06d7,7d31da06) +,S(311091dd,9860e8e2,ee13473,c1155f5f,69635e39,4704eaa7,40094522,46cfa9b3,66db656f,87d1f04f,ffd1f047,88c06830,871ec5a6,4feee685,bd80f0b1,286d8374) +,S(34c1fd04,d301be89,b31c0442,d3e6ac24,883928b4,5a934078,1867d423,2ec2dbdf,9414685,e97b1b59,54bd46f7,30174136,d57f1cee,b487443d,c5321857,ba73abee) +,S(f219ea5d,6b54701c,1c14de5b,557eb42a,8d13f3ab,bcd08aff,cc2a5e6b,49b8d63,4cb95957,e83d40b0,f73af454,4cccf6b1,f4b08d3c,7b27fb8,d8c2962a,400766d1) 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+,S(785f4da0,240de52d,bb50b1bd,bc53994a,47318076,9a1fe06e,5a40a8e,e677ce63,9b5759d2,f77bbb9,e40ac169,a01500ca,6dd6bd70,6a003871,e7ba4d66,b32db9e6) +,S(a7f20615,593850c3,27aaa06f,c03e0d46,d3ff20a0,9b849810,1759638d,8cbb9cf,13b9ebb6,f0cd59ef,54e0f935,87a14fe1,2337e346,94f5e8f1,10323fbd,d7604d3c) +,S(cf083e4f,e0ed4444,85dbd99d,8e6823bb,483eb749,b94ce672,8671de8,6105aa4a,36eaa305,37378494,17050dc2,8290c74d,d9ff9df4,cbfa434a,2b89de00,e06f3099) +,S(9fb8c370,bca485d1,dcadc251,ee906f58,6f3e177,be37baec,6912e535,f5c7ab0a,df5cf77e,1ad07532,7150136e,7ebe7f35,1db47415,74444b24,e9cf2f4f,31ec683c) +,S(ff9e2f29,170dd456,2c94d48c,eeb0390d,db783702,c13574f,8a8c6a79,6427adca,784c7b68,3c824603,5077911f,957aa33b,47534180,d70a60d9,f248b860,736a24c2) +,S(802343c3,e07f9f9d,ed2ca436,3e455427,367b852c,d23ffd7f,fd690eab,90b4162a,b093f0c5,f0fc7d01,a5dfb7f6,bf9d90d8,8595140a,a13fbfc0,f7d6af2f,54ff5ce0) +,S(ae74ed87,11a1a684,9e558e05,47ff8f9b,f6337551,1dd3d272,ee0597fb,fc2d6914,c304897c,e5afb5b9,a383cb64,e85071a3,cfbb2981,93ea6ce0,55257ba4,cf15bec6) +,S(c099b05a,dceb601a,14892c97,7b267152,f29ea71e,fed6090e,7267249e,43c2390f,6c3ad3eb,8c95c72f,e0030a7d,34329945,fd1eb71d,8c4aa1f9,8fa4656c,6bef067f) +,S(97c6949,a25581f5,945814e9,9d590dff,67d936d5,94101005,4cac33d0,fb3658a5,cdc7faad,5bc387ce,a16a10f6,6971e5ee,6d32756b,596adc14,57081ad4,1dbd2e4e) +,S(14a19edc,a1ec89e9,524548ef,cf3dbc03,81b14b46,928f7425,87b11df1,7aa721f7,f83c4d0,aca08709,63a017b6,8db3434d,6088015c,2ff1d8bd,739fd620,35d1a19e) +,S(4742af63,c7597424,e6d04a8c,cb43142c,54c5b350,175bf5a7,27c39820,2187d00e,bb1f2f72,b21e15f,ec17af32,2147edfe,1ca80ac8,3e030dfe,8be39fdd,f340c56d) +,S(a6597869,4d168b00,d9df41de,fcd48ae9,68313394,db683407,330ffae9,f2559a11,6bf65c42,13317a5d,fb561e8c,872c8b1b,90bdabc8,8a8d2e1e,39919f8e,5043ced3) +,S(9e62e468,1e22abde,4d7a2fa1,2f7867f6,ecbfc15b,54990e26,821a8cde,fed76985,4877297b,a64fa8ed,c039ab1a,e62ac72d,8d7bbf05,7513d1,4237b8dd,9f1acd37) +,S(d24333b4,de55b0f5,d47c72e4,88cee8ee,8c960903,260a64d2,c89bca45,db7352c5,688b20b0,617ac12d,5be38fa2,ab52e785,69766a83,2d8b44d5,cfd6ee88,b19b9f1d) +,S(d203301a,13d1c8ae,a8c79007,1ef8116c,3916bb3e,dd5110a7,304b9145,465be838,a606dcea,398dc313,e61c8fbb,dbbc3874,3c103297,164e66a1,4412a21a,5319e55c) +,S(d1aa98ab,7010146f,16a9d6b,cd911535,2595bfa5,1bccb3d5,5e3a4a87,62666610,3abafa4,999294e8,80e3fae9,edb4206b,9b9786d,bddcaec,e2d01cf1,ab715690) +,S(1e20823e,81051b2,65535085,9aefed6,3631dbe,23b4e79,abd3c17c,21f053f4,e238adb6,86592008,f7fe34b9,9b934060,15c323ec,55981b27,85feae6e,5fde7186) +,S(d878afb8,8527a861,4b4276d8,fba39300,72196017,6f437014,980b7bbf,d4320ffc,7403107b,fca8ac64,baa94a4b,128e72ee,4a015675,845519ba,d5609331,1680e7) +,S(53f86d45,61deef96,ca88a685,38fd35ec,a95740a4,3a52c601,faaad0c2,aa3ab72f,667a6ece,bfb97682,c5e9e5df,b6d29156,9604f63,d9ab00ab,8cb10000,e6b01514) +,S(20990660,f1055420,b885fb0a,38824740,3b141c37,5aa20dce,8a29191a,e77bbb16,7d434476,9e302e38,9e14c02e,f5fd8a5c,64cfcf3d,e9813f1c,f53bc6d3,4da93559) +,S(1e70619c,381a6adc,e5d925e0,c9c74f97,3c02ff64,ff2662d7,34efc485,d2bce895,c923f771,f543ffed,42935c28,8474aaaf,80a46ad4,3c579ce0,bb5e663d,668b24b3) +#endif +}; +static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { + S(8f68b9d2,f63b5f33,9239c1ad,981f162e,e88c5678,723ea335,1b7b444c,9ec4c0da,662a9f2d,ba063986,de1d90c2,b6be215d,bbea2cfe,95510bfd,f23cbf79,501fff82) +#if ECMULT_TABLE_SIZE(WINDOW_G) > 1 +,S(38381dbe,2e509f22,8ba93363,f2451f08,fd845cb3,51d954be,18e2b8ed,d23809fa,e4a32d0a,fb917dc,b09405a5,520eb1cc,3681fccb,32d8f24d,bd707518,331fed52) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 2 +,S(49262724,e4372ae6,f6921b82,aa4699a1,f186aea5,40122630,3ea42648,97c2a310,1337e773,bca7abf9,5a2cfa56,9714303b,6d163612,a75ff8ce,c41b681,5e27ded0) +,S(e306568c,1a240c90,d5e253b3,e477e2f8,4dcc1a56,ff06db8d,1384b079,cebd2d31,eac6fe3,78934260,888f2b10,7f7d0db6,ffbc8042,be373826,692b4083,92546e44) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 4 +,S(3b9e100e,2428cefc,271b0e76,23fbd633,74ebf8d9,aab41dd9,c530c39e,363136b0,fafb9815,2d16bb71,df1533eb,8f475b26,a2ae28a3,3ad31f81,953ec16f,6cdbbc8a) +,S(bb0aad49,712ac9a9,2b76ca80,f5dedef7,17ca0768,8107beee,9608f047,2f485d3f,ea699c53,c5835479,8ecd201f,7297da34,895a5afa,31670bff,e7939250,3ca2f975) +,S(79090ac8,e4eefcc0,d4e8eb19,7afe0113,e1e58b4d,b01123de,4aeed33a,36718dc9,eaab722b,91905b8f,13d816cb,cd9aaa56,dd36afb7,ba9008b,963322b1,1cfae7c5) +,S(e77c81ad,e9f97b55,1c03dbbc,e549ba66,8dd71de7,cd775ad2,a269694c,7f60c7d1,3acf1478,eef81321,c5fc3b32,3ea81543,631470f7,1c2986d3,4ec581f2,82d72449) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 8 +,S(de2b5ce9,dbce511c,f2d8878e,3ded87cc,3d633dae,a2d45341,501fb3a4,55ccf6b0,f10576f3,d3c3e0e1,bbf717e9,8b1a3744,65b8c45a,c66318bb,34829eb7,11100666) +,S(d07bddff,d491a2fe,1ea59fbd,7c121217,29659ca5,de46658b,26b1460b,13c03c56,b2ad4708,cd3c97dd,f9c40e2,a1de04d5,61d963ff,8cc2eea7,6be3f60c,2b405ce7) +,S(82403e7c,5d3016af,3765ec4c,396ce8e1,f8da45c,434b8257,10edab41,bb6a4d51,d09661b,e27cb767,4456badd,b3e84051,99ab6ccc,4ec67c1b,11e92ead,7b463b19) +,S(eadc3131,fbd626f5,263faa58,c4caf4d9,930f933d,9541c23f,438cb486,750680cf,d3c977b1,c9b4a897,5c64b36c,972d5d01,a388fb9d,c3791a74,36094ff1,2c87a914) +,S(3903ee5f,6758ff24,c518a4b3,86748f4f,36bdd65c,b77e78ac,609f2909,fc7987d9,e92194e,a15241d6,40915934,bd234749,8d222a18,4927a8da,b0cfe2ae,182be83b) +,S(d0803b78,39ab48a3,8475bdcc,f9a9f219,5759c343,dbbf8e93,23e1f882,5be6a5d9,2cc3b180,ff29c97e,a12ec15f,b38bafa4,4ecf06c,e51d1d24,2894a926,64582f0b) +,S(1f56f096,b18a7499,a153a5ae,acf8be05,8496dd23,da8e6c19,215628fb,c0567ed0,fef22b8a,3b52f490,83004436,b65cd69,c94189f4,1a93c0d5,1fc13cb4,379dff58) +,S(1d9f69b1,a4a47432,e386f525,234aa30,79e947cf,cf203297,4e0fc05b,638e213b,d898ec17,949c0761,b38500c3,a2b1da24,5438d5b3,d3f6f720,41f15d6e,e4d4ccbb) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 16 +,S(128c913,4d9dcb78,12fc4361,5c67ad0,55213354,dc8008b1,aeb5a9dc,fb629efd,fee3e54a,dd152610,d9725936,99d662,c160c8e4,ec6f76e4,5ff41818,be67c96) +,S(21ec012f,5a95b94d,244b8d51,9756075c,301f2854,8e2c51fc,49c0e3d9,d1a9685,2def2105,77af497f,4c7fef71,6949f28e,7418eda6,fd5fc162,d128de19,3cde08ae) +,S(688f5202,fb9d8bc0,9e480e89,4c7cfc74,761c3be7,7dafb11c,58422836,3e331cc5,96ba7d59,63b541a7,2ec7cabd,92403434,1a393eaf,89eebd94,62d9c218,c7302cd3) +,S(fb5c9eea,1cb9a8f5,b3314c30,a50d35,744d0ef,e8bbf68,2e4d3ab4,f7f02baf,29fb8844,e18fc551,fb28bd26,95c5e95c,6868e0cc,7e526af0,91157e9d,fb630418) +,S(f1479fe2,2eedae3f,2f5f6a5d,84a9de1d,593168ec,7b52380d,e0b3625c,cac03421,1a642d5d,2fd88b82,13b50d1a,3fbd3419,c0b4630c,48352131,cb856b2e,22764606) +,S(2273edc5,e8199774,93c5b0e0,9fe0effa,f60f7b,2898565a,69f5c7b2,bf1a7950,b3aea238,8fd978d9,29f1a1df,98495358,b64691fc,4f50b530,906ae39e,fe7bda12) +,S(99f8480c,30504378,b47d10b3,2b39da2f,496d59f4,b1462856,56f05ad7,9bef5214,e001d55d,8e224286,8d8bd397,cb5aa99e,d930e437,e4e62151,71da7ae6,6264b2cd) +,S(382257f,e4751280,d74fdfc6,993c8642,9c000d5,87f57635,bc9656ba,996a6f1f,c2dc733d,fe52cb06,265a4f1d,a6b5f1f9,30dbfa39,e3659973,1c672aad,8b51d474) +,S(23a13632,9125386b,e45f4e1b,2acc847a,62e5eaf9,f6d5f452,6e145e7f,ecefb24b,9129777e,643ba22,2bf817a1,af7155f1,413cc370,3734ba6f,49f15f55,996854c0) +,S(6659ea60,58a664de,a35791a1,8c5cded4,8cf5593d,c440b9d4,8a30ac35,79149f0b,2adcc705,a85d836f,b347b69e,742fc6c3,5300d1d8,e534f1ff,c820c6d6,b2f2199d) +,S(52dc3bc6,e1acd3b4,7ece6f6c,89fd2a3e,2899b487,41421033,37a67dd,1ba939fc,5daeb346,32ad107f,bd83d9da,15a3c4ff,1e8f6ba3,ee5193e2,709e89c3,43d05746) +,S(524b2a97,93cd5745,bd9189ba,9c947bc1,693fbceb,75f074f6,17376b10,d5573551,9e8099d6,cb23fb1a,9deb92cc,3e8a2fb5,a6865ac6,3dececa0,2d146e1b,bcc80b71) +,S(732181a8,e2bc5953,923e6c3d,d960e9b7,525b7b95,e5906997,6fe79156,1782756e,2516c6b3,5592eb0a,42ba193c,bae98ab,e3c42d96,148f1d84,edac621a,722e4823) +,S(b8e8942d,926e38fd,f338496a,c2ef6fca,49a7ae3d,f76eb15d,8d570111,e502664b,7990d56e,7dea588e,4d670ba2,2031e6c7,97248641,69e51d77,f792f5ed,befaf8eb) +,S(144e88f6,3e73abff,72cac11e,7ddccf79,19e744e6,278941ae,18d1b797,e098e4e5,63cdbf3,5df3c655,c58197f,ea54633d,158705cf,7dc2eb3b,4e09f83c,3021837c) +,S(9436e3dc,489ecd8e,2d16a739,c9c73e3d,60e5bc93,68157039,75b8efbd,5c3a9081,1460531f,50cb6ebf,d1aa7806,ea84e7f7,8e8d76b2,b3a66d5e,3a0bf60,39a7e59c) +#endif +#if ECMULT_TABLE_SIZE(WINDOW_G) > 32 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+,S(c117681e,b55bff67,feda80a1,ae88b4be,c806860d,91916619,288a7ce0,b31aef86,d94ae124,dca678bc,b69c9421,f295405f,d6dc1fac,de96a2b4,58ba5fd2,72faa032) +,S(5ccc0619,92744a57,683de5e3,7b956fa1,fd7287d,b4516fc9,f8635be3,a0db42a9,af1f73ea,4d2168e1,7550ffc,dcbba288,8397931b,e457ce6f,3f8082f8,cfc5f03) +,S(858b019c,8a93524f,6c86738d,cb10b534,d8caaf86,5c0ce75c,fc9b83b0,7c661a0a,7c59d30,1ffc8ce1,b0767ed7,91f84bc5,60bb8ca,ed3464ba,698a53c,160ec570) +,S(e1e217b8,69da0c77,599dcc38,40fa1d8c,a8d08b1a,4ac9a882,da1476cc,cc76fa56,83f0ef77,905f0801,4bd86e17,63b8c2cf,ab2018a8,9586620a,b49a15,9fc314ca) +,S(15a1ae40,b4fc51dc,554b75d4,db0c2bfd,62dfbbfc,dede18e1,4edbb689,91525cff,4f0453b7,e4e0e99d,9663e5c6,bb018007,b52c8e14,d78a28d,c4a888e4,8c4326c2) +,S(1b9a142f,fc4d03ea,4b079f2d,b05fad98,8ddb2d32,b359967f,c173801f,63320825,59bda7ed,5b691c20,4fc8f8ac,f53be298,ae628954,a8134d0f,dd097e67,be9ff9b6) +#endif +}; +#endif +#undef S +#endif diff --git a/src/gen_ecmult_static_pre_g.c b/src/gen_ecmult_static_pre_g.c new file mode 100644 index 0000000000..796be9cfa3 --- /dev/null +++ b/src/gen_ecmult_static_pre_g.c @@ -0,0 +1,246 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +/* Autotools creates libsecp256k1-config.h, of which ECMULT_WINDOW_SIZE is needed. + ifndef guard so downstream users can define their own if they do not use autotools. */ +#if !defined(ECMULT_WINDOW_SIZE) +#include "libsecp256k1-config.h" +#endif + +/* In principle we could use external ASM, but this yields only a minor speedup in + build time and it's very complicated. In particular when cross-compiling, we'd + need to build the external ASM for the build and the host machine. */ +#undef USE_EXTERNAL_ASM + +#include "../include/secp256k1.h" +#include "assumptions.h" +#include "util.h" +#include "field_impl.h" +#include "group_impl.h" +#include "ecmult.h" + +static secp256k1_ge_storage pre[ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE) < ECMULT_TABLE_SIZE(8) + ? ECMULT_TABLE_SIZE(8) + : ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE)]; + +static void secp256k1_ecmult_odd_multiples_table_storage(const int n, const secp256k1_gej *a) { + secp256k1_gej d; + secp256k1_ge d_ge, p_ge; + secp256k1_gej pj; + secp256k1_fe zi; + secp256k1_fe zr; + secp256k1_fe dx_over_dz_squared; + int i; + + secp256k1_gej_double_var(&d, a, NULL); + + /* First, we perform all the additions in an isomorphic curve obtained by multiplying + * all `z` coordinates by 1/`d.z`. In these coordinates `d` is affine so we can use + * `secp256k1_gej_add_ge_var` to perform the additions. For each addition, we store + * the resulting y-coordinate and the z-ratio, since we only have enough memory to + * store two field elements. These are sufficient to efficiently undo the isomorphism + * and recompute all the `x`s. + */ + d_ge.x = d.x; + d_ge.y = d.y; + d_ge.infinity = 0; + + secp256k1_ge_set_gej_zinv(&p_ge, a, &d.z); + pj.x = p_ge.x; + pj.y = p_ge.y; + pj.z = a->z; + pj.infinity = 0; + + for (i = 0; i < (n - 1); i++) { + secp256k1_fe_normalize_var(&pj.y); + secp256k1_fe_to_storage(&pre[i].y, &pj.y); + secp256k1_gej_add_ge_var(&pj, &pj, &d_ge, &zr); + secp256k1_fe_normalize_var(&zr); + secp256k1_fe_to_storage(&pre[i].x, &zr); + } + + /* Invert d.z in the same batch, preserving pj.z so we can extract 1/d.z */ + secp256k1_fe_mul(&zi, &pj.z, &d.z); + secp256k1_fe_inv_var(&zi, &zi); + + /* Directly set `pre[n - 1]` to `pj`, saving the inverted z-coordinate so + * that we can combine it with the saved z-ratios to compute the other zs + * without any more inversions. */ + secp256k1_ge_set_gej_zinv(&p_ge, &pj, &zi); + secp256k1_ge_to_storage(&pre[n - 1], &p_ge); + + /* Compute the actual x-coordinate of D, which will be needed below. */ + secp256k1_fe_mul(&d.z, &zi, &pj.z); /* d.z = 1/d.z */ + secp256k1_fe_sqr(&dx_over_dz_squared, &d.z); + secp256k1_fe_mul(&dx_over_dz_squared, &dx_over_dz_squared, &d.x); + + /* Going into the second loop, we have set `pre[n-1]` to its final affine + * form, but still need to set `pre[i]` for `i` in 0 through `n-2`. We + * have `zi = (p.z * d.z)^-1`, where + * + * `p.z` is the z-coordinate of the point on the isomorphic curve + * which was ultimately assigned to `pre[n-1]`. + * `d.z` is the multiplier that must be applied to all z-coordinates + * to move from our isomorphic curve back to secp256k1; so the + * product `p.z * d.z` is the z-coordinate of the secp256k1 + * point assigned to `pre[n-1]`. + * + * All subsequent inverse-z-coordinates can be obtained by multiplying this + * factor by successive z-ratios, which is much more efficient than directly + * computing each one. + * + * Importantly, these inverse-zs will be coordinates of points on secp256k1, + * while our other stored values come from computations on the isomorphic + * curve. So in the below loop, we will take care not to actually use `zi` + * or any derived values until we're back on secp256k1. + */ + i = n - 1; + while (i > 0) { + secp256k1_fe zi2, zi3; + const secp256k1_fe *rzr; + i--; + + secp256k1_ge_from_storage(&p_ge, &pre[i]); + + /* For each remaining point, we extract the z-ratio from the stored + * x-coordinate, compute its z^-1 from that, and compute the full + * point from that. */ + rzr = &p_ge.x; + secp256k1_fe_mul(&zi, &zi, rzr); + secp256k1_fe_sqr(&zi2, &zi); + secp256k1_fe_mul(&zi3, &zi2, &zi); + /* To compute the actual x-coordinate, we use the stored z ratio and + * y-coordinate, which we obtained from `secp256k1_gej_add_ge_var` + * in the loop above, as well as the inverse of the square of its + * z-coordinate. We store the latter in the `zi2` variable, which is + * computed iteratively starting from the overall Z inverse then + * multiplying by each z-ratio in turn. + * + * Denoting the z-ratio as `rzr`, we observe that it is equal to `h` + * from the inside of the above `gej_add_ge_var` call. This satisfies + * + * rzr = d_x * z^2 - x * d_z^2 + * + * where (`d_x`, `d_z`) are Jacobian coordinates of `D` and `(x, z)` + * are Jacobian coordinates of our desired point -- except both are on + * the isomorphic curve that we were using when we called `gej_add_ge_var`. + * To get back to secp256k1, we must multiply both `z`s by `d_z`, or + * equivalently divide both `x`s by `d_z^2`. Our equation then becomes + * + * rzr = d_x * z^2 / d_z^2 - x + * + * (The left-hand-side, being a ratio of z-coordinates, is unaffected + * by the isomorphism.) + * + * Rearranging to solve for `x`, we have + * + * x = d_x * z^2 / d_z^2 - rzr + * + * But what we actually want is the affine coordinate `X = x/z^2`, + * which will satisfy + * + * X = d_x / d_z^2 - rzr / z^2 + * = dx_over_dz_squared - rzr * zi2 + */ + secp256k1_fe_mul(&p_ge.x, rzr, &zi2); + secp256k1_fe_negate(&p_ge.x, &p_ge.x, 1); + secp256k1_fe_add(&p_ge.x, &dx_over_dz_squared); + /* y is stored_y/z^3, as we expect */ + secp256k1_fe_mul(&p_ge.y, &p_ge.y, &zi3); + /* Store */ + secp256k1_ge_to_storage(&pre[i], &p_ge); + } +} + +void printTable(FILE* fp, const char * name, int window_g, const secp256k1_gej * gj, int with_conditionals) { + int j; + int i; + + secp256k1_ecmult_odd_multiples_table_storage(ECMULT_TABLE_SIZE(window_g), gj); + fprintf(fp, "static const secp256k1_ge_storage %s[ECMULT_TABLE_SIZE(WINDOW_G)] = {\n", name); + fprintf(fp," S(%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x)\n", SECP256K1_GE_STORAGE_CONST_GET(pre[0])); + j = 1; + for(i = 3; i <= window_g; ++i) { + if (with_conditionals) { + fprintf(fp,"#if ECMULT_TABLE_SIZE(WINDOW_G) > %ld\n", ECMULT_TABLE_SIZE(i-1)); + } + for(;j < ECMULT_TABLE_SIZE(i); ++j) { + fprintf(fp,",S(%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x,%x)\n", SECP256K1_GE_STORAGE_CONST_GET(pre[j])); + } + if (with_conditionals) { + fprintf(fp,"#endif\n"); + } + } + fprintf(fp, "};\n"); + +} + +void printTwoTables(FILE* fp, int window_g, secp256k1_gej * gj, int with_conditionals) { + int i; + + printTable(fp, "secp256k1_pre_g", window_g, gj, with_conditionals); + for (i = 0; i < 128; ++i) { + secp256k1_gej_double_var(gj, gj, NULL); + } + printTable(fp, "secp256k1_pre_g_128", window_g, gj, with_conditionals); +} + +int main(void) { + const secp256k1_ge g = SECP256K1_G; + const secp256k1_ge g_13 = SECP256K1_G_ORDER_13; + const secp256k1_ge g_199 = SECP256K1_G_ORDER_199; + const int window_g_13 = 4; + const int window_g_199 = 8; + FILE* fp; + secp256k1_gej gj; + + fp = fopen("src/ecmult_static_pre_g.h","w"); + if (fp == NULL) { + fprintf(stderr, "Could not open src/ecmult_static_pre_g.h for writing!\n"); + return -1; + } + + fprintf(fp, "/* This file was automatically generated by gen_ecmult_static_pre_g. */\n"); + fprintf(fp, "#ifndef SECP256K1_ECMULT_STATIC_PRE_G_H\n"); + fprintf(fp, "#define SECP256K1_ECMULT_STATIC_PRE_G_H\n"); + fprintf(fp, "#include \"src/group.h\"\n"); + fprintf(fp, "#ifdef S\n"); + fprintf(fp, " #error macro identifier S already in use.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) " + "SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); + fprintf(fp, "#if ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE) > %ld\n", ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE)); + fprintf(fp, " #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting ecmult_static_pre_g.h before the build.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#if defined(EXHAUSTIVE_TEST_ORDER)\n"); + fprintf(fp, "#if EXHAUSTIVE_TEST_ORDER == 13\n"); + fprintf(fp, "#define WINDOW_G %d\n", window_g_13); + + secp256k1_gej_set_ge(&gj, &g_13); + printTwoTables(fp, window_g_13, &gj, 0); + + fprintf(fp, "#elif EXHAUSTIVE_TEST_ORDER == 199\n"); + fprintf(fp, "#define WINDOW_G %d\n", window_g_199); + + secp256k1_gej_set_ge(&gj, &g_199); + printTwoTables(fp, window_g_199, &gj, 0); + + fprintf(fp, "#else\n"); + fprintf(fp, " #error No known generator for the specified exhaustive test group order.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#else\n"); + fprintf(fp, "#define WINDOW_G ECMULT_WINDOW_SIZE\n"); + + secp256k1_gej_set_ge(&gj, &g); + printTwoTables(fp, ECMULT_WINDOW_SIZE, &gj, 1); + + fprintf(fp, "#endif\n"); + fprintf(fp, "#undef S\n"); + fprintf(fp, "#endif\n"); + fclose(fp); + + return 0; +} diff --git a/src/group_impl.h b/src/group_impl.h index 47aea32be1..6fc58ea015 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -10,6 +10,27 @@ #include "field.h" #include "group.h" +#define SECP256K1_G_ORDER_13 SECP256K1_GE_CONST(\ + 0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,\ + 0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,\ + 0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,\ + 0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24\ +) +#define SECP256K1_G_ORDER_199 SECP256K1_GE_CONST(\ + 0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,\ + 0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,\ + 0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,\ + 0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae\ +) +/** Generator for secp256k1, value 'g' defined in + * "Standards for Efficient Cryptography" (SEC2) 2.7.1. + */ +#define SECP256K1_G SECP256K1_GE_CONST(\ + 0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,\ + 0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,\ + 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,\ + 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL\ +) /* These exhaustive group test orders and generators are chosen such that: * - The field size is equal to that of secp256k1, so field code is the same. * - The curve equation is of the form y^2=x^3+B for some constant B. @@ -21,23 +42,15 @@ */ #if defined(EXHAUSTIVE_TEST_ORDER) # if EXHAUSTIVE_TEST_ORDER == 13 -static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( - 0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f, - 0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb, - 0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2, - 0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24 -); +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_13; + static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST( 0x3d3486b2, 0x159a9ca5, 0xc75638be, 0xb23a69bc, 0x946a45ab, 0x24801247, 0xb4ed2b8e, 0x26b6a417 ); # elif EXHAUSTIVE_TEST_ORDER == 199 -static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( - 0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9, - 0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18, - 0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c, - 0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae -); +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G_ORDER_199; + static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST( 0x2cca28fa, 0xfc614b80, 0x2a3db42b, 0x00ba00b1, 0xbea8d943, 0xdace9ab2, 0x9536daea, 0x0074defb @@ -46,15 +59,7 @@ static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST( # error No known generator for the specified exhaustive test group order. # endif #else -/** Generator for secp256k1, value 'g' defined in - * "Standards for Efficient Cryptography" (SEC2) 2.7.1. - */ -static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_GE_CONST( - 0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL, - 0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL, - 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL, - 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL -); +static const secp256k1_ge secp256k1_ge_const_g = SECP256K1_G; static const secp256k1_fe secp256k1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7); #endif