From ad63bb4c296e6007dab22cda05fd599b20139362 Mon Sep 17 00:00:00 2001 From: Tim Ruffing Date: Fri, 27 Aug 2021 17:53:44 +0200 Subject: [PATCH] build: Prebuild and distribute ecmult_gen table - Improve Makefile.am for both prebuilt tables files - On the way, tidy EXTRA_DIST: Move the header files to noinst_HEADERS, where they conceptually belong, and add missing SECURITY.md to EXTRA_DIST --- .gitattributes | 1 + .gitignore | 1 - Makefile.am | 49 +- configure.ac | 3 - src/ecmult_gen_static_prec_table.h | 9748 ++++++++++++++++++++++++++++ 5 files changed, 9776 insertions(+), 26 deletions(-) create mode 100644 src/ecmult_gen_static_prec_table.h diff --git a/.gitattributes b/.gitattributes index 9cf2163..a0fa567 100644 --- a/.gitattributes +++ b/.gitattributes @@ -1 +1,2 @@ src/ecmult_static_pre_g.h linguist-generated +src/ecmult_gen_static_prec_table.h linguist-generated diff --git a/.gitignore b/.gitignore index 908bb27..22cd500 100644 --- a/.gitignore +++ b/.gitignore @@ -41,7 +41,6 @@ coverage.*.html src/libsecp256k1-config.h src/libsecp256k1-config.h.in -src/ecmult_static_context.h build-aux/config.guess build-aux/config.sub build-aux/depcomp diff --git a/Makefile.am b/Makefile.am index 5aba4ac..2623b9e 100644 --- a/Makefile.am +++ b/Makefile.am @@ -1,3 +1,5 @@ +.PHONY: clean-precomp precomp + ACLOCAL_AMFLAGS = -I build-aux/m4 # AM_CFLAGS will be automatically prepended to CFLAGS by Automake when compiling some foo @@ -52,6 +54,7 @@ noinst_HEADERS += src/hash_impl.h noinst_HEADERS += src/field.h noinst_HEADERS += src/field_impl.h noinst_HEADERS += src/bench.h +noinst_HEADERS += src/basic-config.h noinst_HEADERS += contrib/lax_der_parsing.h noinst_HEADERS += contrib/lax_der_parsing.c noinst_HEADERS += contrib/lax_der_privatekey_parsing.h @@ -125,37 +128,39 @@ exhaustive_tests_LDFLAGS = -static TESTS += exhaustive_tests endif -EXTRA_PROGRAMS = gen_ecmult_static_pre_g +### Precomputed tables +EXTRA_PROGRAMS = gen_ecmult_static_pre_g gen_ecmult_gen_static_prec_table +CLEANFILES = $(EXTRA_PROGRAMS) gen_ecmult_static_pre_g_SOURCES = src/gen_ecmult_static_pre_g.c -# See Automake manual, Section "Errors with distclean" +gen_ecmult_gen_static_prec_table_SOURCES = src/gen_ecmult_gen_static_prec_table.c + +# See Automake manual, Section "Errors with distclean". +# We don't list any dependencies for the prebuilt files here because +# otherwise make's decision whether to rebuild them (even in the first +# build by a normal user) depends on mtimes, and thus is very fragile. +# This means that rebuilds of the prebuilt files always need to be +# forced by deleting them, e.g., by invoking `make clean-precomp`. src/ecmult_static_pre_g.h: $(MAKE) $(AM_MAKEFLAGS) gen_ecmult_static_pre_g$(EXEEXT) ./gen_ecmult_static_pre_g$(EXEEXT) +src/ecmult_gen_static_prec_table.h: + $(MAKE) $(AM_MAKEFLAGS) gen_ecmult_gen_static_prec_table$(EXEEXT) + ./gen_ecmult_gen_static_prec_table$(EXEEXT) -if USE_ECMULT_STATIC_PRECOMPUTATION -CPPFLAGS_FOR_BUILD +=-I$(top_srcdir) -I$(builddir)/src +PRECOMP = src/ecmult_gen_static_prec_table.h src/ecmult_static_pre_g.h +noinst_HEADERS += $(PRECOMP) +precomp: $(PRECOMP) -gen_ecmult_gen_static_prec_table_OBJECTS = gen_ecmult_gen_static_prec_table.o -gen_ecmult_gen_static_prec_table_BIN = gen_ecmult_gen_static_prec_table$(BUILD_EXEEXT) -$(gen_ecmult_gen_static_prec_table_OBJECTS): src/gen_ecmult_gen_static_prec_table.c src/libsecp256k1-config.h - $(CC_FOR_BUILD) $(DEFS) $(CPPFLAGS_FOR_BUILD) $(SECP_CFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) -c $< -o $@ +# Ensure the prebuilt files will be build first (only if they don't exist, +# e.g., after `make maintainer-clean`). +BUILT_SOURCES = $(PRECOMP) -$(gen_ecmult_gen_static_prec_table_BIN): $(gen_ecmult_gen_static_prec_table_OBJECTS) - $(CC_FOR_BUILD) $(SECP_CFLAGS_FOR_BUILD) $(CFLAGS_FOR_BUILD) $(LDFLAGS_FOR_BUILD) $^ -o $@ +maintainer-clean-local: clean-precomp -$(libsecp256k1_la_OBJECTS): src/ecmult_gen_static_prec_table.h -$(tests_OBJECTS): src/ecmult_gen_static_prec_table.h -$(exhaustive_tests_OBJECTS): src/ecmult_gen_static_prec_table.h -$(bench_internal_OBJECTS): src/ecmult_gen_static_prec_table.h -$(bench_ecmult_OBJECTS): src/ecmult_gen_static_prec_table.h +clean-precomp: + rm -f $(PRECOMP) -src/ecmult_gen_static_prec_table.h: $(gen_ecmult_gen_static_prec_table_BIN) - ./$(gen_ecmult_gen_static_prec_table_BIN) - -CLEANFILES = $(gen_ecmult_gen_static_prec_table_BIN) src/ecmult_gen_static_prec_table.h -endif - -EXTRA_DIST = autogen.sh src/gen_ecmult_gen_static_prec_table.c src/ecmult_static_pre_g.h src/basic-config.h +EXTRA_DIST = autogen.sh SECURITY.md if ENABLE_MODULE_ECDH include src/modules/ecdh/Makefile.am.include diff --git a/configure.ac b/configure.ac index 82d1965..2c22f66 100644 --- a/configure.ac +++ b/configure.ac @@ -125,9 +125,6 @@ AC_ARG_ENABLE(exhaustive_tests, [use_exhaustive_tests=$enableval], [use_exhaustive_tests=yes]) -# Force static precomputation. The code handling this will be removed in a later commit. -use_ecmult_static_precomputation=yes - AC_ARG_ENABLE(module_ecdh, AS_HELP_STRING([--enable-module-ecdh],[enable ECDH shared secret computation]), [enable_module_ecdh=$enableval], diff --git a/src/ecmult_gen_static_prec_table.h b/src/ecmult_gen_static_prec_table.h new file mode 100644 index 0000000..bf4e5ea --- /dev/null +++ b/src/ecmult_gen_static_prec_table.h @@ -0,0 +1,9748 @@ +/* This file was automatically generated by gen_ecmult_gen_static_prec_table. */ +/* See ecmult_gen_impl.h for details about the contents of this file. */ +#ifndef SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H +#define SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H +#include "group.h" +#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) +#ifdef EXHAUSTIVE_TEST_ORDER +static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; +#else +static const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = { +#if ECMULT_GEN_PREC_BITS == 2 +{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), +S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), +S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb), +S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823)}, +{S(1b8462eb,1ccdf7b2,b8372f2f,cec1f479,ab07c09f,cb26d6c3,965ec73,4d654f81,62f6755,b4a7891d,55de6427,fbc37d33,e4eea418,a2c04392,a3d11807,ccc9025), +S(c3b55f99,9cd9113c,fcb4f29,be00c785,cc70d1c1,f1cfd0ed,593abe8d,260bd2bb,8945790b,5696225a,1c6a1f45,1d6b085e,cde2f332,df068271,f6279877,6d1015aa), +S(a4b41b41,1a255142,ee62144d,96ccfdc,a3cdf5a6,af32bdd8,d1c3d26b,d6aab0b9,3ade7f6a,299ee56c,299fcaad,72a146d2,62db1dcd,2ea1a355,d6e00294,ee34c3), +S(d4af67c6,75f97f30,4a621fe5,343dfa5b,e432d9f1,43758d4d,62df1e09,b79abfe8,d0fea700,2a851a85,33929e5f,1f41d4a9,68b9e520,6c19f3b0,35ce96a5,12b61921)}, +{S(6ae991de,18418b49,160194f,a735eb72,c299b987,1981a4f9,aa717ad2,bcdcf13,7ee8011a,40f384f2,e50add2d,97005173,2787cc7c,89dafb66,301bc94d,24b913f), +S(c28203a6,e0f93259,778bddca,10f994be,67cec8a3,109d0001,d830a8e7,b452794b,18df3a42,ec24b713,2ac4b6ec,dd7605e4,169aa07a,41d7559e,bde808d9,bbfbcb14), 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+{S(f307f4b,b76a7bcf,1fe75d85,60a4c64,c748b32f,489e30b6,170057ed,225c9e95,fc200ac2,3ba3be6d,aa4d4f86,c89fdc5b,8eb00f8c,ebcf6a41,51411042,ad181fb5), +S(dbcf10f2,e43ae854,85fd600d,ca9ab27d,7ba393d,e6a333c0,7901cfc4,55352569,48d4448d,8ce674df,d254f09,17fdc390,de9aa8ff,29869da7,4c2529cc,dd476fb8), +S(38a07202,a23d26fd,663fa7e1,8e8a02a9,2631011e,57731024,3e717ac3,a0390078,fb6057ac,aa4fabb7,c4e922cb,ab2b7fb1,e4f0b3a7,6be215f7,7de296d3,ed709def), +S(5bd3e7ac,5f8619f,5db77e69,f7416149,b4afa5c7,95d25fbb,fb1da1ad,9e4617e3,9ae709f0,d7278b4e,b66919b,c666d63b,46bc228,8ca956eb,2e20238b,24725d56)}, +{S(35e48872,5074158a,8d2ed392,d178f6e2,e4c43fc9,689b32d,5f374c05,d637a53b,95143742,7bb0105b,5e7f60f2,d95ff164,ff808b7b,c2ad592d,68988e5e,bb5d5679), +S(8619863a,d49d8ab5,6c999e77,4653e1a7,4acb7a63,edb65840,76f3b3ae,903f3579,451500a1,3dac87a8,ace7fe4e,64dc6174,896b5002,67163bea,1d3db275,b8274cc5), 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+{S(86592c40,71b619fd,27e3825,ca585cdd,ea068958,7b59e3bb,b3581075,a3cb8a96,923844bf,2a197b85,b232b973,2922ce0c,a2431dc4,a59d27f0,2ff3b2f4,af7703bf), +S(e82a2871,fbff9467,96109300,26ffb096,d9509b43,6e786697,e85c57b3,389f4fbd,7732b419,f0d682a7,9ab047a7,d4a51685,fcaa3c8c,cd8115bc,4f7514f4,1717c804), +S(9c079fba,32d2288e,a0829fa1,1482dbb,8032397e,c676d744,c7b0ce84,a1c4f539,2b171739,85fa643a,ba7314d3,86f086c0,d4884b63,4062a4c8,3f7f05aa,575936a6), +S(78ea5f31,1d3c1943,e438601e,a885ae8e,efee93e9,26768d82,3e88a71d,9c22d773,953cb0dd,893aed33,9021e63b,277cca61,4d772c7e,a2b8ea3f,bd151b14,5cb144bc)}, +{S(4929a368,f9842917,73f5236f,dd5cbd7f,a8e8dd9f,261cbab,5948ad57,798cbf79,26a2a40b,33630e55,7b376fd8,134a8d48,542c08e8,c2d01a99,586d33c,66d37426), +S(bb4b9ce4,b8dd22bf,2873b2de,f29c494f,621d89e4,aebf3c23,566e0cd4,b4ffd288,d4f81742,4f778966,1274fc8,e8aa5c54,4434fca7,6b73b639,a04aab65,8bb77c2f), +S(6ff70715,17bdc2a4,c0267caa,38ca96ad,8a235744,2a24db87,a07cdec6,c3b022fa,2f16b295,a2db7a6d,321280c3,a53dfcf4,674dc215,38e2a556,75cd37e5,d3ee7362), +S(b5619c5e,edbc92f0,c88a9cad,9955a08b,764dd683,361bb7f2,8c611857,d473c45b,11f6864b,36116181,d2af3f6c,fe738c84,7820ebe1,53f0c82b,14e5c67a,b3a2213e)}, +{S(c7452697,d7691662,ae3b754c,7be11df8,ac70cc8c,e2e80a9b,9638b0f2,a323ecd5,fe84e963,3231caac,63a5c7cc,90cef693,a69ea140,c846e1b3,b96a6fc6,68b43c68), +S(c797ca59,95cda70a,a33093bc,4f7f83c6,1a31ab1e,dbd6f10d,31e0da05,64f41407,ce4a64f9,ae7eef1b,7abfad94,f4a6a7f1,c746268e,9006995e,8f7d311,1b81f85e), +S(288a2e26,8fb8fb28,29bd9d21,4ec5860b,fc1ed577,f40c6184,79a0b921,c2f4b67a,8343d03d,556bfee4,b66ca598,f4fecbcb,aa2723c2,f3c35203,ee12710d,d9ff0b52), +S(7aa02a72,adefd779,fd994c77,697ee142,dd25d168,38c8b8a0,5178b7e7,37f33032,a060f7d4,8e0c2929,864208a7,1668129b,3b3908c3,7e89ba0,e7e55aa6,5e3ed98e)}, +{S(34925d1a,b1c7c081,e945d66d,60ed394e,f474e38a,423562b3,95bc51d4,c4f55321,8ef8dd58,ae1661b5,a7c327ba,ac4105e6,d02d6a30,2263c5f8,62b712fa,b064e562), +S(2bbf19eb,9a6211a,7881c7e0,5483a318,c9d91280,d09e0634,2a54a9f2,b5654be8,3cf7b41,bfab218d,e182cf34,32450abf,88da1e16,fdb79699,ecfeb962,39d422d3), +S(97f1b30a,6ce2dd8e,1d0358fb,45b432fe,be6d9916,34ecc7a4,b7cb4f3c,f1663fb8,c7cba22b,88a5f5c4,498f0f22,cea6830e,1bb44e1c,7f9d9833,60139c2e,97dab7da), +S(b5d0e718,621a0a40,c2adf34a,3e1e64d6,bbad3598,e6944436,f8f87450,575d61ef,2e43eb70,8fb8e2a0,f24a1a12,7a890c07,d79b51d,60e3a281,649afa3c,182d5b77)}, +{S(463080f9,19ecd42f,593dc20a,2d3160cc,74d9592e,446f299d,be5446f4,236a5b17,2a65200d,e1b16975,9d5c75d6,fa6c666,ba45728d,343d6339,48233391,60c14a16), +S(547eef23,516851a2,2f160ec0,781a49f1,1480d07d,2607ab5a,89656c94,2f774b5a,eb6f249d,ee624cae,cbc59f02,63da0fcc,e33a515c,843c3632,661f13e4,39c4f0e4), +S(77f0c9a2,51d48b39,62f92e2a,679fd9cc,f458f17a,edf588be,d4bd6448,47f9306f,355f4827,b10e614b,4590242b,da546e53,dbd419de,1d1a7fa3,208d9350,3496db0c), +S(81e606c1,19b6ef80,418aa008,7ebaf9d3,7adff1ff,a81f739a,172a580b,27c7545c,ddb0404c,e56113c5,93920382,6d2adab2,6590b509,45865406,ce1fd256,6565209a)}, +{S(92d469ed,e0969dd6,7e9d7b31,f0f703e3,97cad53b,e6101b2e,eeb8714d,645eaa9c,24a0a786,916297f4,6a53c7c2,29a3c95,80eec521,355b823,f0488460,39595dd2), +S(e5035341,5c49c24d,f672a74e,4eb2d108,57fa987a,afc50178,ffba8797,5503006f,38522661,fe682984,7b6dda61,9dbbe47b,35c0c9eb,b79b5d2f,2c6ba882,26cb95d4), +S(d0777020,cf6dc469,cf020ce5,e64bc2e4,1e2bf116,4f4e814f,18bbbc4f,f468b0b8,997b2163,c4670401,281ad84b,a914cbe4,e76a5cb1,cb90c1bd,ecdac585,621cb0a6), +S(881abd9c,717f0a2,360de50d,66a9b655,b9459e62,80a985da,e811f2b2,154e307a,beec571,1375031f,354dda5c,b9d8377d,1cb49816,1f4c738d,f6b9d323,f9acacd)}, +{S(ab7d18ba,955fdaaa,b1a0bb25,25844e2a,9d2e204d,ff224588,ae96c41,e690e010,4e0090b1,dcd619c3,10ff5027,9c534612,84ec2467,77b63179,c80724c4,42d00204), +S(1a5982e3,37e3eb50,e679f24e,c3473b4d,1af3dcbe,ac3c7a96,a95f51f9,a9875266,dca6c614,85d55985,1fdc229,56ee59cd,fac74069,6276299b,a199f39c,869e5c9c), +S(bcdf870f,8d5394b4,f1f3446c,a25ec6d,5b4c939,b598e596,814a6dda,a054bb2f,71cfbdd,d1aa7722,892f83e4,ea2dec50,81c4d14e,548a16c4,2818b76d,5721fb7c), +S(cb28eeda,338a5088,db505da,949cddf2,741e071e,378f92f1,dbba270e,9c322c57,d98cba61,cceca53f,7d84d71f,f892b962,6f26e156,841d2dfb,7aaab839,3f515903)} +#endif +#if ECMULT_GEN_PREC_BITS == 4 +{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), +S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), 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+{S(6ae991de,18418b49,160194f,a735eb72,c299b987,1981a4f9,aa717ad2,bcdcf13,7ee8011a,40f384f2,e50add2d,97005173,2787cc7c,89dafb66,301bc94d,24b913f), +S(22165bce,e76e1594,5b9041e5,ccdee553,eba60e4f,1ece2d9f,e0ad7440,565f2665,fe8f383b,bae7e284,d1d890bd,569ab7b3,ebe5f1bb,b60ee19e,8e8de65f,88f3ab96), +S(a2600e0e,9265b7d8,fcc46a5,51872122,66ad5334,4ddedbf3,ac8cdf2a,b86f2b8e,d00f90a0,97fe3863,b4854dce,fa5a36e7,3f94015e,f892303f,2e5cb2c7,aefbf15), +S(38758ff9,5cefa7c1,b7a2443a,ba29b65b,aee1fa81,5ed49595,a4ec760f,b995df1d,43bc94bf,dfff3c59,7a6e41c0,52194d41,c1601b91,792f42a,6872ded2,a5e8f4cf), +S(57122897,d98019ae,a6dcbe99,49682895,c95471e8,d53680ac,49927e23,16abfd27,c30cb105,d9edc36c,9e237e93,2edd6bef,3d553d67,fec3a37b,fbe0ef56,a3cb6c), +S(7b7247c7,73470f13,2477c974,7820ce4d,51dde95b,dd14923d,e31dfb13,5a8aacdf,2e7054f4,a33361a7,a4282bb2,7e738884,3a91b211,3f71e160,60fb2235,6b40ffc1), 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+S(f5da1419,be3e268d,b51dea4b,af8867f0,a02a29c9,599266e6,e0e37b,d569d8b,1ecd596,4748be32,44cfe953,6fa9ae30,104b1e6b,8ccd69f4,1e5891e2,242db1c8), +S(eaae3a45,5aa38fed,381ed64f,b6353d0f,2236d267,97f5dc1a,4e7a511,1654be5b,24f1dedd,7f3d9cef,572e7819,b09be2a0,de1f2f4a,6b2314f7,57a81b18,cd1fdd08), +S(a997a9f1,e9fb824d,768fa890,b91ec55f,c851127,5c16eb4a,99577fe4,87d155e5,9cf136a2,c3fd76f8,d4921bba,9d61917,b6ebbfa,f55a4cf5,69665d47,bce7a44c), +S(f20287b,958ffe72,72d443cd,de9fa6f5,f9ab208f,a74c6147,10c44c33,3777f1,ce614f5f,87c3a366,65d7f574,5446d80a,35a8113,1fb4dd2a,aabed948,b9e09931), +S(f9fb85f3,fc4e45a1,6b6eef55,cd8656db,de777390,f20b576,a28110da,e8ce5713,51de9f5a,7b2f0101,cd02e6c7,c98cdf93,a430d62a,1fec4f3e,95bdc3bf,a2212e13), +S(d5fa0933,f13c1f4e,89caeba4,101f44c0,420da5c6,7bfe1ea9,66cf01a5,ef48b1d8,5efc8918,8b9eb65d,faa6e0e9,812407ef,35d8db,76f9e722,ff63bc3c,3afc3b1a), +S(93899e6f,fc291a4b,e986f938,b8b378be,bf4c3d35,f9a1bdd3,ecea5f04,d8f4bada,a19a2983,55cb62fc,43334649,1c89f26d,fbb67bc3,872f7512,9229cb73,d126293e), +S(8fe07488,b5b173c,d530d796,a18eac08,80164c2a,ed787b05,90ac8dce,3bb120d8,829abce1,43ea8009,e4f5f481,125ca6d4,ecff3f32,577cdbf1,c054a23e,67f18b0b), +S(10c3b093,5461407c,369494a7,631eb4a2,365b122e,ce0a6b95,7c1bdbee,387394a4,f09d69ec,925c9a43,57648509,f7db85a9,22f609cd,32b400ce,3a80567,88a74627), +S(cfe48dfc,f5566fbd,7562ed68,576a7911,baef64f0,dc63e158,1a29bf23,3e1a058e,440c6051,19f2a948,b4b6c3a2,7e711cea,c7983d7,f4a2db9,537536db,fdebab76)}, +{S(53d772b6,b18211f7,1478e9d3,3a0c061e,2d232358,44177867,af91508d,e014f22d,b2e85a07,8160d31c,3ca32d9c,ba025904,1bea0368,d9eb13de,8af8f505,73142ed8), +S(b9d6067c,fc26ba4a,1f5bab8e,d5f28ffc,bb6bd6,b61990c4,1b091ec8,2cba973f,532d0ab,7731c02d,91cc7e51,71b625b3,af5a605,d92d02a5,fc4cee4f,afa09ebb), +S(e8a93ceb,3db0a4a3,9a3b768c,700fb504,652161e0,4a1d4d92,df52cd4b,83e65e38,791b967f,22543fea,9ec38e5e,a14a94cc,9d11ea8a,73ca0c13,e022d53b,f8bf1148), +S(ac6130f7,41e1601f,5a92bb75,90a799a8,3e8ad9c,c911ed7b,7dee1bcf,da14f332,97ea5d16,d5c7e368,c7b97c2d,7283cb03,f215f79c,d1d80276,6f9923e0,ce80ce44), +S(ac34d4c1,1d2d4ade,2f044e88,6b57cd45,c1b23550,538059c4,e9855077,4132643c,7191e155,aeb3b578,6b55db41,652e8af2,bac1f933,d6f62723,808c6172,bf0eb0aa), +S(a7c4bafb,f1988992,1ce15754,187d41b9,eb653dd,bc97cf05,ddf449d8,c9ff734c,ccf20733,da4aab6d,81db8d5a,d3f12d1d,9cbc943,8b92165c,e83c5afa,5ee108e3), +S(c04ba857,e758fdb0,29c02712,1671fe33,9b7184b3,50ad952e,9d234681,43f7568d,9ce5d9ca,65f96b76,b4b06f57,f34de7e3,c64a1d21,f07fd6fd,eb7d47e7,bbf4e6c8), +S(8230e7e7,81259e58,e9b74a49,340733dc,252bef7b,5b7dc82,a4e99f0b,2998ba67,9c71921,3b3254d1,f53b4f30,d0a8e665,186e272c,d0e5d316,a7451eb3,2ac8bb3f), +S(720c2f5f,6465d38d,3916939f,8d095657,e547cc5f,849f4a41,30485b1,2d94b5c7,8635961f,5f74d176,e4ae0ec6,e4b3b394,6d5b1766,fcb902fd,9f9bd982,2ad4e4c4), +S(263b45ca,b3547cf1,5eca4381,3d1c402e,5c209d3e,34a288cf,182aa4a3,f04304f,3516b1f3,524bbdcc,fddd94bc,fb86a43a,27a7a78a,fcbbefdd,6692fc21,87364438), +S(4edb7d61,a45ebb51,1fb0c220,6f16fe60,5a202976,9007c3e7,11b94889,a983d0c8,b482fee3,fe824b1a,3251cd2c,3f38ab4f,adad1fee,d398be92,58d2c81d,79b0eb36), +S(f44c286a,b8196e25,87c225f7,2091db05,e47f18b,5b9a0b9,79d2cd3b,15441767,b7aa2018,5925845e,661ad980,a6c215d5,fd7072cb,46010930,ae64089,4c8a0af8), +S(593f9bdd,b246bd1e,19eeaafa,17e348e,5199decc,8e63ef68,ed8bff89,bdffad48,5201d11f,a4ac67db,dd66fbaf,5c2ba20f,8bb1a6b3,18cdfbac,6b257aa8,d30dd316), +S(823b4c96,8be9e125,262d52d9,4aaff240,55def10d,6353a347,e4248de0,7889ecb2,adfafa7a,fb1c60e,e7fb3e2e,73c66063,5a9e97e0,4a38a120,b7a81f17,7d1a6c41), +S(8daef78b,c46e0f5f,858fd74c,68be31bd,3b474d9,6bd74deb,eeba69af,5ef3056a,15db0684,bb6d4e7f,b135a4ab,f4b81d4a,a9fc7e93,c26e3616,b7b938da,25d44a06), +S(2b7616ca,eb608427,5a14eb53,b67a2ee3,b831fb55,6f63e0b2,e01650f6,e6900a0d,915e7dbc,62f8e349,8ffdf22d,d3604d77,bb701137,b6c36543,84cce993,c4613ca4)} +#endif +#if ECMULT_GEN_PREC_BITS == 8 +{S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), +S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), +S(6ada98a4,8118166f,e7082591,d6cda51e,914b60b1,49696270,3350249b,ee8d4770,c234dfad,f3847877,a0a7bcda,112dba85,1cdddf00,84d0c07,df1d1a,a3ec3aeb), +S(a94ae8,63264dfb,b910ea95,4ce9ca7e,4f86f92d,9f3a95d1,ed61552a,7a3f5743,7f53f7f1,6ad2d08f,15e73314,6d80467,41557acf,19556c0f,ed7117ce,37040823), +S(b692c750,d23d3674,c351e3b7,e1a8a87b,14a5df81,852eaf35,209d0ec5,6e22a2cf,b18c4f17,252db89f,838de32f,b3340ea2,bb961a39,54b38c47,f9a8219c,4820a0cb), +S(691fc741,80e75b55,47b375f1,1bf60abe,451d27de,1743a436,5f8e4bac,ad421c09,8eb5fd9d,f3c03240,6cebf370,8125955f,bf2ef703,475d3fd6,1a0291b6,69b52d9d), +S(703b5f14,a7d82473,1196b52f,ae9ca8cb,b245b004,7a9928d7,d0c42f33,391411dc,5ed74eaa,49f276c0,4d61f31b,6da4137c,bde5673d,8e3f815d,efea7951,f88585c), +S(29b8ec47,d241eda1,e51bbb1e,3928444c,3747b4fe,7cecb365,2bbc4587,2f504875,88693238,8562f8bf,f7d72324,62ebc54,6b93a95f,77936b02,eb1cd6a7,d4199bcb), +S(444a07ad,e81916c9,32bdeec2,21c556c4,6b7f6491,e99b479,2cfec82f,4ec17910,2e084c2f,eead5200,77c151b6,eff9375a,713b9d15,5306708d,b3f538e1,8eb18cf), +S(e0dd618b,226ceddc,f560527e,20b4fe58,e5fcf28,39911ea6,c3e8a4a7,e15f9121,a063a157,3377bbbf,1b9a5ebe,afbe11aa,660c1e65,df1392b8,97205858,3c86a3fc), +S(9b99461a,2e8360f2,f2ba0bb8,bcaeb699,159e0652,69d9042a,fa0c4e30,a7b6f30d,3fe7fe04,3cb45303,3d4f5560,7d41cd76,9036a49b,82912350,6d8b9995,254154fd), +S(504da3a9,d9d9c81b,c2065398,4ed28cb1,b5beec9b,6ce5dfb6,cea94e54,fdff044b,cbd40d1e,858133c9,cd20b9e4,ff9fe94,f7cc9579,39e6df49,7a6bd702,797f96cf), +S(ddec0aac,1ebce6aa,ad6300d5,60f0e503,829f0bc6,479641f9,b19d9f6,484376fb,332ff5b1,fc83085e,736736bf,3c265e4c,8f80925e,6f38479d,6563bc34,e5faea1), +S(dc530ceb,b82c246e,41c522f1,d2571d31,4b14edf3,91577a2b,64e42172,b23562c1,563ddd93,857d6529,8b81de24,19e5cede,7a4c5b7,a2fe98f6,9efb8906,6f32a98a), +S(7604d60f,418dd132,78058942,fb2d2153,c0a2bfeb,e83c5011,a451bcb1,58db0773,38be14ae,d9e1c404,63ef92bd,d62c599a,b37625a8,182a3763,4fa2de90,535d50a9), +S(cb896744,77b20829,f5e2bd42,8852c70b,91cbd0af,cadf219,a69727b4,cbec8d7a,5710d17a,20ea0dff,980d3f06,38d8b910,b8940d00,dd4a323f,d777d942,213e1093), +S(501915b1,391e083d,e88c795f,8464c846,f699a79e,edb1b963,3e29f71a,9ce4d022,9e1dcc94,17ceb0e,15762f8f,7d0db85f,3bce3ad6,fecbe2c3,567853ef,ccd6d0f9), +S(a63c0b8a,4eb2cb10,1e556904,a7246356,9909055,f45aa4c0,e89c2237,cbffafca,9650b428,12374811,738f4ac3,a2ac0505,396339be,4eeeda8b,c35e6fdd,c51a1e56), +S(a16760e5,c3643d19,da15c034,5feced27,488ccafa,ad5298fa,6ee1070d,a258a761,736a7c7e,69db053,6f541079,158d671d,598efb1c,d75ec804,c7b2b49b,1ad7638a), +S(840693fe,73b96819,bb1b24a9,35d5dc83,f361273c,d0989e76,1edc35ef,50faf90b,4294e19b,49558667,bc6237c6,86c30aba,a2660580,563d465a,fde9875d,74c9a57f), +S(97273c3e,26e12369,1d0ade3,3aa261cd,a45b2d2c,d749af71,a60c0d15,85e18e03,2700c565,dbb08439,fb74317e,60776fca,d0efc1a5,5d0ad87c,18f82f2d,a97caf19), +S(978d68a0,5ce30528,e4db2dae,99f6a245,f69cbd04,3c7171ce,ce2bee57,60e68b9,ffef379c,1515b068,df562f3f,bdadacfb,8aabe5aa,466105d1,97a8febc,1596915b), +S(dfaea7bc,c78d275d,9f6a74fd,21fdec14,bcabfa45,e44070c1,9c44d449,c5d52231,927b810b,c2994b8d,2ed5124d,98e2f5cc,58410607,82b1ed80,d0fae288,8c42d538), +S(ca0b766b,8b8d76fd,ce471a88,18e043d2,604d1ad2,b689cbce,70ceae78,fddf5a27,ddf9e3bc,935ea0bc,22f977ab,98a92414,643140ae,be0448a3,35d6d44a,1bedfc48), +S(11dcc001,3be8d4b7,85e87153,e060d13,57cabb5,34a2c1de,2a4a70cb,9803a031,5b5d46b0,6a96c30c,b1901c12,eaa1c656,3a2f35b1,e9026954,36e087aa,3deb777e), +S(a828121a,18d23262,bce26648,ab44c45d,c5027ae3,f74786b9,598f22b3,c408bf08,37893209,80d7d2de,6074778b,2e8916f0,4043a616,982a9b61,d4089623,31375cab), +S(291ec5eb,e010daff,3ac00825,3452b065,d9f7fcb3,66e125af,22f11358,6263fbaf,4647cba2,45d190d8,2337f217,c278c98c,370120b3,d4e04110,e6df2c54,92d63bb7), +S(44735d48,4c584d70,6afc573e,8ece7670,c79c7b99,99eb0141,4a73905d,34a1cf01,30a27c9f,67b47348,583f1e84,5e7af221,438d4c9f,a1e0cc19,7312ec6b,908d613b), 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