Generate curve25519 tables with a script.
This is to make it easier to add new field element representations. The
Ed25519 logic in the script is partially adapted from RFC 8032's Python
code, but I replaced the point addition logic with the naive textbook
formula since this script only cares about being obviously correct.
Change-Id: I0b90bf470993c177070fd1010ac5865fedb46c82
Reviewed-on: https://boringssl-review.googlesource.com/24745
Commit-Queue: David Benjamin <davidben@google.com>
CQ-Verified: CQ bot account: commit-bot@chromium.org <commit-bot@chromium.org>
Reviewed-by: Adam Langley <agl@google.com>
diff --git a/third_party/fiat/curve25519_tables.h b/third_party/fiat/curve25519_tables.h
index b459660..a05702d 100644
--- a/third_party/fiat/curve25519_tables.h
+++ b/third_party/fiat/curve25519_tables.h
@@ -9,8 +9,8 @@
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
-// The above copyright notice and this permission notice shall be included in all
-// copies or substantial portions of the Software.
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
@@ -20,6 +20,10 @@
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
+// This file is generated from
+// ./make_curve25519_tables.py > curve25519_tables.h
+
+
#if defined(OPENSSL_SMALL)
// This block of code replaces the standard base-point table with a much smaller
@@ -120,2182 +124,2183 @@
{
{
{{25967493, 19198397, 29566455, 3660896, 54414519, 4014786,
- 27544626, 21800161, 61029707, 2047604}},
+ 27544626, 21800161, 61029707, 2047604}},
{{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
- 5043384, 19500929, 18085054}},
+ 5043384, 19500929, 18085054}},
{{58370664, 4489569, 9688441, 18769238, 10184608, 21191052,
- 29287918, 11864899, 42594502, 29115885}},
+ 29287918, 11864899, 42594502, 29115885}},
},
{
{{54292951, 20578084, 45527620, 11784319, 41753206, 30803714,
- 55390960, 29739860, 66750418, 23343128}},
+ 55390960, 29739860, 66750418, 23343128}},
{{45405608, 6903824, 27185491, 6451973, 37531140, 24000426,
- 51492312, 11189267, 40279186, 28235350}},
+ 51492312, 11189267, 40279186, 28235350}},
{{26966623, 11152617, 32442495, 15396054, 14353839, 20802097,
- 63980037, 24013313, 51636816, 29387734}},
+ 63980037, 24013313, 51636816, 29387734}},
},
{
{{15636272, 23865875, 24204772, 25642034, 616976, 16869170,
- 27787599, 18782243, 28944399, 32004408}},
+ 27787599, 18782243, 28944399, 32004408}},
{{16568933, 4717097, 55552716, 32452109, 15682895, 21747389,
- 16354576, 21778470, 7689661, 11199574}},
+ 16354576, 21778470, 7689661, 11199574}},
{{30464137, 27578307, 55329429, 17883566, 23220364, 15915852,
- 7512774, 10017326, 49359771, 23634074}},
+ 7512774, 10017326, 49359771, 23634074}},
},
{
{{50071967, 13921891, 10945806, 27521001, 27105051, 17470053,
- 38182653, 15006022, 3284568, 27277892}},
+ 38182653, 15006022, 3284568, 27277892}},
{{23599295, 25248385, 55915199, 25867015, 13236773, 10506355,
- 7464579, 9656445, 13059162, 10374397}},
+ 7464579, 9656445, 13059162, 10374397}},
{{7798537, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
- 29715387, 66467155, 33453106}},
+ 29715387, 66467155, 33453106}},
},
{
{{10861363, 11473154, 27284546, 1981175, 37044515, 12577860,
- 32867885, 14515107, 51670560, 10819379}},
+ 32867885, 14515107, 51670560, 10819379}},
{{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
- 12483687, 54440373, 5581305}},
+ 12483687, 54440373, 5581305}},
{{19563141, 16186464, 37722007, 4097518, 10237984, 29206317,
- 28542349, 13850243, 43430843, 17738489}},
+ 28542349, 13850243, 43430843, 17738489}},
},
{
{{51736881, 20691677, 32573249, 4720197, 40672342, 5875510,
- 47920237, 18329612, 57289923, 21468654}},
+ 47920237, 18329612, 57289923, 21468654}},
{{58559652, 109982, 15149363, 2178705, 22900618, 4543417, 3044240,
- 17864545, 1762327, 14866737}},
+ 17864545, 1762327, 14866737}},
{{48909169, 17603008, 56635573, 1707277, 49922944, 3916100,
- 38872452, 3959420, 27914454, 4383652}},
+ 38872452, 3959420, 27914454, 4383652}},
},
{
{{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
- 5230134, 43156425, 18378665}},
+ 5230134, 43156425, 18378665}},
{{36839857, 30090922, 7665485, 10083793, 28475525, 1649722,
- 20654025, 16520125, 30598449, 7715701}},
- {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315,
- 35708204, 1370707, 29794553, 32145132}},
+ 20654025, 16520125, 30598449, 7715701}},
+ {{28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
+ 1370707, 29794553, 32145132}},
},
{
{{14499471, 30824833, 33917750, 29299779, 28494861, 14271267,
- 30290735, 10876454, 33954766, 2381725}},
- {{59913433, 30899068, 52378708, 462250, 39384538, 3941371,
- 60872247, 3696004, 34808032, 15351954}},
+ 30290735, 10876454, 33954766, 2381725}},
+ {{59913433, 30899068, 52378708, 462250, 39384538, 3941371, 60872247,
+ 3696004, 34808032, 15351954}},
{{27431194, 8222322, 16448760, 29646437, 48401861, 11938354,
- 34147463, 30583916, 29551812, 10109425}},
+ 34147463, 30583916, 29551812, 10109425}},
},
},
{
{
{{53451805, 20399000, 35825113, 11777097, 21447386, 6519384,
- 64730580, 31926875, 10092782, 28790261}},
+ 64730580, 31926875, 10092782, 28790261}},
{{27939166, 14210322, 4677035, 16277044, 44144402, 21156292,
- 34600109, 12005537, 49298737, 12803509}},
+ 34600109, 12005537, 49298737, 12803509}},
{{17228999, 17892808, 65875336, 300139, 65883994, 21839654,
- 30364212, 24516238, 18016356, 4397660}},
+ 30364212, 24516238, 18016356, 4397660}},
},
{
{{56150021, 25864224, 4776340, 18600194, 27850027, 17952220,
- 40489757, 14544524, 49631360, 982638}},
- {{29253598, 15796703, 64244882, 23645547, 10057022, 3163536, 7332899,
- 29434304, 46061167, 9934962}},
+ 40489757, 14544524, 49631360, 982638}},
+ {{29253598, 15796703, 64244882, 23645547, 10057022, 3163536,
+ 7332899, 29434304, 46061167, 9934962}},
{{5793284, 16271923, 42977250, 23438027, 29188559, 1206517,
- 52360934, 4559894, 36984942, 22656481}},
+ 52360934, 4559894, 36984942, 22656481}},
},
{
{{39464912, 22061425, 16282656, 22517939, 28414020, 18542168,
- 24191033, 4541697, 53770555, 5500567}},
+ 24191033, 4541697, 53770555, 5500567}},
{{12650548, 32057319, 9052870, 11355358, 49428827, 25154267,
- 49678271, 12264342, 10874051, 13524335}},
+ 49678271, 12264342, 10874051, 13524335}},
{{25556948, 30508442, 714650, 2510400, 23394682, 23139102, 33119037,
- 5080568, 44580805, 5376627}},
+ 5080568, 44580805, 5376627}},
},
{
{{41020600, 29543379, 50095164, 30016803, 60382070, 1920896,
- 44787559, 24106988, 4535767, 1569007}},
+ 44787559, 24106988, 4535767, 1569007}},
{{64853442, 14606629, 45416424, 25514613, 28430648, 8775819,
- 36614302, 3044289, 31848280, 12543772}},
+ 36614302, 3044289, 31848280, 12543772}},
{{45080285, 2943892, 35251351, 6777305, 13784462, 29262229,
- 39731668, 31491700, 7718481, 14474653}},
+ 39731668, 31491700, 7718481, 14474653}},
},
{
{{2385296, 2454213, 44477544, 46602, 62670929, 17874016, 656964,
- 26317767, 24316167, 28300865}},
+ 26317767, 24316167, 28300865}},
{{13741529, 10911568, 33875447, 24950694, 46931033, 32521134,
- 33040650, 20129900, 46379407, 8321685}},
+ 33040650, 20129900, 46379407, 8321685}},
{{21060490, 31341688, 15712756, 29218333, 1639039, 10656336,
- 23845965, 21679594, 57124405, 608371}},
+ 23845965, 21679594, 57124405, 608371}},
},
{
{{53436132, 18466845, 56219170, 25997372, 61071954, 11305546,
- 1123968, 26773855, 27229398, 23887}},
+ 1123968, 26773855, 27229398, 23887}},
{{43864724, 33260226, 55364135, 14712570, 37643165, 31524814,
- 12797023, 27114124, 65475458, 16678953}},
- {{37608244, 4770661, 51054477, 14001337, 7830047, 9564805,
- 65600720, 28759386, 49939598, 4904952}},
+ 12797023, 27114124, 65475458, 16678953}},
+ {{37608244, 4770661, 51054477, 14001337, 7830047, 9564805, 65600720,
+ 28759386, 49939598, 4904952}},
},
{
{{24059538, 14617003, 19037157, 18514524, 19766092, 18648003,
- 5169210, 16191880, 2128236, 29227599}},
+ 5169210, 16191880, 2128236, 29227599}},
{{50127693, 4124965, 58568254, 22900634, 30336521, 19449185,
- 37302527, 916032, 60226322, 30567899}},
+ 37302527, 916032, 60226322, 30567899}},
{{44477957, 12419371, 59974635, 26081060, 50629959, 16739174,
- 285431, 2763829, 15736322, 4143876}},
+ 285431, 2763829, 15736322, 4143876}},
},
{
{{2379333, 11839345, 62998462, 27565766, 11274297, 794957, 212801,
- 18959769, 23527083, 17096164}},
+ 18959769, 23527083, 17096164}},
{{33431108, 22423954, 49269897, 17927531, 8909498, 8376530,
- 34483524, 4087880, 51919953, 19138217}},
+ 34483524, 4087880, 51919953, 19138217}},
{{1767664, 7197987, 53903638, 31531796, 54017513, 448825, 5799055,
- 4357868, 62334673, 17231393}},
+ 4357868, 62334673, 17231393}},
},
},
{
{
{{6721966, 13833823, 43585476, 32003117, 26354292, 21691111,
- 23365146, 29604700, 7390889, 2759800}},
+ 23365146, 29604700, 7390889, 2759800}},
{{4409022, 2052381, 23373853, 10530217, 7676779, 20668478, 21302352,
- 29290375, 1244379, 20634787}},
- {{62687625, 7169618, 4982368, 30596842, 30256824, 30776892, 14086412,
- 9208236, 15886429, 16489664}},
+ 29290375, 1244379, 20634787}},
+ {{62687625, 7169618, 4982368, 30596842, 30256824, 30776892,
+ 14086412, 9208236, 15886429, 16489664}},
},
{
{{1996056, 10375649, 14346367, 13311202, 60234729, 17116020,
- 53415665, 398368, 36502409, 32841498}},
+ 53415665, 398368, 36502409, 32841498}},
{{41801399, 9795879, 64331450, 14878808, 33577029, 14780362,
- 13348553, 12076947, 36272402, 5113181}},
+ 13348553, 12076947, 36272402, 5113181}},
{{49338080, 11797795, 31950843, 13929123, 41220562, 12288343,
- 36767763, 26218045, 13847710, 5387222}},
+ 36767763, 26218045, 13847710, 5387222}},
},
{
{{48526701, 30138214, 17824842, 31213466, 22744342, 23111821,
- 8763060, 3617786, 47508202, 10370990}},
+ 8763060, 3617786, 47508202, 10370990}},
{{20246567, 19185054, 22358228, 33010720, 18507282, 23140436,
- 14554436, 24808340, 32232923, 16763880}},
+ 14554436, 24808340, 32232923, 16763880}},
{{9648486, 10094563, 26416693, 14745928, 36734546, 27081810,
- 11094160, 15689506, 3140038, 17044340}},
+ 11094160, 15689506, 3140038, 17044340}},
},
{
- {{50948792, 5472694, 31895588, 4744994, 8823515, 10365685,
- 39884064, 9448612, 38334410, 366294}},
+ {{50948792, 5472694, 31895588, 4744994, 8823515, 10365685, 39884064,
+ 9448612, 38334410, 366294}},
{{19153450, 11523972, 56012374, 27051289, 42461232, 5420646,
- 28344573, 8041113, 719605, 11671788}},
+ 28344573, 8041113, 719605, 11671788}},
{{8678006, 2694440, 60300850, 2517371, 4964326, 11152271, 51675948,
- 18287915, 27000812, 23358879}},
+ 18287915, 27000812, 23358879}},
},
{
{{51950941, 7134311, 8639287, 30739555, 59873175, 10421741, 564065,
- 5336097, 6750977, 19033406}},
+ 5336097, 6750977, 19033406}},
{{11836410, 29574944, 26297893, 16080799, 23455045, 15735944,
- 1695823, 24735310, 8169719, 16220347}},
+ 1695823, 24735310, 8169719, 16220347}},
{{48993007, 8653646, 17578566, 27461813, 59083086, 17541668,
- 55964556, 30926767, 61118155, 19388398}},
+ 55964556, 30926767, 61118155, 19388398}},
},
{
{{43800366, 22586119, 15213227, 23473218, 36255258, 22504427,
- 27884328, 2847284, 2655861, 1738395}},
+ 27884328, 2847284, 2655861, 1738395}},
{{39571412, 19301410, 41772562, 25551651, 57738101, 8129820,
- 21651608, 30315096, 48021414, 22549153}},
+ 21651608, 30315096, 48021414, 22549153}},
{{1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092,
- 5821408, 10478196, 8544890}},
+ 5821408, 10478196, 8544890}},
},
{
{{32173102, 17425121, 24896206, 3921497, 22579056, 30143578,
- 19270448, 12217473, 17789017, 30158437}},
+ 19270448, 12217473, 17789017, 30158437}},
{{36555903, 31326030, 51530034, 23407230, 13243888, 517024,
- 15479401, 29701199, 30460519, 1052596}},
+ 15479401, 29701199, 30460519, 1052596}},
{{55493970, 13323617, 32618793, 8175907, 51878691, 12596686,
- 27491595, 28942073, 3179267, 24075541}},
+ 27491595, 28942073, 3179267, 24075541}},
},
{
{{31947050, 19187781, 62468280, 18214510, 51982886, 27514722,
- 52352086, 17142691, 19072639, 24043372}},
+ 52352086, 17142691, 19072639, 24043372}},
{{11685058, 11822410, 3158003, 19601838, 33402193, 29389366,
- 5977895, 28339415, 473098, 5040608}},
+ 5977895, 28339415, 473098, 5040608}},
{{46817982, 8198641, 39698732, 11602122, 1290375, 30754672,
- 28326861, 1721092, 47550222, 30422825}},
+ 28326861, 1721092, 47550222, 30422825}},
},
},
{
{
{{7881532, 10687937, 7578723, 7738378, 48157852, 31000479, 21820785,
- 8076149, 39240368, 11538388}},
+ 8076149, 39240368, 11538388}},
{{47173198, 3899860, 18283497, 26752864, 51380203, 22305220,
- 8754524, 7446702, 61432810, 5797015}},
+ 8754524, 7446702, 61432810, 5797015}},
{{55813245, 29760862, 51326753, 25589858, 12708868, 25098233,
- 2014098, 24503858, 64739691, 27677090}},
+ 2014098, 24503858, 64739691, 27677090}},
},
{
{{44636488, 21985690, 39426843, 1146374, 18956691, 16640559,
- 1192730, 29840233, 15123618, 10811505}},
- {{14352079, 30134717, 48166819, 10822654, 32750596, 4699007, 67038501,
- 15776355, 38222085, 21579878}},
+ 1192730, 29840233, 15123618, 10811505}},
+ {{14352079, 30134717, 48166819, 10822654, 32750596, 4699007,
+ 67038501, 15776355, 38222085, 21579878}},
{{38867681, 25481956, 62129901, 28239114, 29416930, 1847569,
- 46454691, 17069576, 4714546, 23953777}},
+ 46454691, 17069576, 4714546, 23953777}},
},
{
{{15200332, 8368572, 19679101, 15970074, 35236190, 1959450,
- 24611599, 29010600, 55362987, 12340219}},
+ 24611599, 29010600, 55362987, 12340219}},
{{12876937, 23074376, 33134380, 6590940, 60801088, 14872439,
- 9613953, 8241152, 15370987, 9608631}},
- {{62965568, 21540023, 8446280, 33162829, 4407737, 13629032, 59383996,
- 15866073, 38898243, 24740332}},
+ 9613953, 8241152, 15370987, 9608631}},
+ {{62965568, 21540023, 8446280, 33162829, 4407737, 13629032,
+ 59383996, 15866073, 38898243, 24740332}},
},
{
{{26660628, 17876777, 8393733, 358047, 59707573, 992987, 43204631,
- 858696, 20571223, 8420556}},
+ 858696, 20571223, 8420556}},
{{14620696, 13067227, 51661590, 8264466, 14106269, 15080814,
- 33531827, 12516406, 45534429, 21077682}},
+ 33531827, 12516406, 45534429, 21077682}},
{{236881, 10476226, 57258, 18877408, 6472997, 2466984, 17258519,
- 7256740, 8791136, 15069930}},
+ 7256740, 8791136, 15069930}},
},
{
{{1276391, 24182514, 22949634, 17231625, 43615824, 27852245,
- 14711874, 4874229, 36445724, 31223040}},
+ 14711874, 4874229, 36445724, 31223040}},
{{5855666, 4990204, 53397016, 7294283, 59304582, 1924646, 65685689,
- 25642053, 34039526, 9234252}},
+ 25642053, 34039526, 9234252}},
{{20590503, 24535444, 31529743, 26201766, 64402029, 10650547,
- 31559055, 21944845, 18979185, 13396066}},
+ 31559055, 21944845, 18979185, 13396066}},
},
{
{{24474287, 4968103, 22267082, 4407354, 24063882, 25229252,
- 48291976, 13594781, 33514650, 7021958}},
+ 48291976, 13594781, 33514650, 7021958}},
{{55541958, 26988926, 45743778, 15928891, 40950559, 4315420,
- 41160136, 29637754, 45628383, 12868081}},
+ 41160136, 29637754, 45628383, 12868081}},
{{38473832, 13504660, 19988037, 31421671, 21078224, 6443208,
- 45662757, 2244499, 54653067, 25465048}},
+ 45662757, 2244499, 54653067, 25465048}},
},
{
{{36513336, 13793478, 61256044, 319135, 41385692, 27290532,
- 33086545, 8957937, 51875216, 5540520}},
+ 33086545, 8957937, 51875216, 5540520}},
{{55478669, 22050529, 58989363, 25911358, 2620055, 1022908,
- 43398120, 31985447, 50980335, 18591624}},
+ 43398120, 31985447, 50980335, 18591624}},
{{23152952, 775386, 27395463, 14006635, 57407746, 4649511, 1689819,
- 892185, 55595587, 18348483}},
+ 892185, 55595587, 18348483}},
},
{
{{9770129, 9586738, 26496094, 4324120, 1556511, 30004408, 27453818,
- 4763127, 47929250, 5867133}},
+ 4763127, 47929250, 5867133}},
{{34343820, 1927589, 31726409, 28801137, 23962433, 17534932,
- 27846558, 5931263, 37359161, 17445976}},
+ 27846558, 5931263, 37359161, 17445976}},
{{27461885, 30576896, 22380809, 1815854, 44075111, 30522493,
- 7283489, 18406359, 47582163, 7734628}},
+ 7283489, 18406359, 47582163, 7734628}},
},
},
{
{
{{59098600, 23963614, 55988460, 6196037, 29344158, 20123547,
- 7585294, 30377806, 18549496, 15302069}},
+ 7585294, 30377806, 18549496, 15302069}},
{{34450527, 27383209, 59436070, 22502750, 6258877, 13504381,
- 10458790, 27135971, 58236621, 8424745}},
+ 10458790, 27135971, 58236621, 8424745}},
{{24687186, 8613276, 36441818, 30320886, 1863891, 31723888,
- 19206233, 7134917, 55824382, 32725512}},
+ 19206233, 7134917, 55824382, 32725512}},
},
{
{{11334899, 24336410, 8025292, 12707519, 17523892, 23078361,
- 10243737, 18868971, 62042829, 16498836}},
- {{8911542, 6887158, 57524604, 26595841, 11145640, 24010752, 17303924,
- 19430194, 6536640, 10543906}},
+ 10243737, 18868971, 62042829, 16498836}},
+ {{8911542, 6887158, 57524604, 26595841, 11145640, 24010752,
+ 17303924, 19430194, 6536640, 10543906}},
{{38162480, 15479762, 49642029, 568875, 65611181, 11223453,
- 64439674, 16928857, 39873154, 8876770}},
+ 64439674, 16928857, 39873154, 8876770}},
},
{
{{41365946, 20987567, 51458897, 32707824, 34082177, 32758143,
- 33627041, 15824473, 66504438, 24514614}},
+ 33627041, 15824473, 66504438, 24514614}},
{{10330056, 70051, 7957388, 24551765, 9764901, 15609756, 27698697,
- 28664395, 1657393, 3084098}},
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{{66923210, 9921304, 31456609, 20017994, 55095045, 13348922,
- 33142652, 6546660, 47123585, 29606055}},
+ 33142652, 6546660, 47123585, 29606055}},
},
{
{{34648249, 11266711, 55911757, 25655328, 31703693, 3855903,
- 58571733, 20721383, 36336829, 18068118}},
+ 58571733, 20721383, 36336829, 18068118}},
{{49102387, 12709067, 3991746, 27075244, 45617340, 23004006,
- 35973516, 17504552, 10928916, 3011958}},
+ 35973516, 17504552, 10928916, 3011958}},
{{60151107, 17960094, 31696058, 334240, 29576716, 14796075,
- 36277808, 20749251, 18008030, 10258577}},
+ 36277808, 20749251, 18008030, 10258577}},
},
{
{{44660220, 15655568, 7018479, 29144429, 36794597, 32352840,
- 65255398, 1367119, 25127874, 6671743}},
+ 65255398, 1367119, 25127874, 6671743}},
{{29701166, 19180498, 56230743, 9279287, 67091296, 13127209,
- 21382910, 11042292, 25838796, 4642684}},
+ 21382910, 11042292, 25838796, 4642684}},
{{46678630, 14955536, 42982517, 8124618, 61739576, 27563961,
- 30468146, 19653792, 18423288, 4177476}},
+ 30468146, 19653792, 18423288, 4177476}},
},
},
};
#endif // OPENSSL_SMALL
+// Bi[i] = (2*i+1)*B
static const ge_precomp Bi[8] = {
{
{{25967493, 19198397, 29566455, 3660896, 54414519, 4014786, 27544626,
- 21800161, 61029707, 2047604}},
+ 21800161, 61029707, 2047604}},
{{54563134, 934261, 64385954, 3049989, 66381436, 9406985, 12720692,
- 5043384, 19500929, 18085054}},
+ 5043384, 19500929, 18085054}},
{{58370664, 4489569, 9688441, 18769238, 10184608, 21191052, 29287918,
- 11864899, 42594502, 29115885}},
+ 11864899, 42594502, 29115885}},
},
{
{{15636272, 23865875, 24204772, 25642034, 616976, 16869170, 27787599,
- 18782243, 28944399, 32004408}},
+ 18782243, 28944399, 32004408}},
{{16568933, 4717097, 55552716, 32452109, 15682895, 21747389, 16354576,
- 21778470, 7689661, 11199574}},
+ 21778470, 7689661, 11199574}},
{{30464137, 27578307, 55329429, 17883566, 23220364, 15915852, 7512774,
- 10017326, 49359771, 23634074}},
+ 10017326, 49359771, 23634074}},
},
{
{{10861363, 11473154, 27284546, 1981175, 37044515, 12577860, 32867885,
- 14515107, 51670560, 10819379}},
+ 14515107, 51670560, 10819379}},
{{4708026, 6336745, 20377586, 9066809, 55836755, 6594695, 41455196,
- 12483687, 54440373, 5581305}},
+ 12483687, 54440373, 5581305}},
{{19563141, 16186464, 37722007, 4097518, 10237984, 29206317, 28542349,
- 13850243, 43430843, 17738489}},
+ 13850243, 43430843, 17738489}},
},
{
{{5153727, 9909285, 1723747, 30776558, 30523604, 5516873, 19480852,
- 5230134, 43156425, 18378665}},
+ 5230134, 43156425, 18378665}},
{{36839857, 30090922, 7665485, 10083793, 28475525, 1649722, 20654025,
- 16520125, 30598449, 7715701}},
+ 16520125, 30598449, 7715701}},
{{28881826, 14381568, 9657904, 3680757, 46927229, 7843315, 35708204,
- 1370707, 29794553, 32145132}},
+ 1370707, 29794553, 32145132}},
},
{
{{44589871, 26862249, 14201701, 24808930, 43598457, 8844725, 18474211,
- 32192982, 54046167, 13821876}},
+ 32192982, 54046167, 13821876}},
{{60653668, 25714560, 3374701, 28813570, 40010246, 22982724, 31655027,
- 26342105, 18853321, 19333481}},
+ 26342105, 18853321, 19333481}},
{{4566811, 20590564, 38133974, 21313742, 59506191, 30723862, 58594505,
- 23123294, 2207752, 30344648}},
+ 23123294, 2207752, 30344648}},
},
{
{{41954014, 29368610, 29681143, 7868801, 60254203, 24130566, 54671499,
- 32891431, 35997400, 17421995}},
+ 32891431, 35997400, 17421995}},
{{25576264, 30851218, 7349803, 21739588, 16472781, 9300885, 3844789,
- 15725684, 171356, 6466918}},
+ 15725684, 171356, 6466918}},
{{23103977, 13316479, 9739013, 17404951, 817874, 18515490, 8965338,
- 19466374, 36393951, 16193876}},
+ 19466374, 36393951, 16193876}},
},
{
{{33587053, 3180712, 64714734, 14003686, 50205390, 17283591, 17238397,
- 4729455, 49034351, 9256799}},
+ 4729455, 49034351, 9256799}},
{{41926547, 29380300, 32336397, 5036987, 45872047, 11360616, 22616405,
- 9761698, 47281666, 630304}},
+ 9761698, 47281666, 630304}},
{{53388152, 2639452, 42871404, 26147950, 9494426, 27780403, 60554312,
- 17593437, 64659607, 19263131}},
+ 17593437, 64659607, 19263131}},
},
{
{{63957664, 28508356, 9282713, 6866145, 35201802, 32691408, 48168288,
- 15033783, 25105118, 25659556}},
- {{42782475, 15950225, 35307649, 18961608, 55446126, 28463506,
- 1573891, 30928545, 2198789, 17749813}},
+ 15033783, 25105118, 25659556}},
+ {{42782475, 15950225, 35307649, 18961608, 55446126, 28463506, 1573891,
+ 30928545, 2198789, 17749813}},
{{64009494, 10324966, 64867251, 7453182, 61661885, 30818928, 53296841,
- 17317989, 34647629, 21263748}},
+ 17317989, 34647629, 21263748}},
},
};
diff --git a/third_party/fiat/make_curve25519_tables.py b/third_party/fiat/make_curve25519_tables.py
new file mode 100755
index 0000000..3318dbf
--- /dev/null
+++ b/third_party/fiat/make_curve25519_tables.py
@@ -0,0 +1,209 @@
+#!/usr/bin/env python
+# coding=utf-8
+# The MIT License (MIT)
+#
+# Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in all
+# copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+# SOFTWARE.
+
+import StringIO
+import subprocess
+
+# Base field Z_p
+p = 2**255 - 19
+
+def modp_inv(x):
+ return pow(x, p-2, p)
+
+# Compute corresponding x-coordinate, with low bit corresponding to
+# sign, or return None on failure
+def recover_x(y, sign):
+ if y >= p:
+ return None
+ x2 = (y*y-1) * modp_inv(d*y*y+1)
+ if x2 == 0:
+ if sign:
+ return None
+ else:
+ return 0
+
+ # Compute square root of x2
+ x = pow(x2, (p+3) // 8, p)
+ if (x*x - x2) % p != 0:
+ x = x * modp_sqrt_m1 % p
+ if (x*x - x2) % p != 0:
+ return None
+
+ if (x & 1) != sign:
+ x = p - x
+ return x
+
+# Curve constant
+d = -121665 * modp_inv(121666) % p
+
+# Base point
+g_y = 4 * modp_inv(5) % p
+g_x = recover_x(g_y, 0)
+
+# Points are represented as affine tuples (x, y).
+
+def point_add(P, Q):
+ x1, y1 = P
+ x2, y2 = Q
+ x3 = ((x1*y2 + y1*x2) * modp_inv(1 + d*x1*x2*y1*y2)) % p
+ y3 = ((y1*y2 + x1*x2) * modp_inv(1 - d*x1*x2*y1*y2)) % p
+ return (x3, y3)
+
+# Computes Q = s * P
+def point_mul(s, P):
+ Q = (0, 1) # Neutral element
+ while s > 0:
+ if s & 1:
+ Q = point_add(Q, P)
+ P = point_add(P, P)
+ s >>= 1
+ return Q
+
+def to_bytes(x):
+ ret = bytearray(32)
+ for i in range(len(ret)):
+ ret[i] = x % 256
+ x >>= 8
+ assert x == 0
+ return ret
+
+def to_ge_precomp(P):
+ # typedef struct {
+ # fe_loose yplusx;
+ # fe_loose yminusx;
+ # fe_loose xy2d;
+ # } ge_precomp;
+ x, y = P
+ return ((y + x) % p, (y - x) % p, (x * y * 2 * d) % p)
+
+def to_base_25_5(x):
+ limbs = (26, 25, 26, 25, 26, 25, 26, 25, 26, 25)
+ ret = []
+ for l in limbs:
+ ret.append(x & ((1<<l) - 1))
+ x >>= l
+ assert x == 0
+ return ret
+
+def main():
+ small_precomp = bytearray()
+ for i in range(1, 16):
+ s = (i&1) | ((i&2) << (64-1)) | ((i&4) << (128-2)) | ((i&8) << (192-3))
+ P = point_mul(s, (g_x, g_y))
+ small_precomp += to_bytes(P[0])
+ small_precomp += to_bytes(P[1])
+
+ large_precomp = []
+ for i in range(32):
+ large_precomp.append([])
+ for j in range(8):
+ P = point_mul((j + 1) << (i * 8), (g_x, g_y))
+ large_precomp[-1].append(to_ge_precomp(P))
+
+ bi_precomp = []
+ for i in range(8):
+ P = point_mul(2*i + 1, (g_x, g_y))
+ bi_precomp.append(to_ge_precomp(P))
+
+
+ buf = StringIO.StringIO()
+ buf.write("""// The MIT License (MIT)
+//
+// Copyright (c) 2015-2016 the fiat-crypto authors (see the AUTHORS file).
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+// This file is generated from
+// ./make_curve25519_tables.py > curve25519_tables.h
+
+
+#if defined(OPENSSL_SMALL)
+
+// This block of code replaces the standard base-point table with a much smaller
+// one. The standard table is 30,720 bytes while this one is just 960.
+//
+// This table contains 15 pairs of group elements, (x, y), where each field
+// element is serialised with |fe_tobytes|. If |i| is the index of the group
+// element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀
+// is the most significant bit). The value of the group element is then:
+// (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator.
+static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = {""")
+ for i, b in enumerate(small_precomp):
+ buf.write("0x%02x, " % b)
+ buf.write("""
+};
+
+#else
+
+// k25519Precomp[i][j] = (j+1)*256^i*B
+static const ge_precomp k25519Precomp[32][8] = {
+""")
+ for child in large_precomp:
+ buf.write("{\n")
+ for val in child:
+ buf.write("{\n")
+ for term in val:
+ buf.write("{{")
+ buf.write(", ".join(map(str, to_base_25_5(term))))
+ buf.write("}},\n")
+ buf.write("},\n")
+ buf.write("},\n")
+ buf.write("""};
+
+#endif // OPENSSL_SMALL
+
+// Bi[i] = (2*i+1)*B
+static const ge_precomp Bi[8] = {
+""")
+ for val in bi_precomp:
+ buf.write("{\n")
+ for term in val:
+ buf.write("{{")
+ buf.write(", ".join(map(str, to_base_25_5(term))))
+ buf.write("}},\n")
+ buf.write("},\n")
+ buf.write("""};
+""")
+
+ proc = subprocess.Popen(["clang-format"], stdin=subprocess.PIPE)
+ proc.communicate(buf.getvalue())
+
+if __name__ == "__main__":
+ main()
