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working out sign bugs; then on to invert elligator ristretto

master
Michael Hamburg 7 years ago
parent
2cc6ebfb67
commit
2d04fa7b43
10 changed files with 261 additions and 182 deletions
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  1. +3
    -1
      aux/ristretto/ristretto.sage
  2. +11
    -5
      src/GENERATED/c/curve25519/decaf.c
  3. +162
    -162
      src/GENERATED/c/curve25519/decaf_tables.c
  4. +10
    -4
      src/GENERATED/c/ed448goldilocks/decaf.c
  5. +6
    -0
      src/GENERATED/include/decaf/point_255.hxx
  6. +6
    -0
      src/GENERATED/include/decaf/point_448.hxx
  7. +3
    -1
      src/generator/curve_data.py
  8. +11
    -5
      src/per_curve/decaf.tmpl.c
  9. +6
    -0
      src/per_curve/point.tmpl.hxx
  10. +43
    -4
      test/ristretto.cxx

+ 3
- 1
aux/ristretto/ristretto.sage View File

@@ -49,7 +49,9 @@ def isqrt(x,exn=InvalidEncodingException("Not on curve")):
"""Return 1/sqrt(x)"""
if x==0: return 0
if not is_square(x): raise exn
return 1/sqrt(x)
s = sqrt(x)
if negative(s): s=-s
return 1/s

def isqrt_i(x):
"""Return 1/sqrt(x) or 1/sqrt(zeta * x)"""


+ 11
- 5
src/GENERATED/c/curve25519/decaf.c View File

@@ -49,7 +49,7 @@ static const scalar_t point_scalarmul_adjustment = {{{
const uint8_t decaf_x25519_base_point[DECAF_X25519_PUBLIC_BYTES] = { 0x09 };

static const gf RISTRETTO_ISOMAGIC = {{{
0x702557fa2bf03, 0x514b7d1a82cc6, 0x7f89efd8b43a7, 0x1aef49ec23700, 0x079376fa30500
0x0fdaa805d40ea, 0x2eb482e57d339, 0x007610274bc58, 0x6510b613dc8ff, 0x786c8905cfaff
}}};

#if COFACTOR==8 || EDDSA_USE_SIGMA_ISOGENY
@@ -247,7 +247,7 @@ decaf_error_t API_NS(point_decode) (
succ &= bool_to_mask(allow_identity) | ~gf_eq(s, ZERO);
succ &= ~gf_lobit(s);
gf_sqr(s2,s); /* s^2 */
gf_sqr(s2,s); /* s^2 = -as^2 */
#if IMAGINE_TWIST
gf_sub(s2,ZERO,s2); /* -as^2 */
#endif
@@ -1083,8 +1083,13 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, SQRT_ONE_MINUS_D );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
#endif
decaf_bzero(u,sizeof(u));
}
#elif IMAGINE_TWIST
@@ -1104,7 +1109,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_add( u, x, t );
gf_add( z, q->y, q->x );
gf_sqr ( y, z);
gf_sub ( y, u, y );
gf_sub ( y, y, u );
gf_sub ( z, t, x );
gf_sqr ( x, q->z );
gf_add ( t, x, x);
@@ -1163,7 +1168,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
succ &= gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
gf_cond_neg(p->x,~gf_lobit(p->x)^low);
gf_cond_neg(p->x,gf_lobit(p->x)^low);
gf_copy(p->z,ONE);
#if EDDSA_USE_SIGMA_ISOGENY
@@ -1232,6 +1237,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
decaf_bzero(enc2,sizeof(enc2));
assert(API_NS(point_valid)(p) || ~succ);
return decaf_succeed_if(mask_to_bool(succ));
}



+ 162
- 162
src/GENERATED/c/curve25519/decaf_tables.c View File

@@ -5,254 +5,254 @@

#define API_NS(_id) decaf_255_##_id
const API_NS(point_t) API_NS(point_base) = {{
{FIELD_LITERAL(0x0000485cca7e8859,0x00041dc396dfb8fc,0x0005584743ad3a93,0x0006ae1e23d9233c,0x00056f798c3a929c)},
{FIELD_LITERAL(0x0007b7a335817794,0x0003e23c69204703,0x0002a7b8bc52c56c,0x000151e1dc26dcc3,0x0002908673c56d63)},
{FIELD_LITERAL(0x0004ccccccccccc2,0x0001999999999999,0x0003333333333333,0x0006666666666666,0x0004cccccccccccc)},
{FIELD_LITERAL(0x0000000000000001,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000)},
{FIELD_LITERAL(0x0004f837acb251cf,0x0000dea88db96efd,0x00019b5df567eff2,0x00059babaf1be1f1,0x000342e2875657f7)}
{FIELD_LITERAL(0x000307c8534dae1e,0x0007215772469102,0x000664a20a98100d,0x0002645450e41e0e,0x0004bd1d78a9a808)}
}};
const gf API_NS(precomputed_base_as_fe)[144]
VECTOR_ALIGNED __attribute__((visibility("hidden"))) = {
{FIELD_LITERAL(0x000787c06838438e,0x000079b93ae8d43f,0x0006ce4230c8d2e4,0x0001e958b5ba51e1,0x000581f2251d4761)},
{FIELD_LITERAL(0x00028065bd02efcb,0x00072c06ae982429,0x0001a39392af7f7c,0x000398aaf36dab32,0x0004c8a8c4525fae)},
{FIELD_LITERAL(0x00006ff0bb7501fc,0x00044e6268755a4b,0x0007e0db395959b3,0x0005f7807150348a,0x00056f78b81a7a18)},
{FIELD_LITERAL(0x00013c159d969f7f,0x00038046e416d34a,0x00030a05d3333cd8,0x0003fc17afcf330a,0x0001456fcd6c2c06)},
{FIELD_LITERAL(0x000787c06838438e,0x000079b93ae8d43f,0x0006ce4230c8d2e4,0x0001e958b5ba51e1,0x000581f2251d4761)},
{FIELD_LITERAL(0x0007900f448afdf1,0x0003b19d978aa5b4,0x00001f24c6a6a64c,0x0002087f8eafcb75,0x0002908747e585e7)},
{FIELD_LITERAL(0x0001b3b052f3a00d,0x00050d154cc33fb6,0x000570a09253802b,0x0006af26330b8f09,0x000503fdb7977d73)},
{FIELD_LITERAL(0x0006efde66a0b284,0x0003f75278c5b57a,0x000615404a959ab1,0x0007366d656ec17f,0x00077638e2d52a04)},
{FIELD_LITERAL(0x00002d288a8a8e1c,0x000029f655eeea29,0x00069ca769b47ee2,0x0002d41c299b6574,0x0002fcdb7d8bda37)},
{FIELD_LITERAL(0x00013c159d969f7f,0x00038046e416d34a,0x00030a05d3333cd8,0x0003fc17afcf330a,0x0001456fcd6c2c06)},
{FIELD_LITERAL(0x00011021995f4d69,0x000408ad873a4a85,0x0001eabfb56a654e,0x0000c9929a913e80,0x000089c71d2ad5fb)},
{FIELD_LITERAL(0x0005883fa323a11e,0x000241047ad9c769,0x000233d3283fbb6d,0x000041bda7280e1d,0x00018a85382540f5)},
{FIELD_LITERAL(0x000398ee02172d95,0x00038f1cb6853c1d,0x00066b51fca8ad2e,0x00035176a3f540ea,0x00022227f7ee52d9)},
{FIELD_LITERAL(0x000790607ffeebfe,0x000725f8959cf0e0,0x00016b68dcd68a0f,0x00046f439e78680b,0x00026be3a14518fd)},
{FIELD_LITERAL(0x00002d288a8a8e1c,0x000029f655eeea29,0x00069ca769b47ee2,0x0002d41c299b6574,0x0002fcdb7d8bda37)},
{FIELD_LITERAL(0x00046711fde8d258,0x000470e3497ac3e2,0x000194ae035752d1,0x0004ae895c0abf15,0x0005ddd80811ad26)},
{FIELD_LITERAL(0x0002216f73946c7d,0x0000f4eb865cbfbf,0x0003c96750df440c,0x000655188ab63a68,0x0002a93e3b59098a)},
{FIELD_LITERAL(0x0004e738f3d06b92,0x0003dc62717f856b,0x0003e77175c6195f,0x000261d11fdad1f7,0x0003ff975f3e99ff)},
{FIELD_LITERAL(0x00031becbaeb1b98,0x0007912ee9ea6632,0x0004e42e201b640f,0x0007e5a0ef458ef1,0x000383f3cebfcbef)},
{FIELD_LITERAL(0x000790607ffeebfe,0x000725f8959cf0e0,0x00016b68dcd68a0f,0x00046f439e78680b,0x00026be3a14518fd)},
{FIELD_LITERAL(0x000318c70c2f945b,0x0004239d8e807a94,0x0004188e8a39e6a0,0x00059e2ee0252e08,0x00040068a0c16600)},
{FIELD_LITERAL(0x00004a9f30d26d26,0x0001838b85de7867,0x0006904531c39e2b,0x0000b5c478c98d49,0x0007d059931f87d8)},
{FIELD_LITERAL(0x000740d5eeae1f56,0x0004b490c85d90e3,0x000136df23a50d87,0x000495a021130ba9,0x0007d8b1c66d2535)},
{FIELD_LITERAL(0x000711d059bc6cef,0x0000ea1c699aeba1,0x0006371a8052c525,0x000699f87dd13a72,0x00021319ac452786)},
{FIELD_LITERAL(0x00031becbaeb1b98,0x0007912ee9ea6632,0x0004e42e201b640f,0x0007e5a0ef458ef1,0x000383f3cebfcbef)},
{FIELD_LITERAL(0x0000bf2a1151e097,0x00034b6f37a26f1c,0x0006c920dc5af278,0x00036a5fdeecf456,0x0000274e3992daca)},
{FIELD_LITERAL(0x0004179c92b1b0bb,0x00046e9ddba894d8,0x0001e24442ec9a91,0x0004c132a51620b3,0x0006d110187f3653)},
{FIELD_LITERAL(0x0004752d8b4757d6,0x0003037d1074a2a3,0x0003e42cfdb0ba8b,0x0002a28dce1000aa,0x00073a9ba5d3f201)},
{FIELD_LITERAL(0x000605edf6ba1a36,0x000013aba4619a54,0x0007ad04bb3634df,0x0007d3751dadf975,0x0007857a65f3ad25)},
{FIELD_LITERAL(0x000711d059bc6cef,0x0000ea1c699aeba1,0x0006371a8052c525,0x000699f87dd13a72,0x00021319ac452786)},
{FIELD_LITERAL(0x00038ad274b8a817,0x0004fc82ef8b5d5c,0x00041bd3024f4574,0x00055d7231efff55,0x0000c5645a2c0dfe)},
{FIELD_LITERAL(0x0003117ab7b95c2b,0x0000f4a313b2a63d,0x0006eb78029227ec,0x00043b924f138238,0x00073aad45f02122)},
{FIELD_LITERAL(0x0005c12191e279b9,0x00075a9e7e4e8c5d,0x0003a9d09d2551e0,0x0002d7e92ba557cc,0x000000a7d4499ac3)},
{FIELD_LITERAL(0x0005b75a63605042,0x0001fb3e9b1e1738,0x00054c87b6f7d7b6,0x0003b73e6812d3e8,0x000633794ff51d12)},
{FIELD_LITERAL(0x000605edf6ba1a36,0x000013aba4619a54,0x0007ad04bb3634df,0x0007d3751dadf975,0x0007857a65f3ad25)},
{FIELD_LITERAL(0x00023ede6e1d8634,0x0000a56181b173a2,0x0004562f62daae1f,0x00052816d45aa833,0x0007ff582bb6653c)},
{FIELD_LITERAL(0x00058b7c046273ac,0x0000464dc4a43f06,0x0004eb0e5479c3c5,0x00036c45d45ee21a,0x00047b89a5b4d946)},
{FIELD_LITERAL(0x0002c15e3b3687ba,0x0005209d2ce7fc91,0x0005773da0f5711a,0x00004d96ced4966e,0x0001fa8fc1035b8b)},
{FIELD_LITERAL(0x00075c8cfdf08431,0x0003e5ee1a32e561,0x00017f242d52abcb,0x00070b795ca26857,0x0002cb36d5df0af3)},
{FIELD_LITERAL(0x0005b75a63605042,0x0001fb3e9b1e1738,0x00054c87b6f7d7b6,0x0003b73e6812d3e8,0x000633794ff51d12)},
{FIELD_LITERAL(0x00053ea1c4c97833,0x0002df62d318036e,0x000288c25f0a8ee5,0x0007b269312b6991,0x000605703efca474)},
{FIELD_LITERAL(0x0006a3037380c025,0x0005f0b9e09cee4c,0x000333017642af74,0x00023fd62c2cfe7a,0x00070eee8fed21d2)},
{FIELD_LITERAL(0x0001744e9770fe63,0x0002635b0761a50e,0x0001322c61f83f00,0x00063be3797d570c,0x0005afe452e6b7e9)},
{FIELD_LITERAL(0x00005fff6e9b6af7,0x0003e58a55a575a1,0x000616d026c6eff2,0x000186a3124f745b,0x0002eec52ffe33c4)},
{FIELD_LITERAL(0x00075c8cfdf08431,0x0003e5ee1a32e561,0x00017f242d52abcb,0x00070b795ca26857,0x0002cb36d5df0af3)},
{FIELD_LITERAL(0x00068bb1688f018a,0x00059ca4f89e5af1,0x0006cdd39e07c0ff,0x0001c41c8682a8f3,0x0002501bad194816)},
{FIELD_LITERAL(0x0001ee0dff83b7ca,0x00022805e31c6873,0x0006fd7df7edeaef,0x0002f0f61779d562,0x0004deb8f2bacd10)},
{FIELD_LITERAL(0x0003df7b4c0f2a59,0x000302d0b8eb81a7,0x0001c2717df33aff,0x0006f3f90b3ffde9,0x0003428115ee6c46)},
{FIELD_LITERAL(0x0001ab77a68de949,0x0005da9c4d9a1ae9,0x0003ce86c23f9b7c,0x00007c893f16e3d9,0x000190c2b28c32a8)},
{FIELD_LITERAL(0x00005fff6e9b6af7,0x0003e58a55a575a1,0x000616d026c6eff2,0x000186a3124f745b,0x0002eec52ffe33c4)},
{FIELD_LITERAL(0x00042084b3f0d594,0x0004fd2f47147e58,0x00063d8e820cc500,0x00010c06f4c00216,0x0004bd7eea1193b9)},
{FIELD_LITERAL(0x0000bae92c40e17e,0x0004a8ef7ffd05e8,0x0005e3a63cc24e24,0x0001ed40c1f74c12,0x000258c0a1c13ff6)},
{FIELD_LITERAL(0x0001674175148292,0x00036d3d03e1f95c,0x00049ecbbb4c9924,0x000603782041936d,0x000521d1cc84c8d6)},
{FIELD_LITERAL(0x0004c7d5df621bb3,0x00063a78ba5518cb,0x00050af726ccf0a4,0x0003745ad4fb4c6d,0x0004b598e9a94c84)},
{FIELD_LITERAL(0x0001ab77a68de949,0x0005da9c4d9a1ae9,0x0003ce86c23f9b7c,0x00007c893f16e3d9,0x000190c2b28c32a8)},
{FIELD_LITERAL(0x000698be8aeb7d5b,0x000492c2fc1e06a3,0x0003613444b366db,0x0001fc87dfbe6c92,0x0002de2e337b3729)},
{FIELD_LITERAL(0x000546d94d9e537c,0x0001f783b157c7bb,0x00034c7f212657b4,0x0006ea763a87171a,0x00074beeb5597da9)},
{FIELD_LITERAL(0x00009c1897ee2bb3,0x00022cbd1740946f,0x00051e8f81dd639f,0x00044423bda03112,0x00025d54e5b5f216)},
{FIELD_LITERAL(0x00037efe726b959f,0x000251179afe0af9,0x00027abb104aaf2d,0x0000409b36a0b0c0,0x0007f20165baf2eb)},
{FIELD_LITERAL(0x0004c7d5df621bb3,0x00063a78ba5518cb,0x00050af726ccf0a4,0x0003745ad4fb4c6d,0x0004b598e9a94c84)},
{FIELD_LITERAL(0x000763e76811d43a,0x0005d342e8bf6b90,0x0002e1707e229c60,0x0003bbdc425fceed,0x0005a2ab1a4a0de9)},
{FIELD_LITERAL(0x0001e7dc70d2e455,0x00079f1c0b114486,0x0002b9b9c0211476,0x000420d65df5b9c1,0x0007ad32d88f4e65)},
{FIELD_LITERAL(0x0000f4d9cbd1dced,0x0000ca815a5fa452,0x00040cdd0b2e26d2,0x0005ab32035de1dc,0x0004387b97d56e74)},
{FIELD_LITERAL(0x0004282b73d9d3e6,0x0006f6ae3911c629,0x0007e698e17d290f,0x000064657542456d,0x00022eaf07413105)},
{FIELD_LITERAL(0x00037efe726b959f,0x000251179afe0af9,0x00027abb104aaf2d,0x0000409b36a0b0c0,0x0007f20165baf2eb)},
{FIELD_LITERAL(0x00070b26342e2300,0x0007357ea5a05bad,0x0003f322f4d1d92d,0x000254cdfca21e23,0x0003c784682a918b)},
{FIELD_LITERAL(0x0004d9e24bbb1c38,0x00001d0b9cb4f6e6,0x00008953dd712c89,0x00062f9f338dc8e9,0x0005b270d74b9a0b)},
{FIELD_LITERAL(0x000735ad38a70d62,0x0007c2c0047359b6,0x00053ecc0dd53647,0x0000fa507a3b1320,0x000362d0b0c5919d)},
{FIELD_LITERAL(0x0001e756ac51c2d7,0x0002fb982df272d3,0x0002bcba823c3ff6,0x00000e8c28e674f5,0x0001511ccec93f3e)},
{FIELD_LITERAL(0x0004282b73d9d3e6,0x0006f6ae3911c629,0x0007e698e17d290f,0x000064657542456d,0x00022eaf07413105)},
{FIELD_LITERAL(0x0000ca52c758f28b,0x00003d3ffb8ca649,0x0002c133f22ac9b8,0x000705af85c4ecdf,0x00049d2f4f3a6e62)},
{FIELD_LITERAL(0x0005d9d5f3a4d0f4,0x00014e0b6acbbb8a,0x0004c935dce28917,0x0004e84532fe74e9,0x0003532b26c5bdd3)},
{FIELD_LITERAL(0x0002c7c6bf08ea52,0x0004ce9cf3905bbd,0x0006eff528517cdf,0x00051c7e30819d9f,0x00078ddfe6e8eaf0)},
{FIELD_LITERAL(0x00040b28295a488c,0x00058f3942269291,0x0002eae04529af91,0x0005a950aa509a31,0x00051d13d423f3cc)},
{FIELD_LITERAL(0x0001e756ac51c2d7,0x0002fb982df272d3,0x0002bcba823c3ff6,0x00000e8c28e674f5,0x0001511ccec93f3e)},
{FIELD_LITERAL(0x0005383940f7159b,0x000331630c6fa442,0x0001100ad7ae8320,0x0002e381cf7e6260,0x000072201917150f)},
{FIELD_LITERAL(0x00075bbfd400a649,0x0002c84af6f7554f,0x00010589298f1c45,0x0002df1c4551d7a3,0x00040ada606a7008)},
{FIELD_LITERAL(0x0000cb4829d47de1,0x00035279e3dcb0f4,0x0000796e2b17fc93,0x0000f7471379a59e,0x0004cb38c4a47f2d)},
{FIELD_LITERAL(0x00063d326152d536,0x0001f0f272df8e88,0x00020d57f1ef5f0b,0x000049ae733cd741,0x000789b0bd910484)},
{FIELD_LITERAL(0x00040b28295a488c,0x00058f3942269291,0x0002eae04529af91,0x0005a950aa509a31,0x00051d13d423f3cc)},
{FIELD_LITERAL(0x000734b7d62b820c,0x0004ad861c234f0b,0x00078691d4e8036c,0x000708b8ec865a61,0x000334c73b5b80d2)},
{FIELD_LITERAL(0x00049e000de68a33,0x0002569532faf05e,0x0002c360e2577651,0x00023e58038a73d4,0x0005cfd1c66aa5db)},
{FIELD_LITERAL(0x0005219445517667,0x00052a931068f3ea,0x0006cc6f70494867,0x00050f70ab70bd44,0x0004939aea5e18ae)},
{FIELD_LITERAL(0x0002a678bc8c2008,0x0001fd399c8dcbff,0x0006dbf73cfc616e,0x00011a6e85d57176,0x00002f713757e057)},
{FIELD_LITERAL(0x00063d326152d536,0x0001f0f272df8e88,0x00020d57f1ef5f0b,0x000049ae733cd741,0x000789b0bd910484)},
{FIELD_LITERAL(0x0002de6bbaae8986,0x0002d56cef970c15,0x000133908fb6b798,0x0002f08f548f42bb,0x00036c6515a1e751)},
{FIELD_LITERAL(0x0006d9cd93b1ccdc,0x00043d4ce72bf50a,0x0003e999e2d35c59,0x00001ae0db65d2ee,0x0007c4b601137e07)},
{FIELD_LITERAL(0x0004bc6553755ebf,0x00056e8f93c8dfe2,0x000323b34a8ed19f,0x000571befc514dab,0x00036f0d981e9dde)},
{FIELD_LITERAL(0x000787c0309c0a03,0x0003dd7fb3241327,0x000256b73edcaac5,0x00071a11d2f00b44,0x0000f142397f3232)},
{FIELD_LITERAL(0x0002a678bc8c2008,0x0001fd399c8dcbff,0x0006dbf73cfc616e,0x00011a6e85d57176,0x00002f713757e057)},
{FIELD_LITERAL(0x0003439aac8aa12e,0x000291706c37201d,0x0004dc4cb5712e60,0x00028e4103aeb254,0x000490f267e16221)},
{FIELD_LITERAL(0x0006a965074f090a,0x000042537473c8c0,0x000479b523a03430,0x000302e712f49521,0x0001608d67c58b1d)},
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{FIELD_LITERAL(0x000679b185adb791,0x0003ccd7cdbcb48b,0x0001e6934282172d,0x000112213a7ca210,0x00045089bd5cfb9c)},
{FIELD_LITERAL(0x0002877a97e6aec5,0x00050083ca5fa04a,0x0006a401497d8419,0x0003ce63a2c47d37,0x00014809d3f5339b)},
{FIELD_LITERAL(0x00026e50855da5de,0x00004d0fc457ea77,0x0001e1f5e1f41496,0x000175c0cd2b4571,0x0001722f7954d4e2)},
{FIELD_LITERAL(0x000175bf84b82b29,0x00065e0ea17de536,0x0006b02a0010a208,0x0000bbfa9b7e8884,0x0003c21f98c815b6)},
{FIELD_LITERAL(0x0005788568195128,0x0002ff7c35a05fb5,0x00015bfeb6827be6,0x0004319c5d3b82c8,0x0006b7f62c0acc64)},
{FIELD_LITERAL(0x0007ac38211e7835,0x00063d213473cbbf,0x00005b9eada0052f,0x0003477219f26d7f,0x000453ce683f056f)},
{FIELD_LITERAL(0x000726f104629123,0x000482b184152205,0x00054242cd088a37,0x00032fb6be9f2837,0x000734ca9dc7f7c3)},
{FIELD_LITERAL(0x00062509dec41627,0x000072099496b712,0x0007712db0b3effb,0x0001e9c85c77fd36,0x0007f4ceff4f568c)},
{FIELD_LITERAL(0x00026e50855da5de,0x00004d0fc457ea77,0x0001e1f5e1f41496,0x000175c0cd2b4571,0x0001722f7954d4e2)},
{FIELD_LITERAL(0x0000d90efb9d6eca,0x00037d4e7beaddfa,0x0002bdbd32f775c8,0x0004d0494160d7c8,0x0000cb356238083c)},
{FIELD_LITERAL(0x0002b1990238e0e3,0x0006c1901505e91e,0x00019f32cc8628f9,0x00011218171b4b26,0x0006dbdb25ce79e2)},
{FIELD_LITERAL(0x0005370ef67b47ee,0x0001580466943896,0x0003297e2638eea5,0x000416db4e7a73ef,0x0004b3ce39e7ef57)},
{FIELD_LITERAL(0x00071cc5c1b2d84d,0x0003fa3f1fe5ba11,0x0004520e1812cf04,0x000612f4378d5d14,0x00019041e8a9771c)},
{FIELD_LITERAL(0x00062509dec41627,0x000072099496b712,0x0007712db0b3effb,0x0001e9c85c77fd36,0x0007f4ceff4f568c)},
{FIELD_LITERAL(0x0002c8f10984b7ff,0x0006a7fb996bc769,0x0004d681d9c7115a,0x0003e924b1858c10,0x00034c31c61810a8)},
{FIELD_LITERAL(0x00037a9adac7f13d,0x0004513446d45ac8,0x0004862022a5e9c2,0x00046d1fee26d322,0x00050314790c0eb5)},
{FIELD_LITERAL(0x00009f958ec7782b,0x000532691db95f11,0x0000787b85edae84,0x0003347ccb5b1b48,0x00048f02d0fe2f5f)},
{FIELD_LITERAL(0x0001bd035445c3cb,0x00020697cdb801da,0x00027c9cd108f106,0x0007f03792eba8ff,0x000785b24c8954e8)},
{FIELD_LITERAL(0x00071cc5c1b2d84d,0x0003fa3f1fe5ba11,0x0004520e1812cf04,0x000612f4378d5d14,0x00019041e8a9771c)},
{FIELD_LITERAL(0x0007606a713887c2,0x0002cd96e246a0ee,0x000787847a12517b,0x0004cb8334a4e4b7,0x000370fd2f01d0a0)},
{FIELD_LITERAL(0x0003d9815d5b1459,0x00079cc56b9e7bce,0x00072c9f1a31c024,0x00053d9b96409fbf,0x0003527718dcab2f)},
{FIELD_LITERAL(0x00003c0929520d8a,0x0005b4e8fb91f6d2,0x0003f2da27d5d5df,0x0001c4bb87d9118d,0x00026b9976202bed)},
{FIELD_LITERAL(0x000395fd8480a669,0x0001dc9000e23bd0,0x000065404c59dfc6,0x000125765d7383d3,0x0000c7ff2cbfdb58)},
{FIELD_LITERAL(0x0001bd035445c3cb,0x00020697cdb801da,0x00027c9cd108f106,0x0007f03792eba8ff,0x000785b24c8954e8)},
{FIELD_LITERAL(0x0007c3f6d6adf263,0x00024b17046e092d,0x00040d25d82a2a20,0x00063b447826ee72,0x0005946689dfd412)},
{FIELD_LITERAL(0x00038f76c23acfef,0x0005a6ffbb722028,0x0000ce1434dbd9ba,0x000128b22b63ce7d,0x0007e28492f0e311)},
{FIELD_LITERAL(0x0004ef6dec07d978,0x0001814721d17298,0x0002f3010824e385,0x0004dec0df1030ea,0x000732ccad416ca1)}
{FIELD_LITERAL(0x000395fd8480a669,0x0001dc9000e23bd0,0x000065404c59dfc6,0x000125765d7383d3,0x0000c7ff2cbfdb58)},
{FIELD_LITERAL(0x0003109213f82675,0x00067eb8de2e8d67,0x00050cfef7db1c7a,0x0003213f20efcf15,0x0000cd3352be935e)}
};
const gf API_NS(precomputed_wnaf_as_fe)[96]
VECTOR_ALIGNED __attribute__((visibility("hidden"))) = {
{FIELD_LITERAL(0x000642380127222b,0x0006bdeb015cf04e,0x0006ed75f7c2fc4f,0x0007dc242146a194,0x0003aea9a0491d17)},
{FIELD_LITERAL(0x00068a94cba5aa97,0x0002dbae983ca94a,0x000445bd3b7036e3,0x00068a42451fc4d1,0x00011e232c83afb4)},
{FIELD_LITERAL(0x00025391b7203b96,0x000347c30d05c477,0x0007c933299a261d,0x00041480324ee8a6,0x00064ca19224efdf)},
{FIELD_LITERAL(0x0005870a7d58f0a0,0x0001b114a243c47e,0x00041892d3f588cf,0x0000dd81de11287e,0x00017356a5582dd5)},
{FIELD_LITERAL(0x000642380127222b,0x0006bdeb015cf04e,0x0006ed75f7c2fc4f,0x0007dc242146a194,0x0003aea9a0491d17)},
{FIELD_LITERAL(0x0005ac6e48dfc457,0x0004b83cf2fa3b88,0x000036ccd665d9e2,0x0003eb7fcdb11759,0x0001b35e6ddb1020)},
{FIELD_LITERAL(0x00010182955b295c,0x00066c5c9ffd69b2,0x00061b151a710972,0x000283e92443fc68,0x0006d37a5c5e317b)},
{FIELD_LITERAL(0x00036a7b29fa190d,0x0006935273c5f4eb,0x00054075caf2ffbd,0x00014270ef756d90,0x000533e2a110cfc9)},
{FIELD_LITERAL(0x0001629db13df925,0x0005b8e4096d6111,0x0003f69f6e1fa07d,0x0000ad2fb64a4e21,0x0003804eca6f1a1b)},
{FIELD_LITERAL(0x0005870a7d58f0a0,0x0001b114a243c47e,0x00041892d3f588cf,0x0000dd81de11287e,0x00017356a5582dd5)},
{FIELD_LITERAL(0x00049584d605e6e0,0x00016cad8c3a0b14,0x0002bf8a350d0042,0x0006bd8f108a926f,0x0002cc1d5eef3036)},
{FIELD_LITERAL(0x00004152d30c2a52,0x0002c24984123284,0x00042e97ac31b344,0x00019fefd67353e1,0x0004e8cd7188a7e4)},
{FIELD_LITERAL(0x00045570b5e270ed,0x0005573633198d89,0x0007ca223ccd5afc,0x0007869c9de046c4,0x00069e89310811bf)},
{FIELD_LITERAL(0x0006d9d11e7eae02,0x0000be17c117a8e5,0x0005bd1bacc035a8,0x00055263e886a24c,0x0004f490d4442b45)},
{FIELD_LITERAL(0x0001629db13df925,0x0005b8e4096d6111,0x0003f69f6e1fa07d,0x0000ad2fb64a4e21,0x0003804eca6f1a1b)},
{FIELD_LITERAL(0x0003aa8f4a1d8f00,0x0002a8c9cce67276,0x000035ddc332a503,0x00007963621fb93b,0x00016176cef7ee40)},
{FIELD_LITERAL(0x000011c8b01f8feb,0x0007bf1c4cb192c2,0x000326354b21cbf2,0x000488390b6dfc94,0x0005ba34838ba4de)},
{FIELD_LITERAL(0x0007c67ff54be7cc,0x0007da997c07b329,0x00035eca964abf79,0x000706e02cff65ab,0x0007cd234d25af3c)},
{FIELD_LITERAL(0x0001fb4c93b5f593,0x0007144dc0cada1e,0x0000d50f94b1cb97,0x0006df9cbaf29c61,0x0003edfa4c8c2b32)},
{FIELD_LITERAL(0x0006d9d11e7eae02,0x0000be17c117a8e5,0x0005bd1bacc035a8,0x00055263e886a24c,0x0004f490d4442b45)},
{FIELD_LITERAL(0x000039800ab41821,0x0000256683f84cd6,0x0004a13569b54086,0x0000f91fd3009a54,0x000032dcb2da50c3)},
{FIELD_LITERAL(0x0007271443c9ba84,0x00016f294c6baac0,0x00044dfa59cab659,0x0002fe9702828a2a,0x0007db9144c036dd)},
{FIELD_LITERAL(0x00047163cd6e88a8,0x0003c312ab4945e1,0x0003021e7db7375a,0x00055fbc7b3f6c06,0x000272ecf2d95b4e)},
{FIELD_LITERAL(0x00038b922c70ed29,0x000253866fc7c488,0x000576f12a312db9,0x00045d4f321497af,0x00018e5445d11403)},
{FIELD_LITERAL(0x0001fb4c93b5f593,0x0007144dc0cada1e,0x0000d50f94b1cb97,0x0006df9cbaf29c61,0x0003edfa4c8c2b32)},
{FIELD_LITERAL(0x00038e9c32917745,0x00043ced54b6ba1e,0x0004fde18248c8a5,0x0002a04384c093f9,0x00058d130d26a4b1)},
{FIELD_LITERAL(0x0003f8e7ccec15a0,0x00052340d38e8703,0x0001fe25f1ae8f20,0x0003ddd469f772d0,0x000462fbbea67ca2)},
{FIELD_LITERAL(0x00011da13f2e0e8c,0x0002aa8f508e1fd7,0x000412a7c33e7f8e,0x000350c2a112bd8f,0x0003903a4aae1e31)},
{FIELD_LITERAL(0x0007f9daed4a4867,0x0002b6b4ed700133,0x0002630bb5d53e2d,0x00052b6f0617a8d5,0x0003a71ea3b7dd75)},
{FIELD_LITERAL(0x00038b922c70ed29,0x000253866fc7c488,0x000576f12a312db9,0x00045d4f321497af,0x00018e5445d11403)},
{FIELD_LITERAL(0x0006e25ec0d1f161,0x00055570af71e028,0x0003ed583cc18071,0x0004af3d5eed4270,0x00046fc5b551e1ce)},
{FIELD_LITERAL(0x000784badf35d97a,0x000130c033b608d3,0x0004d1ca333b988c,0x00046996c1106167,0x00006cd17cb32faf)},
{FIELD_LITERAL(0x000017f0bb6265b4,0x0004b7b14a32f828,0x00038355613c060b,0x0002ff107843a525,0x00067859833d0bcf)},
{FIELD_LITERAL(0x0007efb1526681aa,0x0005d3f09cc25381,0x0005070ed313624a,0x0007dc7c70fcf2e6,0x00035f22ab001ece)},
{FIELD_LITERAL(0x0007f9daed4a4867,0x0002b6b4ed700133,0x0002630bb5d53e2d,0x00052b6f0617a8d5,0x0003a71ea3b7dd75)},
{FIELD_LITERAL(0x0007e80f449d9a39,0x0003484eb5cd07d7,0x00047caa9ec3f9f4,0x000500ef87bc5ada,0x000187a67cc2f430)},
{FIELD_LITERAL(0x0001d03d7131822b,0x00041269a071318a,0x00066b533c7c2f0e,0x00079eb2962ac445,0x0007c84f8b7d6434)},
{FIELD_LITERAL(0x0007bdf697319f65,0x000733aeaf20753c,0x0003e8ef6225fd72,0x0004a5b9853164cc,0x0007e0c9a1e3a2c0)},
{FIELD_LITERAL(0x0000ea923f718b41,0x0003ed3cdc5c1206,0x0007fcd7e9778042,0x000087a1037b0d5d,0x00007a7a0abbab1c)},
{FIELD_LITERAL(0x0007efb1526681aa,0x0005d3f09cc25381,0x0005070ed313624a,0x0007dc7c70fcf2e6,0x00035f22ab001ece)},
{FIELD_LITERAL(0x0000420968ce6088,0x0000cc5150df8ac3,0x000417109dda028d,0x00035a467ace9b33,0x00001f365e1c5d3f)},
{FIELD_LITERAL(0x0001f75504e732eb,0x00022ebe847278d8,0x0007ea9ffc7568b3,0x0005ce813453dcf8,0x000487735ef97869)},
{FIELD_LITERAL(0x0005724daa8d895d,0x0000dc4fb5cda1a1,0x0005caeaaa9fb58e,0x0002cc7ce3532d7a,0x00078cb9c16aa739)},
{FIELD_LITERAL(0x000132663b80f4fb,0x0003569bb0747910,0x0001254f43541bae,0x0005ef6302e41398,0x0000f0739e94acdc)},
{FIELD_LITERAL(0x0000ea923f718b41,0x0003ed3cdc5c1206,0x0007fcd7e9778042,0x000087a1037b0d5d,0x00007a7a0abbab1c)},
{FIELD_LITERAL(0x00028db255727690,0x000723b04a325e5e,0x0002351555604a71,0x000533831cacd285,0x000073463e9558c6)},
{FIELD_LITERAL(0x00062c278d9a1d30,0x000160f59d5d7ddb,0x0003a13c02fd4a4c,0x0003ae8e19ec0313,0x0007ff33d0402d0a)},
{FIELD_LITERAL(0x000779188d9101bd,0x0003907b5e2acb57,0x0000f2016ad328f1,0x0002563d8843c96e,0x000325477c857086)},
{FIELD_LITERAL(0x0002b91f27fd54d4,0x0006396d4db9c2ed,0x0001910e4a18d580,0x00013a22c5bab363,0x0007a440ee553a25)},
{FIELD_LITERAL(0x000132663b80f4fb,0x0003569bb0747910,0x0001254f43541bae,0x0005ef6302e41398,0x0000f0739e94acdc)},
{FIELD_LITERAL(0x000086e7726efe30,0x00046f84a1d534a8,0x00070dfe952cd70e,0x0005a9c277bc3691,0x0004dab8837a8f79)},
{FIELD_LITERAL(0x000490c21e746b15,0x00024b7059991174,0x00008ee694b74d75,0x0005e237b7856642,0x0007642c6cdb680c)},
{FIELD_LITERAL(0x0005dbf419ae9d74,0x00048e711fdf576f,0x00075068ca732b86,0x0006e8b996a54910,0x000772260ac3718e)},
{FIELD_LITERAL(0x000482565fa8a25b,0x0003df033dcf6602,0x00064e0f3b4e7074,0x00021b4575c116f5,0x0002208124f689de)},
{FIELD_LITERAL(0x0002b91f27fd54d4,0x0006396d4db9c2ed,0x0001910e4a18d580,0x00013a22c5bab363,0x0007a440ee553a25)},
{FIELD_LITERAL(0x0002240be6516279,0x0003718ee020a890,0x0000af97358cd479,0x00011746695ab6ef,0x00008dd9f53c8e71)},
{FIELD_LITERAL(0x0007585a86ebfdf4,0x0007b22f0200bb5d,0x0004c01c0570390b,0x00012d4f936a9ace,0x0007061937f48098)},
{FIELD_LITERAL(0x00058c8ef3313e8c,0x0004fe676de9150c,0x000071322bae837f,0x0004719a9c643417,0x0000b3d8da873b81)},
{FIELD_LITERAL(0x0004a783941354c6,0x0004a8dbae0192b1,0x00066e6e2284eb96,0x000328e80b25e8c3,0x000042a8e76bf4d5)},
{FIELD_LITERAL(0x000482565fa8a25b,0x0003df033dcf6602,0x00064e0f3b4e7074,0x00021b4575c116f5,0x0002208124f689de)},
{FIELD_LITERAL(0x000273710ccec161,0x000301989216eaf3,0x00078ecdd4517c80,0x00038e65639bcbe8,0x00074c272578c47e)},
{FIELD_LITERAL(0x0001d8c052051ec3,0x000366a48a8dd65b,0x0002a78e24295abf,0x000129d49470f3e6,0x0006c57172fbfc6f)},
{FIELD_LITERAL(0x00058858b562e4d4,0x0007aa756a9d33c0,0x0000d5156276e848,0x00053461aacbb1be,0x000003d03c677fca)},
{FIELD_LITERAL(0x0004ec9d19b70d7e,0x0006b590207bdecd,0x0001637d3bcc3bb3,0x00000c22df7f92fb,0x00041ea544c47cfa)},
{FIELD_LITERAL(0x0004a783941354c6,0x0004a8dbae0192b1,0x00066e6e2284eb96,0x000328e80b25e8c3,0x000042a8e76bf4d5)},
{FIELD_LITERAL(0x000277a74a9d1b19,0x0000558a9562cc3f,0x00072aea9d8917b7,0x0002cb9e55344e41,0x0007fc2fc3988035)},
{FIELD_LITERAL(0x0005bb2c05450730,0x000699da0443d31e,0x00029833797938dd,0x00047094e611ef5a,0x0003a80296f5af96)},
{FIELD_LITERAL(0x0001ac52918f4c8e,0x00070d18d98c3ff4,0x0003e5732b1553db,0x00072df46e974e9d,0x000122fb863fcfd7)},
{FIELD_LITERAL(0x00000849cf428975,0x000727067cad891a,0x0004f88f61de7005,0x00044257203c4bbb,0x0004c637329a0014)},
{FIELD_LITERAL(0x0004ec9d19b70d7e,0x0006b590207bdecd,0x0001637d3bcc3bb3,0x00000c22df7f92fb,0x00041ea544c47cfa)},
{FIELD_LITERAL(0x000653ad6e70b35f,0x0000f2e72673c00b,0x00041a8cd4eaac24,0x0000d20b9168b162,0x0006dd0479c03028)},
{FIELD_LITERAL(0x000765ea2cf96125,0x00020be964ac2553,0x0006542c16078fcd,0x0007e1c9a694af26,0x000670be61b828ab)},
{FIELD_LITERAL(0x0003e966dcdc760c,0x00047dd5a3cb73ac,0x00061d635f813625,0x0006d76efc6f57ba,0x00054decaca409ff)},
{FIELD_LITERAL(0x00006abffd1f9a07,0x0006a24984b59c94,0x00001c88b2d5ccab,0x00078756f923d472,0x000523ae194c2908)},
{FIELD_LITERAL(0x00000849cf428975,0x000727067cad891a,0x0004f88f61de7005,0x00044257203c4bbb,0x0004c637329a0014)},
{FIELD_LITERAL(0x00041699232389e1,0x0003822a5c348c53,0x0001e29ca07ec9da,0x000128910390a845,0x0002b213535bf600)},
{FIELD_LITERAL(0x000295f6aed6c95f,0x00063835a88edc2f,0x0000d413a8f5d2be,0x0006d19ac30fb51e,0x000209a4daa47af4)},
{FIELD_LITERAL(0x0007b3d422474c11,0x00035fd7bbd41a91,0x00038313d567d746,0x00044be2c7641673,0x0003cfb2e79b0db4)},
{FIELD_LITERAL(0x0007deb72bd44d2d,0x000739424ef1d75e,0x0004018d17e7a6b2,0x0007b6e2a9d39e87,0x000521ea05c6c6dd)},
{FIELD_LITERAL(0x00006abffd1f9a07,0x0006a24984b59c94,0x00001c88b2d5ccab,0x00078756f923d472,0x000523ae194c2908)},
{FIELD_LITERAL(0x00004c2bddb8b3dc,0x0004a028442be56e,0x00047cec2a9828b9,0x0003b41d389be98c,0x0004304d1864f24b)},
{FIELD_LITERAL(0x0001a5e807310023,0x00064308e578ea3e,0x00051e6fd6a01240,0x000274e880dadbdd,0x0001f551c726c373)},
{FIELD_LITERAL(0x0004d3ce8a1f77f7,0x0003167790f075b1,0x0004e6bce7f4a904,0x0004d2ccd17b0874,0x0007dd01b360f566)},
{FIELD_LITERAL(0x00073aa273d83a1f,0x000509605eef38e1,0x0002478a49a7bd9c,0x00037b4fffcc9a8f,0x0003de7bfae4d9c0)},
{FIELD_LITERAL(0x0007deb72bd44d2d,0x000739424ef1d75e,0x0004018d17e7a6b2,0x0007b6e2a9d39e87,0x000521ea05c6c6dd)},
{FIELD_LITERAL(0x00032c3175e087f6,0x0004e9886f0f8a4e,0x00031943180b56fb,0x00032d332e84f78b,0x000022fe4c9f0a99)},
{FIELD_LITERAL(0x00010ab29d20014a,0x0003dad754471f37,0x0005db76f33e4e9e,0x000233bcc4657dd9,0x00064a6db2e9a1a4)},
{FIELD_LITERAL(0x00061971ac718eb9,0x0002cedb4d83bc7c,0x000450581aa489e6,0x000085abee0c4ae9,0x000375e304315ad9)},
{FIELD_LITERAL(0x0004e69a3015eec3,0x00014f8520f65886,0x000603fe316ae01d,0x000266136364ded2,0x0001ca16145255d7)},
{FIELD_LITERAL(0x00073aa273d83a1f,0x000509605eef38e1,0x0002478a49a7bd9c,0x00037b4fffcc9a8f,0x0003de7bfae4d9c0)},
{FIELD_LITERAL(0x0001e68e538e7134,0x00053124b27c4383,0x0003afa7e55b7619,0x00077a5411f3b516,0x00048a1cfbcea526)},
{FIELD_LITERAL(0x000195b299aaa7a2,0x00029dcb30ab6966,0x0007db5d6559e7e8,0x0003080db154f47f,0x00039c84ee5affcf)},
{FIELD_LITERAL(0x00021a432b19e270,0x0006448861623f70,0x0004383a5006d140,0x000426de3a89b443,0x0001296a8b73e4ab)},
{FIELD_LITERAL(0x00026b6e1920377f,0x0001fe04f05868d1,0x00035b308dd430aa,0x0004a38a5bd39fc2,0x0007a2a54f12cec0)},
{FIELD_LITERAL(0x0004e69a3015eec3,0x00014f8520f65886,0x000603fe316ae01d,0x000266136364ded2,0x0001ca16145255d7)},
{FIELD_LITERAL(0x0005e5bcd4e61d7d,0x0001bb779e9dc08f,0x0003c7c5aff92ebf,0x0003d921c5764bbc,0x0006d695748c1b54)},
{FIELD_LITERAL(0x00019031dbbe6961,0x000228c57c496dbd,0x00016d3b12e551b5,0x0006f71b0487b7f1,0x0000576d528efd97)},
{FIELD_LITERAL(0x0006a3af1de65daa,0x00058620d6a4624a,0x00062c5f94e31af3,0x00065f2be517410c,0x00061ed8888aeaad)},
{FIELD_LITERAL(0x000460e8ec01abc0,0x00029d22bb6910a9,0x0000bb5a4290fa5c,0x000761396d21fe81,0x00017529bc98149c)},
{FIELD_LITERAL(0x00026b6e1920377f,0x0001fe04f05868d1,0x00035b308dd430aa,0x0004a38a5bd39fc2,0x0007a2a54f12cec0)},
{FIELD_LITERAL(0x00015c50e219a243,0x000279df295b9db5,0x0001d3a06b1ce50c,0x0001a0d41ae8bef3,0x0001e12777751552)},
{FIELD_LITERAL(0x0001a2d5558fa158,0x00018db5df86dcda,0x000628100de92051,0x0002e1d2985a8b52,0x0000a021ed4469e4)},
{FIELD_LITERAL(0x0003c1838ccb4f06,0x000433f163939d2f,0x0003c45789e20d0e,0x0004cc1dd7cf2cda,0x0004a3d1db8e2fb0)},
{FIELD_LITERAL(0x00078bc9fe3174f7,0x0005463ef645ece5,0x0005977ab88ef0f8,0x000143fe3a6097c1,0x00014e54b582e50b)},
{FIELD_LITERAL(0x000460e8ec01abc0,0x00029d22bb6910a9,0x0000bb5a4290fa5c,0x000761396d21fe81,0x00017529bc98149c)},
{FIELD_LITERAL(0x00043e7c7334b0e7,0x0003cc0e9c6c62d0,0x00043ba8761df2f1,0x000333e22830d325,0x00035c2e2471d04f)},
{FIELD_LITERAL(0x000297c2159dd2ea,0x0002225918017b5d,0x0000fd2c877e4d6d,0x0000a876d935de03,0x0003aa2b685088ec)},
{FIELD_LITERAL(0x000381ec20845ff6,0x00010287499d4119,0x00071f5a1e12659a,0x0007119ecc4ec7fc,0x00065b686f7be346)},
{FIELD_LITERAL(0x00079aa225363911,0x0004401073991c38,0x0002d622e1b2ab01,0x0006d88484b2ff0e,0x0001af6bad1d0067)},
{FIELD_LITERAL(0x00078bc9fe3174f7,0x0005463ef645ece5,0x0005977ab88ef0f8,0x000143fe3a6097c1,0x00014e54b582e50b)},
{FIELD_LITERAL(0x00047e13df7b9ff7,0x0006fd78b662bee6,0x0000e0a5e1ed9a65,0x0000ee6133b13803,0x0001a49790841cb9)},
{FIELD_LITERAL(0x0004a9bd5d80f94a,0x000200829b9a0578,0x00005d3adbbe3535,0x0004a01abc9f4d78,0x000318228e347c33)},
{FIELD_LITERAL(0x00078a9576d93baf,0x0002b2a7e675aabc,0x00077ccfec62185f,0x00030ce0149594eb,0x00079ada3764fe9e)},
{FIELD_LITERAL(0x00019f03aa64e86b,0x000524ed3ec7b93e,0x00051dea71a325e6,0x0006072282cc2dd1,0x0003f6161300548d)},
{FIELD_LITERAL(0x00079aa225363911,0x0004401073991c38,0x0002d622e1b2ab01,0x0006d88484b2ff0e,0x0001af6bad1d0067)},
{FIELD_LITERAL(0x0000756a8926c43e,0x00054d58198a5543,0x00008330139de7a0,0x0004f31feb6a6b14,0x00006525c89b0161)},
{FIELD_LITERAL(0x0003d4e4793a59c5,0x00039088df420d66,0x000059f2dc08ae93,0x0002a529016f70f4,0x00003d508c2008c6)},
{FIELD_LITERAL(0x0000f3116a3baba1,0x000087e19c7c7a88,0x00064eadf2277a4f,0x0007d9a18deea24e,0x000204fcdb56e2b5)},
{FIELD_LITERAL(0x000740a868c461a6,0x00008d33fd39e939,0x000546fc277d8361,0x00049a29cc27b47d,0x00066efe0241ab2d)},
{FIELD_LITERAL(0x00019f03aa64e86b,0x000524ed3ec7b93e,0x00051dea71a325e6,0x0006072282cc2dd1,0x0003f6161300548d)},
{FIELD_LITERAL(0x00070cee95c4544c,0x0007781e63838577,0x0001b1520dd885b0,0x0000265e72115db1,0x0005fb0324a91d4a)},
{FIELD_LITERAL(0x0004c02370cdf9e0,0x0002753707967fe5,0x0003e9e845537aa4,0x00052e8412924bcd,0x00035a32466d04a6)},
{FIELD_LITERAL(0x00056e5f94d6709d,0x0000baa9a44a9de5,0x0002f96da022a0e7,0x000522f1a31020d4,0x0002c56138662fb1)},
{FIELD_LITERAL(0x0003a975fed6c7ef,0x0005be0807c70f4d,0x00056cb1100a4f60,0x000039e4317fae1e,0x0002d3e8e7c807c5)},
{FIELD_LITERAL(0x000740a868c461a6,0x00008d33fd39e939,0x000546fc277d8361,0x00049a29cc27b47d,0x00066efe0241ab2d)},
{FIELD_LITERAL(0x000291a06b298f50,0x000745565bb5621a,0x000506925fdd5f18,0x0002dd0e5cefdf2b,0x00053a9ec799d04e)},
{FIELD_LITERAL(0x000049cd79d8153d,0x0005f7f1bfb82d68,0x0006329634d9cab0,0x0007bcb505082b4e,0x00053f1ca734f15f)},
{FIELD_LITERAL(0x0000fdb698137903,0x0005fb51b23a7650,0x00056c97f01bfb0b,0x0002c8a3ede0e6c6,0x0000dffef54d46bd)},
{FIELD_LITERAL(0x000023fde8f23ca3,0x0003e79e97bcb77c,0x0006682d0da044a2,0x0002b5cc9caad587,0x0007053a7396d844)},
{FIELD_LITERAL(0x0003a975fed6c7ef,0x0005be0807c70f4d,0x00056cb1100a4f60,0x000039e4317fae1e,0x0002d3e8e7c807c5)},
{FIELD_LITERAL(0x0007024967ec86ea,0x000204ae4dc589af,0x000293680fe404f4,0x0005375c121f1939,0x000720010ab2b942)},
{FIELD_LITERAL(0x0007325e1ff6a8d7,0x000144c86fd24546,0x000196593acaf904,0x000241f57ca53397,0x00023e58d23dff45)},
{FIELD_LITERAL(0x00066242f578274b,0x00058a001d88f9f8,0x00036ae87b15be37,0x00016dbd43af7f3e,0x0001ce7f64876085)},
{FIELD_LITERAL(0x00015f6b0f790623,0x0007d5b90970fb7b,0x00045b6bd21c9701,0x0003fbe8a13740fc,0x00059a684a214173)},
{FIELD_LITERAL(0x000023fde8f23ca3,0x0003e79e97bcb77c,0x0006682d0da044a2,0x0002b5cc9caad587,0x0007053a7396d844)},
{FIELD_LITERAL(0x00019dbd0a87d8a2,0x000275ffe2770607,0x0004951784ea41c8,0x00069242bc5080c1,0x000631809b789f7a)},
{FIELD_LITERAL(0x00014da626cba741,0x000101c3468580bb,0x0004c6fb5709eea8,0x000354aaf860f432,0x0003d9501bbcc86d)},
{FIELD_LITERAL(0x0004100377e37e11,0x0000ac48fe9245e8,0x000098c5097111d5,0x0000c31ff20e0c11,0x0004d19f0fb6c913)},
{FIELD_LITERAL(0x0007c87f12093bcc,0x000223769c082868,0x00074d424db97824,0x0006d7020a556573,0x0001e0afdef95d3d)},
{FIELD_LITERAL(0x00015f6b0f790623,0x0007d5b90970fb7b,0x00045b6bd21c9701,0x0003fbe8a13740fc,0x00059a684a214173)},
{FIELD_LITERAL(0x0003effc881c81dc,0x000753b7016dba17,0x0007673af68eee2a,0x00073ce00df1f3ee,0x00032e60f04936ec)},
{FIELD_LITERAL(0x000201774f4281a6,0x00040d577fbe10c0,0x0001d96faea48a3a,0x00019d06096a4cb9,0x0000c0410e02b892)},
{FIELD_LITERAL(0x0004ecdd42bcb282,0x00036eb9f22440d6,0x00015738bdfebe58,0x0007da6d7cd185ed,0x000114cd2ee51425)},
{FIELD_LITERAL(0x00061fb7d973a125,0x00060a3d5f860ddc,0x00058032f5a2bae4,0x0001ae3459e6da16,0x0004d8e17bd386cb)},
{FIELD_LITERAL(0x0007c87f12093bcc,0x000223769c082868,0x00074d424db97824,0x0006d7020a556573,0x0001e0afdef95d3d)},
{FIELD_LITERAL(0x00031322bd434d6b,0x000491460ddbbf29,0x0006a8c7420141a7,0x00002592832e7a12,0x0006eb32d11aebda)},
{FIELD_LITERAL(0x0003d4f4a0189763,0x0002ebc953fe02a4,0x00004d165b695009,0x00050cba13806a99,0x0000f5b62c0c84e5)},
{FIELD_LITERAL(0x0006e654bfbff109,0x0006018351bcbbe2,0x00057964df181f22,0x00033e0673d9cfb1,0x00064efdf98a1040)},
{FIELD_LITERAL(0x00073ad6128efea0,0x0007c86bdff5a7c5,0x0001a71115a02aff,0x00049b3a3e67b1f4,0x00033315bb103c63)},
{FIELD_LITERAL(0x00061fb7d973a125,0x00060a3d5f860ddc,0x00058032f5a2bae4,0x0001ae3459e6da16,0x0004d8e17bd386cb)},
{FIELD_LITERAL(0x000119ab40400ee4,0x0001fe7cae43441d,0x0002869b20e7e0dd,0x0004c1f98c26304e,0x0001b1020675efbf)},
{FIELD_LITERAL(0x0006aac38a327053,0x0005351c17ce82af,0x0000f07d6bbd51f7,0x00039497c5b160b1,0x0001ca565d3b0b4c)},
{FIELD_LITERAL(0x00030e1e990f426f,0x0000a0a8e67aac06,0x0005d5c4267d1f6c,0x00051b0ebc5614b8,0x0000ca37a6b5f563)},
{FIELD_LITERAL(0x00009dcbfce95c17,0x0001ea312e0ecf1f,0x0001bfaafa617fde,0x00017565626471ce,0x00057a7e865a0896)},
{FIELD_LITERAL(0x00073ad6128efea0,0x0007c86bdff5a7c5,0x0001a71115a02aff,0x00049b3a3e67b1f4,0x00033315bb103c63)},
{FIELD_LITERAL(0x0004f1e166f0bd7e,0x00075f57198553f9,0x00022a3bd982e093,0x0002e4f143a9eb47,0x000735c8594a0a9c)},
{FIELD_LITERAL(0x00036e4ca4b09fec,0x00070559d5d9b147,0x00035855772927b5,0x000651fbdadbcd73,0x0007aea9eb02eba1)},
{FIELD_LITERAL(0x000447db14883a00,0x0002ccbdfcdd06ca,0x00052ae17d38e284,0x0002d754ce20339c,0x000163594fcc2603)}
{FIELD_LITERAL(0x00009dcbfce95c17,0x0001ea312e0ecf1f,0x0001bfaafa617fde,0x00017565626471ce,0x00057a7e865a0896)},
{FIELD_LITERAL(0x0003b824eb77c5ed,0x000533420322f935,0x0002d51e82c71d7b,0x000528ab31dfcc63,0x00069ca6b033d9fc)}
};

+ 10
- 4
src/GENERATED/c/ed448goldilocks/decaf.c View File

@@ -247,7 +247,7 @@ decaf_error_t API_NS(point_decode) (
succ &= bool_to_mask(allow_identity) | ~gf_eq(s, ZERO);
succ &= ~gf_lobit(s);
gf_sqr(s2,s); /* s^2 */
gf_sqr(s2,s); /* s^2 = -as^2 */
#if IMAGINE_TWIST
gf_sub(s2,ZERO,s2); /* -as^2 */
#endif
@@ -1083,8 +1083,13 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, SQRT_ONE_MINUS_D );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
#endif
decaf_bzero(u,sizeof(u));
}
#elif IMAGINE_TWIST
@@ -1104,7 +1109,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_add( u, x, t );
gf_add( z, q->y, q->x );
gf_sqr ( y, z);
gf_sub ( y, u, y );
gf_sub ( y, y, u );
gf_sub ( z, t, x );
gf_sqr ( x, q->z );
gf_add ( t, x, x);
@@ -1163,7 +1168,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
succ &= gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
gf_cond_neg(p->x,~gf_lobit(p->x)^low);
gf_cond_neg(p->x,gf_lobit(p->x)^low);
gf_copy(p->z,ONE);
#if EDDSA_USE_SIGMA_ISOGENY
@@ -1232,6 +1237,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
decaf_bzero(enc2,sizeof(enc2));
assert(API_NS(point_valid)(p) || ~succ);
return decaf_succeed_if(mask_to_bool(succ));
}



+ 6
- 0
src/GENERATED/include/decaf/point_255.hxx View File

@@ -64,6 +64,9 @@ static inline int bits() { return 255; }
/** The curve's cofactor (removed, but useful for testing) */
static const int REMOVED_COFACTOR = 8;

/** The curve's cofactor (removed, but useful for testing) */
static const int EDDSA_RATIO = 4;

/** Residue class of field modulus: p == this mod 2*(this-1) */
static const int FIELD_MODULUS_TYPE = 5;

@@ -255,6 +258,9 @@ public:
/** Bytes required for hash */
static const size_t HASH_BYTES = DECAF_255_HASH_BYTES;

/** Bytes required for EdDSA encoding */
static const size_t EDDSA_BYTES = DECAF_EDDSA_25519_PUBLIC_BYTES;

/**
* Size of a stegged element.
*


+ 6
- 0
src/GENERATED/include/decaf/point_448.hxx View File

@@ -64,6 +64,9 @@ static inline int bits() { return 448; }
/** The curve's cofactor (removed, but useful for testing) */
static const int REMOVED_COFACTOR = 4;

/** The curve's cofactor (removed, but useful for testing) */
static const int EDDSA_RATIO = 4;

/** Residue class of field modulus: p == this mod 2*(this-1) */
static const int FIELD_MODULUS_TYPE = 3;

@@ -255,6 +258,9 @@ public:
/** Bytes required for hash */
static const size_t HASH_BYTES = DECAF_448_HASH_BYTES;

/** Bytes required for EdDSA encoding */
static const size_t EDDSA_BYTES = DECAF_EDDSA_448_PUBLIC_BYTES;

/**
* Size of a stegged element.
*


+ 3
- 1
src/generator/curve_data.py View File

@@ -74,7 +74,7 @@ def ser(x,bits,paren=None):
first = False
return out

def msqrt(x,p,hi_bit_clear = True):
def msqrt(x,p,hi_bit_clear = True, lo_bit_clear = False):
if p % 4 == 3: ret = pow(x,(p+1)//4,p)
elif p % 8 == 5:
for u in range(1,1000):
@@ -86,6 +86,8 @@ def msqrt(x,p,hi_bit_clear = True):
if (ret**2-x) % p != 0: raise Exception("No sqrt")
if hi_bit_clear and ret > p//2: ret = p-ret
# lo_bit_clear overrides hi_bit_clear because it's not default
if lo_bit_clear and (ret & 1): ret = p-ret
return ret
def ceil_log2(x):


+ 11
- 5
src/per_curve/decaf.tmpl.c View File

@@ -38,7 +38,7 @@ static const scalar_t point_scalarmul_adjustment = {{{
const uint8_t decaf_x$(gf_shortname)_base_point[DECAF_X$(gf_shortname)_PUBLIC_BYTES] = { $(ser(mont_base,8)) };

static const gf RISTRETTO_ISOMAGIC = {{{
$(ser(msqrt(d-1 if imagine_twist else -d,modulus),gf_lit_limb_bits))
$(ser(msqrt(d-1 if imagine_twist else -d,modulus,lo_bit_clear=True),gf_lit_limb_bits))
}}};

#if COFACTOR==8 || EDDSA_USE_SIGMA_ISOGENY
@@ -236,7 +236,7 @@ decaf_error_t API_NS(point_decode) (
succ &= bool_to_mask(allow_identity) | ~gf_eq(s, ZERO);
succ &= ~gf_lobit(s);
gf_sqr(s2,s); /* s^2 */
gf_sqr(s2,s); /* s^2 = -as^2 */
#if IMAGINE_TWIST
gf_sub(s2,ZERO,s2); /* -as^2 */
#endif
@@ -1072,8 +1072,13 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_mul ( y, u, t ); // (x^2+y^2)(2z^2-y^2+x^2)
gf_mul ( u, z, t );
gf_copy( z, u );
gf_mul ( u, x, SQRT_ONE_MINUS_D );
gf_mul ( u, x, RISTRETTO_ISOMAGIC );
#if IMAGINE_TWIST
gf_mul_qnr( x, u );
#else
#error "... probably wrong"
gf_copy( x, u );
#endif
decaf_bzero(u,sizeof(u));
}
#elif IMAGINE_TWIST
@@ -1093,7 +1098,7 @@ void API_NS(point_mul_by_cofactor_and_encode_like_eddsa) (
gf_add( u, x, t );
gf_add( z, q->y, q->x );
gf_sqr ( y, z);
gf_sub ( y, u, y );
gf_sub ( y, y, u );
gf_sub ( z, t, x );
gf_sqr ( x, q->z );
gf_add ( t, x, x);
@@ -1152,7 +1157,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
succ &= gf_isr(p->t,p->x); /* 1/sqrt(num * denom) */
gf_mul(p->x,p->t,p->z); /* sqrt(num / denom) */
gf_cond_neg(p->x,~gf_lobit(p->x)^low);
gf_cond_neg(p->x,gf_lobit(p->x)^low);
gf_copy(p->z,ONE);
#if EDDSA_USE_SIGMA_ISOGENY
@@ -1221,6 +1226,7 @@ decaf_error_t API_NS(point_decode_like_eddsa_and_ignore_cofactor) (
decaf_bzero(enc2,sizeof(enc2));
assert(API_NS(point_valid)(p) || ~succ);
return decaf_succeed_if(mask_to_bool(succ));
}



+ 6
- 0
src/per_curve/point.tmpl.hxx View File

@@ -51,6 +51,9 @@ static inline int bits() { return $(gf_bits); }
/** The curve's cofactor (removed, but useful for testing) */
static const int REMOVED_COFACTOR = $(cofactor);

/** The curve's cofactor (removed, but useful for testing) */
static const int EDDSA_RATIO = $(cofactor/2 if eddsa_sigma_iso else cofactor);

/** Residue class of field modulus: p == this mod 2*(this-1) */
static const int FIELD_MODULUS_TYPE = $(modulus &~ (modulus-3));

@@ -242,6 +245,9 @@ public:
/** Bytes required for hash */
static const size_t HASH_BYTES = $(C_NS)_HASH_BYTES;

/** Bytes required for EdDSA encoding */
static const size_t EDDSA_BYTES = DECAF_EDDSA_$(gf_shortname)_PUBLIC_BYTES;

/**
* Size of a stegged element.
*


+ 43
- 4
test/ristretto.cxx View File

@@ -66,11 +66,17 @@ void usage() {
fprintf(stderr,"Usage: %s [points] [operations] ...\n", me);
fprintf(stderr," -b 255|448: Set which group to use (sometimes inferred from lengths)\n");
fprintf(stderr," -E: Display output as Elligator inverses\n");
fprintf(stderr," -D: Display output in EdDSA format (times clearing ratio)\n");
fprintf(stderr," -R: Display raw xyzt\n");
//fprintf(stderr," -C: Display output in X[25519|448] format\n");
fprintf(stderr," -H: ... divide by clearing ratio first\n");
fprintf(stderr,"\n");
fprintf(stderr," Ways to create points:\n");
fprintf(stderr," [hex]: Point from point data as hex\n");
fprintf(stderr," -e [hex]: Create point by hashing to curve using elligator\n");
fprintf(stderr," base: Base point of curve\n");
fprintf(stderr," identity: Identity point of curve\n");
fprintf(stderr,"\n");
fprintf(stderr," Operations:\n");
fprintf(stderr," -n [point]: negative of point\n");
@@ -91,7 +97,8 @@ public:
uint8_t tmp[Group::Point::SER_BYTES];
typename Group::Point a,b;
typename Group::Scalar s;
bool plus=false, empty=true, elligator=false, mul=false, scalar=false, scalarempty=true, neg=false;
bool plus=false, empty=true, elligator=false, mul=false, scalar=false,
scalarempty=true, neg=false, einv=false, like_eddsa=false, decoeff=false, raw=false;
if (done || error) return;
for (int i=1; i<g_argc && !error; i++) {
bool point = false;
@@ -104,6 +111,14 @@ public:
plus = true;
} else if (!strcmp(g_argv[i],"-n")) {
neg = !neg;
} else if (!strcmp(g_argv[i],"-E")) {
einv = true;
} else if (!strcmp(g_argv[i],"-R")) {
raw = true;
} else if (!strcmp(g_argv[i],"-D")) {
like_eddsa = true;
} else if (!strcmp(g_argv[i],"-H")) {
decoeff = true;
} else if (!strcmp(g_argv[i],"*")) {
if (elligator || scalar || scalarempty) usage();
mul = true;
@@ -117,6 +132,10 @@ public:
if (elligator || scalar) usage();
b = b.base();
point = true;
} else if (!strcmp(g_argv[i],"identity")) {
if (elligator || scalar) usage();
b = b.identity();
point = true;
} else if ((strlen(g_argv[i]) == 2*sizeof(tmp)
|| ((scalar || elligator) && strlen(g_argv[i]) <= 2*sizeof(tmp)))
&& !(error=parsehex(tmp,sizeof(tmp),g_argv[i]))) {
@@ -143,9 +162,29 @@ public:
}
if (!error && !empty) {
a.serialize_into(tmp);
printhex(tmp,sizeof(tmp));
printf("\n");
if (decoeff) a /= (Group::EDDSA_RATIO);
if (einv) {
uint8_t buffer[Group::Point::HASH_BYTES];
for (int h=0; h<1<<Group::Point::INVERT_ELLIGATOR_WHICH_BITS; h++) {
if (DECAF_SUCCESS == a.invert_elligator(
Buffer(buffer,sizeof(buffer)), h
)) {
printhex(buffer,sizeof(buffer));
printf("\n");
}
}
} else if (raw) {
printhex((const uint8_t *)&a, sizeof(a));
printf("\n");
} else if (like_eddsa) {
SecureBuffer b = a.mul_by_cofactor_and_encode_like_eddsa();
printhex(b.data(),b.size());
printf("\n");
} else {
a.serialize_into(tmp);
printhex(tmp,sizeof(tmp));
printf("\n");
}
done = true;
}


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