From bfd656b67b92e57de01d36957d8f6e06918bc4ca Mon Sep 17 00:00:00 2001 From: Frank Denis Date: Sun, 5 Nov 2017 17:50:15 +0100 Subject: [PATCH] core/25519: Use 51-bit limbs on platforms supporting 128 bit arithmetic --- .../msvc/vs2010/libsodium/libsodium.vcxproj | 3 + .../libsodium/libsodium.vcxproj.filters | 12 + .../msvc/vs2012/libsodium/libsodium.vcxproj | 3 + .../libsodium/libsodium.vcxproj.filters | 12 + .../msvc/vs2013/libsodium/libsodium.vcxproj | 3 + .../libsodium/libsodium.vcxproj.filters | 12 + .../msvc/vs2015/libsodium/libsodium.vcxproj | 3 + .../libsodium/libsodium.vcxproj.filters | 12 + .../msvc/vs2017/libsodium/libsodium.vcxproj | 3 + .../libsodium/libsodium.vcxproj.filters | 12 + libsodium.vcxproj | 3 + libsodium.vcxproj.filters | 9 + src/libsodium/Makefile.am | 9 +- .../curve25519/ref10/curve25519_ref10.c | 18 +- .../crypto_core/curve25519/ref10/fe_25_5/fe.h | 1127 ++++++++++++++ .../crypto_core/curve25519/ref10/fe_51/base.h | 1344 +++++++++++++++++ .../curve25519/ref10/fe_51/base2.h | 40 + .../crypto_core/curve25519/ref10/fe_51/fe.h | 569 +++++++ .../include/sodium/private/curve25519_ref10.h | 4 + 19 files changed, 3192 insertions(+), 6 deletions(-) create mode 100644 src/libsodium/crypto_core/curve25519/ref10/fe_25_5/fe.h create mode 100644 src/libsodium/crypto_core/curve25519/ref10/fe_51/base.h create mode 100644 src/libsodium/crypto_core/curve25519/ref10/fe_51/base2.h create mode 100644 src/libsodium/crypto_core/curve25519/ref10/fe_51/fe.h diff --git a/builds/msvc/vs2010/libsodium/libsodium.vcxproj b/builds/msvc/vs2010/libsodium/libsodium.vcxproj index 16b3d642..f9ff79e3 100644 --- a/builds/msvc/vs2010/libsodium/libsodium.vcxproj +++ b/builds/msvc/vs2010/libsodium/libsodium.vcxproj @@ -306,6 +306,9 @@ + + + diff --git a/builds/msvc/vs2010/libsodium/libsodium.vcxproj.filters b/builds/msvc/vs2010/libsodium/libsodium.vcxproj.filters index 436021e3..743f7b5c 100644 --- a/builds/msvc/vs2010/libsodium/libsodium.vcxproj.filters +++ b/builds/msvc/vs2010/libsodium/libsodium.vcxproj.filters @@ -707,6 +707,15 @@ crypto_core\curve25519\ref10\fe_25_5 + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + @@ -763,6 +772,9 @@ {e1a65ae7-b847-3441-bb23-e3eebbd63e9c} + + {b346bbaa-bfda-3fab-a0fe-ea02d7e61193} + {8b704d11-af1f-30c0-9981-479da6d88dc3} diff --git a/builds/msvc/vs2012/libsodium/libsodium.vcxproj b/builds/msvc/vs2012/libsodium/libsodium.vcxproj index a44a0894..d2ca1b48 100644 --- a/builds/msvc/vs2012/libsodium/libsodium.vcxproj +++ b/builds/msvc/vs2012/libsodium/libsodium.vcxproj @@ -306,6 +306,9 @@ + + + diff --git a/builds/msvc/vs2012/libsodium/libsodium.vcxproj.filters b/builds/msvc/vs2012/libsodium/libsodium.vcxproj.filters index 436021e3..743f7b5c 100644 --- a/builds/msvc/vs2012/libsodium/libsodium.vcxproj.filters +++ b/builds/msvc/vs2012/libsodium/libsodium.vcxproj.filters @@ -707,6 +707,15 @@ crypto_core\curve25519\ref10\fe_25_5 + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + @@ -763,6 +772,9 @@ {e1a65ae7-b847-3441-bb23-e3eebbd63e9c} + + {b346bbaa-bfda-3fab-a0fe-ea02d7e61193} + {8b704d11-af1f-30c0-9981-479da6d88dc3} diff --git a/builds/msvc/vs2013/libsodium/libsodium.vcxproj b/builds/msvc/vs2013/libsodium/libsodium.vcxproj index 00d8e4ca..a061e03e 100644 --- a/builds/msvc/vs2013/libsodium/libsodium.vcxproj +++ b/builds/msvc/vs2013/libsodium/libsodium.vcxproj @@ -306,6 +306,9 @@ + + + diff --git a/builds/msvc/vs2013/libsodium/libsodium.vcxproj.filters b/builds/msvc/vs2013/libsodium/libsodium.vcxproj.filters index 436021e3..743f7b5c 100644 --- a/builds/msvc/vs2013/libsodium/libsodium.vcxproj.filters +++ b/builds/msvc/vs2013/libsodium/libsodium.vcxproj.filters @@ -707,6 +707,15 @@ crypto_core\curve25519\ref10\fe_25_5 + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + @@ -763,6 +772,9 @@ {e1a65ae7-b847-3441-bb23-e3eebbd63e9c} + + {b346bbaa-bfda-3fab-a0fe-ea02d7e61193} + {8b704d11-af1f-30c0-9981-479da6d88dc3} diff --git a/builds/msvc/vs2015/libsodium/libsodium.vcxproj b/builds/msvc/vs2015/libsodium/libsodium.vcxproj index 9055f9c5..63c3d963 100644 --- a/builds/msvc/vs2015/libsodium/libsodium.vcxproj +++ b/builds/msvc/vs2015/libsodium/libsodium.vcxproj @@ -306,6 +306,9 @@ + + + diff --git a/builds/msvc/vs2015/libsodium/libsodium.vcxproj.filters b/builds/msvc/vs2015/libsodium/libsodium.vcxproj.filters index 436021e3..743f7b5c 100644 --- a/builds/msvc/vs2015/libsodium/libsodium.vcxproj.filters +++ b/builds/msvc/vs2015/libsodium/libsodium.vcxproj.filters @@ -707,6 +707,15 @@ crypto_core\curve25519\ref10\fe_25_5 + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + @@ -763,6 +772,9 @@ {e1a65ae7-b847-3441-bb23-e3eebbd63e9c} + + {b346bbaa-bfda-3fab-a0fe-ea02d7e61193} + {8b704d11-af1f-30c0-9981-479da6d88dc3} diff --git a/builds/msvc/vs2017/libsodium/libsodium.vcxproj b/builds/msvc/vs2017/libsodium/libsodium.vcxproj index 497d43c1..5616979b 100644 --- a/builds/msvc/vs2017/libsodium/libsodium.vcxproj +++ b/builds/msvc/vs2017/libsodium/libsodium.vcxproj @@ -306,6 +306,9 @@ + + + diff --git a/builds/msvc/vs2017/libsodium/libsodium.vcxproj.filters b/builds/msvc/vs2017/libsodium/libsodium.vcxproj.filters index 436021e3..743f7b5c 100644 --- a/builds/msvc/vs2017/libsodium/libsodium.vcxproj.filters +++ b/builds/msvc/vs2017/libsodium/libsodium.vcxproj.filters @@ -707,6 +707,15 @@ crypto_core\curve25519\ref10\fe_25_5 + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + + + crypto_core\curve25519\ref10\fe_51 + @@ -763,6 +772,9 @@ {e1a65ae7-b847-3441-bb23-e3eebbd63e9c} + + {b346bbaa-bfda-3fab-a0fe-ea02d7e61193} + {8b704d11-af1f-30c0-9981-479da6d88dc3} diff --git a/libsodium.vcxproj b/libsodium.vcxproj index 57053ff8..ead75cc1 100644 --- a/libsodium.vcxproj +++ b/libsodium.vcxproj @@ -544,6 +544,9 @@ + + + diff --git a/libsodium.vcxproj.filters b/libsodium.vcxproj.filters index 69d842c0..f88ec6c1 100644 --- a/libsodium.vcxproj.filters +++ b/libsodium.vcxproj.filters @@ -698,5 +698,14 @@ Header Files + + Header Files + + + Header Files + + + Header Files + diff --git a/src/libsodium/Makefile.am b/src/libsodium/Makefile.am index 0cd0f9a0..eea6847f 100644 --- a/src/libsodium/Makefile.am +++ b/src/libsodium/Makefile.am @@ -12,9 +12,6 @@ libsodium_la_SOURCES = \ crypto_box/crypto_box_easy.c \ crypto_box/crypto_box_seal.c \ crypto_box/curve25519xsalsa20poly1305/box_curve25519xsalsa20poly1305.c \ - crypto_core/curve25519/ref10/fe_25_5/base.h \ - crypto_core/curve25519/ref10/fe_25_5/base2_25_5.h \ - crypto_core/curve25519/ref10/fe_25_5/fe.h \ crypto_core/curve25519/ref10/curve25519_ref10.c \ crypto_core/hchacha20/core_hchacha20.c \ crypto_core/hsalsa20/ref2/core_hsalsa20_ref2.c \ @@ -111,10 +108,16 @@ endif if HAVE_TI_MODE libsodium_la_SOURCES += \ + crypto_core/curve25519/ref10/fe_51/base.h \ + crypto_core/curve25519/ref10/fe_51/base2_25_5.h \ + crypto_core/curve25519/ref10/fe_51/fe.h \ crypto_scalarmult/curve25519/donna_c64/curve25519_donna_c64.c \ crypto_scalarmult/curve25519/donna_c64/curve25519_donna_c64.h else libsodium_la_SOURCES += \ + crypto_core/curve25519/ref10/fe_25_5/base.h \ + crypto_core/curve25519/ref10/fe_25_5/base2_25_5.h \ + crypto_core/curve25519/ref10/fe_25_5/fe.h \ crypto_scalarmult/curve25519/ref10/x25519_ref10.c \ crypto_scalarmult/curve25519/ref10/x25519_ref10.h endif diff --git a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c index a56decc5..b9c4e68a 100644 --- a/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c +++ b/src/libsodium/crypto_core/curve25519/ref10/curve25519_ref10.c @@ -32,7 +32,11 @@ load_4(const unsigned char *in) return result; } -#include "fe_25_5/fe.h" +#ifdef HAVE_TI_MODE +# include "fe_51/fe.h" +#else +# include "fe_25_5/fe.h" +#endif void fe_invert(fe out, const fe z) @@ -540,7 +544,11 @@ static void ge_select_base(ge_precomp *t, const int pos, const signed char b) { static const ge_precomp base[32][8] = { /* base[i][j] = (j+1)*256^i*B */ -#include "fe_25_5/base.h" +#ifdef HAVE_TI_MODE +# include "fe_51/base.h" +#else +# include "fe_25_5/base.h" +#endif }; ge_select(t, base[pos], b); } @@ -595,7 +603,11 @@ ge_double_scalarmult_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { static const ge_precomp Bi[8] = { -#include "fe_25_5/base2.h" +#ifdef HAVE_TI_MODE +# include "fe_51/base2.h" +#else +# include "fe_25_5/base2.h" +#endif }; signed char aslide[256]; signed char bslide[256]; diff --git a/src/libsodium/crypto_core/curve25519/ref10/fe_25_5/fe.h b/src/libsodium/crypto_core/curve25519/ref10/fe_25_5/fe.h new file mode 100644 index 00000000..211a53bc --- /dev/null +++ b/src/libsodium/crypto_core/curve25519/ref10/fe_25_5/fe.h @@ -0,0 +1,1127 @@ +/* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ +static const fe d = { -10913610, 13857413, -15372611, 6949391, 114729, + -8787816, -6275908, -3247719, -18696448, -12055116 }; + +/* 2 * d = + * 16295367250680780974490674513165176452449235426866156013048779062215315747161 + */ +static const fe d2 = { -21827239, -5839606, -30745221, 13898782, 229458, + 15978800, -12551817, -6495438, 29715968, 9444199 }; + +/* sqrt(-1) */ +static const fe sqrtm1 = { -32595792, -7943725, 9377950, 3500415, 12389472, + -272473, -25146209, -2005654, 326686, 11406482 }; + +/* + h = 0 + */ + +void +fe_0(fe h) +{ + memset(&h[0], 0, 10 * sizeof h[0]); +} + +/* + h = 1 + */ + +void +fe_1(fe h) +{ + h[0] = 1; + h[1] = 0; + memset(&h[2], 0, 8 * sizeof h[0]); +} + +/* + h = f + g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +void +fe_add(fe h, const fe f, const fe g) +{ + int32_t h0 = f[0] + g[0]; + int32_t h1 = f[1] + g[1]; + int32_t h2 = f[2] + g[2]; + int32_t h3 = f[3] + g[3]; + int32_t h4 = f[4] + g[4]; + int32_t h5 = f[5] + g[5]; + int32_t h6 = f[6] + g[6]; + int32_t h7 = f[7] + g[7]; + int32_t h8 = f[8] + g[8]; + int32_t h9 = f[9] + g[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + h = f - g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +void +fe_sub(fe h, const fe f, const fe g) +{ + int32_t h0 = f[0] - g[0]; + int32_t h1 = f[1] - g[1]; + int32_t h2 = f[2] - g[2]; + int32_t h3 = f[3] - g[3]; + int32_t h4 = f[4] - g[4]; + int32_t h5 = f[5] - g[5]; + int32_t h6 = f[6] - g[6]; + int32_t h7 = f[7] - g[7]; + int32_t h8 = f[8] - g[8]; + int32_t h9 = f[9] - g[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + h = -f + * + Preconditions: + |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + * + Postconditions: + |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. + */ + +static void +fe_neg(fe h, const fe f) +{ + int32_t h0 = -f[0]; + int32_t h1 = -f[1]; + int32_t h2 = -f[2]; + int32_t h3 = -f[3]; + int32_t h4 = -f[4]; + int32_t h5 = -f[5]; + int32_t h6 = -f[6]; + int32_t h7 = -f[7]; + int32_t h8 = -f[8]; + int32_t h9 = -f[9]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; + h[5] = h5; + h[6] = h6; + h[7] = h7; + h[8] = h8; + h[9] = h9; +} + +/* + Replace (f,g) with (g,g) if b == 1; + replace (f,g) with (f,g) if b == 0. + * + Preconditions: b in {0,1}. + */ + +static void +fe_cmov(fe f, const fe g, unsigned int b) +{ + const uint32_t mask = (uint32_t) (-(int32_t) b); + + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t x0 = f0 ^ g[0]; + int32_t x1 = f1 ^ g[1]; + int32_t x2 = f2 ^ g[2]; + int32_t x3 = f3 ^ g[3]; + int32_t x4 = f4 ^ g[4]; + int32_t x5 = f5 ^ g[5]; + int32_t x6 = f6 ^ g[6]; + int32_t x7 = f7 ^ g[7]; + int32_t x8 = f8 ^ g[8]; + int32_t x9 = f9 ^ g[9]; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + x5 &= mask; + x6 &= mask; + x7 &= mask; + x8 &= mask; + x9 &= mask; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; + f[5] = f5 ^ x5; + f[6] = f6 ^ x6; + f[7] = f7 ^ x7; + f[8] = f8 ^ x8; + f[9] = f9 ^ x9; +} + +/* + h = f + */ + +void +fe_copy(fe h, const fe f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; + h[5] = f5; + h[6] = f6; + h[7] = f7; + h[8] = f8; + h[9] = f9; +} + +/* + Ignores top bit of h. + */ + +void +fe_frombytes(fe h, const unsigned char *s) +{ + int64_t h0 = load_4(s); + int64_t h1 = load_3(s + 4) << 6; + int64_t h2 = load_3(s + 7) << 5; + int64_t h3 = load_3(s + 10) << 3; + int64_t h4 = load_3(s + 13) << 2; + int64_t h5 = load_4(s + 16); + int64_t h6 = load_3(s + 20) << 7; + int64_t h7 = load_3(s + 23) << 5; + int64_t h8 = load_3(s + 26) << 4; + int64_t h9 = (load_3(s + 29) & 8388607) << 2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + Preconditions: + |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + * + Write p=2^255-19; q=floor(h/p). + Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). + * + Proof: + Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. + Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. + * + Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). + Then 0> 25; + q = (h0 + q) >> 26; + q = (h1 + q) >> 25; + q = (h2 + q) >> 26; + q = (h3 + q) >> 25; + q = (h4 + q) >> 26; + q = (h5 + q) >> 25; + q = (h6 + q) >> 26; + q = (h7 + q) >> 25; + q = (h8 + q) >> 26; + q = (h9 + q) >> 25; + + /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ + h0 += 19 * q; + /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ + + carry0 = h0 >> 26; + h1 += carry0; + h0 -= carry0 * ((uint32_t) 1L << 26); + carry1 = h1 >> 25; + h2 += carry1; + h1 -= carry1 * ((uint32_t) 1L << 25); + carry2 = h2 >> 26; + h3 += carry2; + h2 -= carry2 * ((uint32_t) 1L << 26); + carry3 = h3 >> 25; + h4 += carry3; + h3 -= carry3 * ((uint32_t) 1L << 25); + carry4 = h4 >> 26; + h5 += carry4; + h4 -= carry4 * ((uint32_t) 1L << 26); + carry5 = h5 >> 25; + h6 += carry5; + h5 -= carry5 * ((uint32_t) 1L << 25); + carry6 = h6 >> 26; + h7 += carry6; + h6 -= carry6 * ((uint32_t) 1L << 26); + carry7 = h7 >> 25; + h8 += carry7; + h7 -= carry7 * ((uint32_t) 1L << 25); + carry8 = h8 >> 26; + h9 += carry8; + h8 -= carry8 * ((uint32_t) 1L << 26); + carry9 = h9 >> 25; + h9 -= carry9 * ((uint32_t) 1L << 25); + /* h10 = carry9 */ + + /* + Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. + Have h0+...+2^230 h9 between 0 and 2^255-1; + evidently 2^255 h10-2^255 q = 0. + Goal: Output h0+...+2^230 h9. + */ + + s[0] = h0 >> 0; + s[1] = h0 >> 8; + s[2] = h0 >> 16; + s[3] = (h0 >> 24) | (h1 * ((uint32_t) 1 << 2)); + s[4] = h1 >> 6; + s[5] = h1 >> 14; + s[6] = (h1 >> 22) | (h2 * ((uint32_t) 1 << 3)); + s[7] = h2 >> 5; + s[8] = h2 >> 13; + s[9] = (h2 >> 21) | (h3 * ((uint32_t) 1 << 5)); + s[10] = h3 >> 3; + s[11] = h3 >> 11; + s[12] = (h3 >> 19) | (h4 * ((uint32_t) 1 << 6)); + s[13] = h4 >> 2; + s[14] = h4 >> 10; + s[15] = h4 >> 18; + s[16] = h5 >> 0; + s[17] = h5 >> 8; + s[18] = h5 >> 16; + s[19] = (h5 >> 24) | (h6 * ((uint32_t) 1 << 1)); + s[20] = h6 >> 7; + s[21] = h6 >> 15; + s[22] = (h6 >> 23) | (h7 * ((uint32_t) 1 << 3)); + s[23] = h7 >> 5; + s[24] = h7 >> 13; + s[25] = (h7 >> 21) | (h8 * ((uint32_t) 1 << 4)); + s[26] = h8 >> 4; + s[27] = h8 >> 12; + s[28] = (h8 >> 20) | (h9 * ((uint32_t) 1 << 6)); + s[29] = h9 >> 2; + s[30] = h9 >> 10; + s[31] = h9 >> 18; +} + +/* + return 1 if f is in {1,3,5,...,q-2} + return 0 if f is in {0,2,4,...,q-1} + * + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +static int +fe_isnegative(const fe f) +{ + unsigned char s[32]; + + fe_tobytes(s, f); + + return s[0] & 1; +} + +/* + return 1 if f == 0 + return 0 if f != 0 + + Preconditions: + |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. + */ + +int +fe_iszero(const fe f) +{ + unsigned char s[32]; + + fe_tobytes(s, f); + + return sodium_is_zero(s, 32); +} + +/* + h = f * g + Can overlap h with f or g. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +/* + Notes on implementation strategy: + * + Using schoolbook multiplication. + Karatsuba would save a little in some cost models. + * + Most multiplications by 2 and 19 are 32-bit precomputations; + cheaper than 64-bit postcomputations. + * + There is one remaining multiplication by 19 in the carry chain; + one *19 precomputation can be merged into this, + but the resulting data flow is considerably less clean. + * + There are 12 carries below. + 10 of them are 2-way parallelizable and vectorizable. + Can get away with 11 carries, but then data flow is much deeper. + * + With tighter constraints on inputs can squeeze carries into int32. + */ + +void +fe_mul(fe h, const fe f, const fe g) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t g0 = g[0]; + int32_t g1 = g[1]; + int32_t g2 = g[2]; + int32_t g3 = g[3]; + int32_t g4 = g[4]; + int32_t g5 = g[5]; + int32_t g6 = g[6]; + int32_t g7 = g[7]; + int32_t g8 = g[8]; + int32_t g9 = g[9]; + + int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + int32_t g3_19 = 19 * g3; + int32_t g4_19 = 19 * g4; + int32_t g5_19 = 19 * g5; + int32_t g6_19 = 19 * g6; + int32_t g7_19 = 19 * g7; + int32_t g8_19 = 19 * g8; + int32_t g9_19 = 19 * g9; + int32_t f1_2 = 2 * f1; + int32_t f3_2 = 2 * f3; + int32_t f5_2 = 2 * f5; + int32_t f7_2 = 2 * f7; + int32_t f9_2 = 2 * f9; + + int64_t f0g0 = f0 * (int64_t) g0; + int64_t f0g1 = f0 * (int64_t) g1; + int64_t f0g2 = f0 * (int64_t) g2; + int64_t f0g3 = f0 * (int64_t) g3; + int64_t f0g4 = f0 * (int64_t) g4; + int64_t f0g5 = f0 * (int64_t) g5; + int64_t f0g6 = f0 * (int64_t) g6; + int64_t f0g7 = f0 * (int64_t) g7; + int64_t f0g8 = f0 * (int64_t) g8; + int64_t f0g9 = f0 * (int64_t) g9; + int64_t f1g0 = f1 * (int64_t) g0; + int64_t f1g1_2 = f1_2 * (int64_t) g1; + int64_t f1g2 = f1 * (int64_t) g2; + int64_t f1g3_2 = f1_2 * (int64_t) g3; + int64_t f1g4 = f1 * (int64_t) g4; + int64_t f1g5_2 = f1_2 * (int64_t) g5; + int64_t f1g6 = f1 * (int64_t) g6; + int64_t f1g7_2 = f1_2 * (int64_t) g7; + int64_t f1g8 = f1 * (int64_t) g8; + int64_t f1g9_38 = f1_2 * (int64_t) g9_19; + int64_t f2g0 = f2 * (int64_t) g0; + int64_t f2g1 = f2 * (int64_t) g1; + int64_t f2g2 = f2 * (int64_t) g2; + int64_t f2g3 = f2 * (int64_t) g3; + int64_t f2g4 = f2 * (int64_t) g4; + int64_t f2g5 = f2 * (int64_t) g5; + int64_t f2g6 = f2 * (int64_t) g6; + int64_t f2g7 = f2 * (int64_t) g7; + int64_t f2g8_19 = f2 * (int64_t) g8_19; + int64_t f2g9_19 = f2 * (int64_t) g9_19; + int64_t f3g0 = f3 * (int64_t) g0; + int64_t f3g1_2 = f3_2 * (int64_t) g1; + int64_t f3g2 = f3 * (int64_t) g2; + int64_t f3g3_2 = f3_2 * (int64_t) g3; + int64_t f3g4 = f3 * (int64_t) g4; + int64_t f3g5_2 = f3_2 * (int64_t) g5; + int64_t f3g6 = f3 * (int64_t) g6; + int64_t f3g7_38 = f3_2 * (int64_t) g7_19; + int64_t f3g8_19 = f3 * (int64_t) g8_19; + int64_t f3g9_38 = f3_2 * (int64_t) g9_19; + int64_t f4g0 = f4 * (int64_t) g0; + int64_t f4g1 = f4 * (int64_t) g1; + int64_t f4g2 = f4 * (int64_t) g2; + int64_t f4g3 = f4 * (int64_t) g3; + int64_t f4g4 = f4 * (int64_t) g4; + int64_t f4g5 = f4 * (int64_t) g5; + int64_t f4g6_19 = f4 * (int64_t) g6_19; + int64_t f4g7_19 = f4 * (int64_t) g7_19; + int64_t f4g8_19 = f4 * (int64_t) g8_19; + int64_t f4g9_19 = f4 * (int64_t) g9_19; + int64_t f5g0 = f5 * (int64_t) g0; + int64_t f5g1_2 = f5_2 * (int64_t) g1; + int64_t f5g2 = f5 * (int64_t) g2; + int64_t f5g3_2 = f5_2 * (int64_t) g3; + int64_t f5g4 = f5 * (int64_t) g4; + int64_t f5g5_38 = f5_2 * (int64_t) g5_19; + int64_t f5g6_19 = f5 * (int64_t) g6_19; + int64_t f5g7_38 = f5_2 * (int64_t) g7_19; + int64_t f5g8_19 = f5 * (int64_t) g8_19; + int64_t f5g9_38 = f5_2 * (int64_t) g9_19; + int64_t f6g0 = f6 * (int64_t) g0; + int64_t f6g1 = f6 * (int64_t) g1; + int64_t f6g2 = f6 * (int64_t) g2; + int64_t f6g3 = f6 * (int64_t) g3; + int64_t f6g4_19 = f6 * (int64_t) g4_19; + int64_t f6g5_19 = f6 * (int64_t) g5_19; + int64_t f6g6_19 = f6 * (int64_t) g6_19; + int64_t f6g7_19 = f6 * (int64_t) g7_19; + int64_t f6g8_19 = f6 * (int64_t) g8_19; + int64_t f6g9_19 = f6 * (int64_t) g9_19; + int64_t f7g0 = f7 * (int64_t) g0; + int64_t f7g1_2 = f7_2 * (int64_t) g1; + int64_t f7g2 = f7 * (int64_t) g2; + int64_t f7g3_38 = f7_2 * (int64_t) g3_19; + int64_t f7g4_19 = f7 * (int64_t) g4_19; + int64_t f7g5_38 = f7_2 * (int64_t) g5_19; + int64_t f7g6_19 = f7 * (int64_t) g6_19; + int64_t f7g7_38 = f7_2 * (int64_t) g7_19; + int64_t f7g8_19 = f7 * (int64_t) g8_19; + int64_t f7g9_38 = f7_2 * (int64_t) g9_19; + int64_t f8g0 = f8 * (int64_t) g0; + int64_t f8g1 = f8 * (int64_t) g1; + int64_t f8g2_19 = f8 * (int64_t) g2_19; + int64_t f8g3_19 = f8 * (int64_t) g3_19; + int64_t f8g4_19 = f8 * (int64_t) g4_19; + int64_t f8g5_19 = f8 * (int64_t) g5_19; + int64_t f8g6_19 = f8 * (int64_t) g6_19; + int64_t f8g7_19 = f8 * (int64_t) g7_19; + int64_t f8g8_19 = f8 * (int64_t) g8_19; + int64_t f8g9_19 = f8 * (int64_t) g9_19; + int64_t f9g0 = f9 * (int64_t) g0; + int64_t f9g1_38 = f9_2 * (int64_t) g1_19; + int64_t f9g2_19 = f9 * (int64_t) g2_19; + int64_t f9g3_38 = f9_2 * (int64_t) g3_19; + int64_t f9g4_19 = f9 * (int64_t) g4_19; + int64_t f9g5_38 = f9_2 * (int64_t) g5_19; + int64_t f9g6_19 = f9 * (int64_t) g6_19; + int64_t f9g7_38 = f9_2 * (int64_t) g7_19; + int64_t f9g8_19 = f9 * (int64_t) g8_19; + int64_t f9g9_38 = f9_2 * (int64_t) g9_19; + + int64_t h0 = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 + + f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38; + int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 + + f7g4_19 + f8g3_19 + f9g2_19; + int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 + + f7g5_38 + f8g4_19 + f9g3_38; + int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 + + f7g6_19 + f8g5_19 + f9g4_19; + int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 + + f7g7_38 + f8g6_19 + f9g5_38; + int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 + + f8g7_19 + f9g6_19; + int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + + f7g9_38 + f8g8_19 + f9g7_38; + int64_t h7 = f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + + f8g9_19 + f9g8_19; + int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 + + f8g0 + f9g9_38; + int64_t h9 = + f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + /* + |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) + i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 + |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) + i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 + */ + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + /* |h1| <= 2^24; from now on fits into int32 */ + /* |h5| <= 2^24; from now on fits into int32 */ + /* |h2| <= 1.41*2^60 */ + /* |h6| <= 1.41*2^60 */ + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + /* |h2| <= 2^25; from now on fits into int32 unchanged */ + /* |h6| <= 2^25; from now on fits into int32 unchanged */ + /* |h3| <= 1.71*2^59 */ + /* |h7| <= 1.71*2^59 */ + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + /* |h3| <= 2^24; from now on fits into int32 unchanged */ + /* |h7| <= 2^24; from now on fits into int32 unchanged */ + /* |h4| <= 1.72*2^34 */ + /* |h8| <= 1.41*2^60 */ + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + /* |h4| <= 2^25; from now on fits into int32 unchanged */ + /* |h8| <= 2^25; from now on fits into int32 unchanged */ + /* |h5| <= 1.01*2^24 */ + /* |h9| <= 1.71*2^59 */ + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + h = f * f + Can overlap h with f. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +void +fe_sq(fe h, const fe f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} + +/* + h = 2 * f * f + Can overlap h with f. + * + Preconditions: + |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. + * + Postconditions: + |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. + */ + +static void +fe_sq2(fe h, const fe f) +{ + int32_t f0 = f[0]; + int32_t f1 = f[1]; + int32_t f2 = f[2]; + int32_t f3 = f[3]; + int32_t f4 = f[4]; + int32_t f5 = f[5]; + int32_t f6 = f[6]; + int32_t f7 = f[7]; + int32_t f8 = f[8]; + int32_t f9 = f[9]; + + int32_t f0_2 = 2 * f0; + int32_t f1_2 = 2 * f1; + int32_t f2_2 = 2 * f2; + int32_t f3_2 = 2 * f3; + int32_t f4_2 = 2 * f4; + int32_t f5_2 = 2 * f5; + int32_t f6_2 = 2 * f6; + int32_t f7_2 = 2 * f7; + int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + + int64_t f0f0 = f0 * (int64_t) f0; + int64_t f0f1_2 = f0_2 * (int64_t) f1; + int64_t f0f2_2 = f0_2 * (int64_t) f2; + int64_t f0f3_2 = f0_2 * (int64_t) f3; + int64_t f0f4_2 = f0_2 * (int64_t) f4; + int64_t f0f5_2 = f0_2 * (int64_t) f5; + int64_t f0f6_2 = f0_2 * (int64_t) f6; + int64_t f0f7_2 = f0_2 * (int64_t) f7; + int64_t f0f8_2 = f0_2 * (int64_t) f8; + int64_t f0f9_2 = f0_2 * (int64_t) f9; + int64_t f1f1_2 = f1_2 * (int64_t) f1; + int64_t f1f2_2 = f1_2 * (int64_t) f2; + int64_t f1f3_4 = f1_2 * (int64_t) f3_2; + int64_t f1f4_2 = f1_2 * (int64_t) f4; + int64_t f1f5_4 = f1_2 * (int64_t) f5_2; + int64_t f1f6_2 = f1_2 * (int64_t) f6; + int64_t f1f7_4 = f1_2 * (int64_t) f7_2; + int64_t f1f8_2 = f1_2 * (int64_t) f8; + int64_t f1f9_76 = f1_2 * (int64_t) f9_38; + int64_t f2f2 = f2 * (int64_t) f2; + int64_t f2f3_2 = f2_2 * (int64_t) f3; + int64_t f2f4_2 = f2_2 * (int64_t) f4; + int64_t f2f5_2 = f2_2 * (int64_t) f5; + int64_t f2f6_2 = f2_2 * (int64_t) f6; + int64_t f2f7_2 = f2_2 * (int64_t) f7; + int64_t f2f8_38 = f2_2 * (int64_t) f8_19; + int64_t f2f9_38 = f2 * (int64_t) f9_38; + int64_t f3f3_2 = f3_2 * (int64_t) f3; + int64_t f3f4_2 = f3_2 * (int64_t) f4; + int64_t f3f5_4 = f3_2 * (int64_t) f5_2; + int64_t f3f6_2 = f3_2 * (int64_t) f6; + int64_t f3f7_76 = f3_2 * (int64_t) f7_38; + int64_t f3f8_38 = f3_2 * (int64_t) f8_19; + int64_t f3f9_76 = f3_2 * (int64_t) f9_38; + int64_t f4f4 = f4 * (int64_t) f4; + int64_t f4f5_2 = f4_2 * (int64_t) f5; + int64_t f4f6_38 = f4_2 * (int64_t) f6_19; + int64_t f4f7_38 = f4 * (int64_t) f7_38; + int64_t f4f8_38 = f4_2 * (int64_t) f8_19; + int64_t f4f9_38 = f4 * (int64_t) f9_38; + int64_t f5f5_38 = f5 * (int64_t) f5_38; + int64_t f5f6_38 = f5_2 * (int64_t) f6_19; + int64_t f5f7_76 = f5_2 * (int64_t) f7_38; + int64_t f5f8_38 = f5_2 * (int64_t) f8_19; + int64_t f5f9_76 = f5_2 * (int64_t) f9_38; + int64_t f6f6_19 = f6 * (int64_t) f6_19; + int64_t f6f7_38 = f6 * (int64_t) f7_38; + int64_t f6f8_38 = f6_2 * (int64_t) f8_19; + int64_t f6f9_38 = f6 * (int64_t) f9_38; + int64_t f7f7_38 = f7 * (int64_t) f7_38; + int64_t f7f8_38 = f7_2 * (int64_t) f8_19; + int64_t f7f9_76 = f7_2 * (int64_t) f9_38; + int64_t f8f8_19 = f8 * (int64_t) f8_19; + int64_t f8f9_38 = f8 * (int64_t) f9_38; + int64_t f9f9_38 = f9 * (int64_t) f9_38; + + int64_t h0 = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38; + int64_t h1 = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38; + int64_t h2 = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19; + int64_t h3 = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38; + int64_t h4 = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38; + int64_t h5 = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38; + int64_t h6 = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19; + int64_t h7 = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38; + int64_t h8 = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38; + int64_t h9 = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2; + + int64_t carry0; + int64_t carry1; + int64_t carry2; + int64_t carry3; + int64_t carry4; + int64_t carry5; + int64_t carry6; + int64_t carry7; + int64_t carry8; + int64_t carry9; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + + carry1 = (h1 + (int64_t)(1L << 24)) >> 25; + h2 += carry1; + h1 -= carry1 * ((uint64_t) 1L << 25); + carry5 = (h5 + (int64_t)(1L << 24)) >> 25; + h6 += carry5; + h5 -= carry5 * ((uint64_t) 1L << 25); + + carry2 = (h2 + (int64_t)(1L << 25)) >> 26; + h3 += carry2; + h2 -= carry2 * ((uint64_t) 1L << 26); + carry6 = (h6 + (int64_t)(1L << 25)) >> 26; + h7 += carry6; + h6 -= carry6 * ((uint64_t) 1L << 26); + + carry3 = (h3 + (int64_t)(1L << 24)) >> 25; + h4 += carry3; + h3 -= carry3 * ((uint64_t) 1L << 25); + carry7 = (h7 + (int64_t)(1L << 24)) >> 25; + h8 += carry7; + h7 -= carry7 * ((uint64_t) 1L << 25); + + carry4 = (h4 + (int64_t)(1L << 25)) >> 26; + h5 += carry4; + h4 -= carry4 * ((uint64_t) 1L << 26); + carry8 = (h8 + (int64_t)(1L << 25)) >> 26; + h9 += carry8; + h8 -= carry8 * ((uint64_t) 1L << 26); + + carry9 = (h9 + (int64_t)(1L << 24)) >> 25; + h0 += carry9 * 19; + h9 -= carry9 * ((uint64_t) 1L << 25); + + carry0 = (h0 + (int64_t)(1L << 25)) >> 26; + h1 += carry0; + h0 -= carry0 * ((uint64_t) 1L << 26); + + h[0] = (int32_t) h0; + h[1] = (int32_t) h1; + h[2] = (int32_t) h2; + h[3] = (int32_t) h3; + h[4] = (int32_t) h4; + h[5] = (int32_t) h5; + h[6] = (int32_t) h6; + h[7] = (int32_t) h7; + h[8] = (int32_t) h8; + h[9] = (int32_t) h9; +} diff --git a/src/libsodium/crypto_core/curve25519/ref10/fe_51/base.h b/src/libsodium/crypto_core/curve25519/ref10/fe_51/base.h new file mode 100644 index 00000000..6b3b833e --- /dev/null +++ b/src/libsodium/crypto_core/curve25519/ref10/fe_51/base.h @@ -0,0 +1,1344 @@ +{ /* 0/31 */ + { + { 1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563 }, + { 62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585 }, + { 301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142 } + }, + { + { 1380971894829527, 790832306631236, 2067202295274102, 1995808275510000, 1566530869037010 }, + { 463307831301544, 432984605774163, 1610641361907204, 750899048855000, 1894842303421586 }, + { 748439484463711, 1033211726465151, 1396005112841647, 1611506220286469, 1972177495910992 } + }, + { + { 1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911 }, + { 316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597 }, + { 1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707 } + }, + { + { 934282339813791, 1846903124198670, 1172395437954843, 1007037127761661, 1830588347719256 }, + { 1694390458783935, 1735906047636159, 705069562067493, 648033061693059, 696214010414170 }, + { 1121406372216585, 192876649532226, 190294192191717, 1994165897297032, 2245000007398739 } + }, + { + { 769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016 }, + { 425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893 }, + { 1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339 } + }, + { + { 1388594989461809, 316767091099457, 394298842192982, 1230079486801005, 1440737038838979 }, + { 7380825640100, 146210432690483, 304903576448906, 1198869323871120, 997689833219095 }, + { 1181317918772081, 114573476638901, 262805072233344, 265712217171332, 294181933805782 } + }, + { + { 665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985 }, + { 2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113 }, + { 965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601 } + }, + { + { 2068619540119183, 1966274918058806, 957728544705549, 729906502578991, 159834893065166 }, + { 2073601412052185, 31021124762708, 264500969797082, 248034690651703, 1030252227928288 }, + { 551790716293402, 1989538725166328, 801169423371717, 2052451893578887, 678432056995012 } + } +}, +{ /* 1/31 */ + { + { 1368953770187805, 790347636712921, 437508475667162, 2142576377050580, 1932081720066286 }, + { 953638594433374, 1092333936795051, 1419774766716690, 805677984380077, 859228993502513 }, + { 1200766035879111, 20142053207432, 1465634435977050, 1645256912097844, 295121984874596 } + }, + { + { 1735718747031557, 1248237894295956, 1204753118328107, 976066523550493, 65943769534592 }, + { 1060098822528990, 1586825862073490, 212301317240126, 1975302711403555, 666724059764335 }, + { 1091990273418756, 1572899409348578, 80968014455247, 306009358661350, 1520450739132526 } + }, + { + { 1480517209436112, 1511153322193952, 1244343858991172, 304788150493241, 369136856496443 }, + { 2151330273626164, 762045184746182, 1688074332551515, 823046109005759, 907602769079491 }, + { 2047386910586836, 168470092900250, 1552838872594810, 340951180073789, 360819374702533 } + }, + { + { 1982622644432056, 2014393600336956, 128909208804214, 1617792623929191, 105294281913815 }, + { 980234343912898, 1712256739246056, 588935272190264, 204298813091998, 841798321043288 }, + { 197561292938973, 454817274782871, 1963754960082318, 2113372252160468, 971377527342673 } + }, + { + { 164699448829328, 3127451757672, 1199504971548753, 1766155447043652, 1899238924683527 }, + { 732262946680281, 1674412764227063, 2182456405662809, 1350894754474250, 558458873295247 }, + { 2103305098582922, 1960809151316468, 715134605001343, 1454892949167181, 40827143824949 } + }, + { + { 1239289043050212, 1744654158124578, 758702410031698, 1796762995074688, 1603056663766 }, + { 2232056027107988, 987343914584615, 2115594492994461, 1819598072792159, 1119305654014850 }, + { 320153677847348, 939613871605645, 641883205761567, 1930009789398224, 329165806634126 } + }, + { + { 980930490474130, 1242488692177893, 1251446316964684, 1086618677993530, 1961430968465772 }, + { 276821765317453, 1536835591188030, 1305212741412361, 61473904210175, 2051377036983058 }, + { 833449923882501, 1750270368490475, 1123347002068295, 185477424765687, 278090826653186 } + }, + { + { 794524995833413, 1849907304548286, 53348672473145, 1272368559505217, 1147304168324779 }, + { 1504846112759364, 1203096289004681, 562139421471418, 274333017451844, 1284344053775441 }, + { 483048732424432, 2116063063343382, 30120189902313, 292451576741007, 1156379271702225 } + } +}, +{ /* 2/31 */ + { + { 928372153029038, 2147692869914564, 1455665844462196, 1986737809425946, 185207050258089 }, + { 137732961814206, 706670923917341, 1387038086865771, 1965643813686352, 1384777115696347 }, + { 481144981981577, 2053319313589856, 2065402289827512, 617954271490316, 1106602634668125 } + }, + { + { 696298019648792, 893299659040895, 1148636718636009, 26734077349617, 2203955659340681 }, + { 657390353372855, 998499966885562, 991893336905797, 810470207106761, 343139804608786 }, + { 791736669492960, 934767652997115, 824656780392914, 1759463253018643, 361530362383518 } + }, + { + { 2022541353055597, 2094700262587466, 1551008075025686, 242785517418164, 695985404963562 }, + { 1287487199965223, 2215311941380308, 1552928390931986, 1664859529680196, 1125004975265243 }, + { 677434665154918, 989582503122485, 1817429540898386, 1052904935475344, 1143826298169798 } + }, + { + { 367266328308408, 318431188922404, 695629353755355, 634085657580832, 24581612564426 }, + { 773360688841258, 1815381330538070, 363773437667376, 539629987070205, 783280434248437 }, + { 180820816194166, 168937968377394, 748416242794470, 1227281252254508, 1567587861004268 } + }, + { + { 478775558583645, 2062896624554807, 699391259285399, 358099408427873, 1277310261461761 }, + { 1984740906540026, 1079164179400229, 1056021349262661, 1659958556483663, 1088529069025527 }, + { 580736401511151, 1842931091388998, 1177201471228238, 2075460256527244, 1301133425678027 } + }, + { + { 1515728832059182, 1575261009617579, 1510246567196186, 191078022609704, 116661716289141 }, + { 1295295738269652, 1714742313707026, 545583042462581, 2034411676262552, 1513248090013606 }, + { 230710545179830, 30821514358353, 760704303452229, 390668103790604, 573437871383156 } + }, + { + { 1169380107545646, 263167233745614, 2022901299054448, 819900753251120, 2023898464874585 }, + { 2102254323485823, 1570832666216754, 34696906544624, 1993213739807337, 70638552271463 }, + { 894132856735058, 548675863558441, 845349339503395, 1942269668326667, 1615682209874691 } + }, + { + { 1287670217537834, 1222355136884920, 1846481788678694, 1150426571265110, 1613523400722047 }, + { 793388516527298, 1315457083650035, 1972286999342417, 1901825953052455, 338269477222410 }, + { 550201530671806, 778605267108140, 2063911101902983, 115500557286349, 2041641272971022 } + } +}, +{ /* 3/31 */ + { + { 717255318455100, 519313764361315, 2080406977303708, 541981206705521, 774328150311600 }, + { 261715221532238, 1795354330069993, 1496878026850283, 499739720521052, 389031152673770 }, + { 1997217696294013, 1717306351628065, 1684313917746180, 1644426076011410, 1857378133465451 } + }, + { + { 1475434724792648, 76931896285979, 1116729029771667, 2002544139318042, 725547833803938 }, + { 2022306639183567, 726296063571875, 315345054448644, 1058733329149221, 1448201136060677 }, + { 1710065158525665, 1895094923036397, 123988286168546, 1145519900776355, 1607510767693874 } + }, + { + { 561605375422540, 1071733543815037, 131496498800990, 1946868434569999, 828138133964203 }, + { 1548495173745801, 442310529226540, 998072547000384, 553054358385281, 644824326376171 }, + { 1445526537029440, 2225519789662536, 914628859347385, 1064754194555068, 1660295614401091 } + }, + { + { 1199690223111956, 24028135822341, 66638289244341, 57626156285975, 565093967979607 }, + { 876926774220824, 554618976488214, 1012056309841565, 839961821554611, 1414499340307677 }, + { 703047626104145, 1266841406201770, 165556500219173, 486991595001879, 1011325891650656 } + }, + { + { 1622861044480487, 1156394801573634, 1869132565415504, 327103985777730, 2095342781472284 }, + { 334886927423922, 489511099221528, 129160865966726, 1720809113143481, 619700195649254 }, + { 1646545795166119, 1758370782583567, 714746174550637, 1472693650165135, 898994790308209 } + }, + { + { 333403773039279, 295772542452938, 1693106465353610, 912330357530760, 471235657950362 }, + { 1811196219982022, 1068969825533602, 289602974833439, 1988956043611592, 863562343398367 }, + { 906282429780072, 2108672665779781, 432396390473936, 150625823801893, 1708930497638539 } + }, + { + { 925664675702328, 21416848568684, 1831436641861340, 601157008940113, 371818055044496 }, + { 1479786007267725, 1738881859066675, 68646196476567, 2146507056100328, 1247662817535471 }, + { 52035296774456, 939969390708103, 312023458773250, 59873523517659, 1231345905848899 } + }, + { + { 643355106415761, 290186807495774, 2013561737429023, 319648069511546, 393736678496162 }, + { 129358342392716, 1932811617704777, 1176749390799681, 398040349861790, 1170779668090425 }, + { 2051980782668029, 121859921510665, 2048329875753063, 1235229850149665, 519062146124755 } + } +}, +{ /* 4/31 */ + { + { 1608170971973096, 415809060360428, 1350468408164766, 2038620059057678, 1026904485989112 }, + { 1837656083115103, 1510134048812070, 906263674192061, 1821064197805734, 565375124676301 }, + { 578027192365650, 2034800251375322, 2128954087207123, 478816193810521, 2196171989962750 } + }, + { + { 1633188840273139, 852787172373708, 1548762607215796, 1266275218902681, 1107218203325133 }, + { 462189358480054, 1784816734159228, 1611334301651368, 1303938263943540, 707589560319424 }, + { 1038829280972848, 38176604650029, 753193246598573, 1136076426528122, 595709990562434 } + }, + { + { 1408451820859834, 2194984964010833, 2198361797561729, 1061962440055713, 1645147963442934 }, + { 4701053362120, 1647641066302348, 1047553002242085, 1923635013395977, 206970314902065 }, + { 1750479161778571, 1362553355169293, 1891721260220598, 966109370862782, 1024913988299801 } + }, + { + { 212699049131723, 1117950018299775, 1873945661751056, 1403802921984058, 130896082652698 }, + { 636808533673210, 1262201711667560, 390951380330599, 1663420692697294, 561951321757406 }, + { 520731594438141, 1446301499955692, 273753264629267, 1565101517999256, 1019411827004672 } + }, + { + { 926527492029409, 1191853477411379, 734233225181171, 184038887541270, 1790426146325343 }, + { 1464651961852572, 1483737295721717, 1519450561335517, 1161429831763785, 405914998179977 }, + { 996126634382301, 796204125879525, 127517800546509, 344155944689303, 615279846169038 } + }, + { + { 738724080975276, 2188666632415296, 1961313708559162, 1506545807547587, 1151301638969740 }, + { 622917337413835, 1218989177089035, 1284857712846592, 970502061709359, 351025208117090 }, + { 2067814584765580, 1677855129927492, 2086109782475197, 235286517313238, 1416314046739645 } + }, + { + { 586844262630358, 307444381952195, 458399356043426, 602068024507062, 1028548203415243 }, + { 678489922928203, 2016657584724032, 90977383049628, 1026831907234582, 615271492942522 }, + { 301225714012278, 1094837270268560, 1202288391010439, 644352775178361, 1647055902137983 } + }, + { + { 1210746697896478, 1416608304244708, 686487477217856, 1245131191434135, 1051238336855737 }, + { 1135604073198207, 1683322080485474, 769147804376683, 2086688130589414, 900445683120379 }, + { 1971518477615628, 401909519527336, 448627091057375, 1409486868273821, 1214789035034363 } + } +}, +{ /* 5/31 */ + { + { 1364039144731711, 1897497433586190, 2203097701135459, 145461396811251, 1349844460790699 }, + { 1045230323257973, 818206601145807, 630513189076103, 1672046528998132, 807204017562437 }, + { 439961968385997, 386362664488986, 1382706320807688, 309894000125359, 2207801346498567 } + }, + { + { 1229004686397588, 920643968530863, 123975893911178, 681423993215777, 1400559197080973 }, + { 2003766096898049, 170074059235165, 1141124258967971, 1485419893480973, 1573762821028725 }, + { 729905708611432, 1270323270673202, 123353058984288, 426460209632942, 2195574535456672 } + }, + { + { 1271140255321235, 2044363183174497, 52125387634689, 1445120246694705, 942541986339084 }, + { 1761608437466135, 583360847526804, 1586706389685493, 2157056599579261, 1170692369685772 }, + { 871476219910823, 1878769545097794, 2241832391238412, 548957640601001, 690047440233174 } + }, + { + { 297194732135507, 1366347803776820, 1301185512245601, 561849853336294, 1533554921345731 }, + { 999628998628371, 1132836708493400, 2084741674517453, 469343353015612, 678782988708035 }, + { 2189427607417022, 699801937082607, 412764402319267, 1478091893643349, 2244675696854460 } + }, + { + { 1712292055966563, 204413590624874, 1405738637332841, 408981300829763, 861082219276721 }, + { 508561155940631, 966928475686665, 2236717801150132, 424543858577297, 2089272956986143 }, + { 221245220129925, 1156020201681217, 491145634799213, 542422431960839, 828100817819207 } + }, + { + { 153756971240384, 1299874139923977, 393099165260502, 1058234455773022, 996989038681183 }, + { 559086812798481, 573177704212711, 1629737083816402, 1399819713462595, 1646954378266038 }, + { 1887963056288059, 228507035730124, 1468368348640282, 930557653420194, 613513962454686 } + }, + { + { 1224529808187553, 1577022856702685, 2206946542980843, 625883007765001, 279930793512158 }, + { 1076287717051609, 1114455570543035, 187297059715481, 250446884292121, 1885187512550540 }, + { 902497362940219, 76749815795675, 1657927525633846, 1420238379745202, 1340321636548352 } + }, + { + { 1129576631190784, 1281994010027327, 996844254743018, 257876363489249, 1150850742055018 }, + { 628740660038789, 1943038498527841, 467786347793886, 1093341428303375, 235413859513003 }, + { 237425418909360, 469614029179605, 1512389769174935, 1241726368345357, 441602891065214 } + } +}, +{ /* 6/31 */ + { + { 1736417953058555, 726531315520508, 1833335034432527, 1629442561574747, 624418919286085 }, + { 1960754663920689, 497040957888962, 1909832851283095, 1271432136996826, 2219780368020940 }, + { 1537037379417136, 1358865369268262, 2130838645654099, 828733687040705, 1999987652890901 } + }, + { + { 629042105241814, 1098854999137608, 887281544569320, 1423102019874777, 7911258951561 }, + { 1811562332665373, 1501882019007673, 2213763501088999, 359573079719636, 36370565049116 }, + { 218907117361280, 1209298913016966, 1944312619096112, 1130690631451061, 1342327389191701 } + }, + { + { 1369976867854704, 1396479602419169, 1765656654398856, 2203659200586299, 998327836117241 }, + { 2230701885562825, 1348173180338974, 2172856128624598, 1426538746123771, 444193481326151 }, + { 784210426627951, 918204562375674, 1284546780452985, 1324534636134684, 1872449409642708 } + }, + { + { 319638829540294, 596282656808406, 2037902696412608, 1557219121643918, 341938082688094 }, + { 1901860206695915, 2004489122065736, 1625847061568236, 973529743399879, 2075287685312905 }, + { 1371853944110545, 1042332820512553, 1949855697918254, 1791195775521505, 37487364849293 } + }, + { + { 687200189577855, 1082536651125675, 644224940871546, 340923196057951, 343581346747396 }, + { 2082717129583892, 27829425539422, 145655066671970, 1690527209845512, 1865260509673478 }, + { 1059729620568824, 2163709103470266, 1440302280256872, 1769143160546397, 869830310425069 } + }, + { + { 1609516219779025, 777277757338817, 2101121130363987, 550762194946473, 1905542338659364 }, + { 2024821921041576, 426948675450149, 595133284085473, 471860860885970, 600321679413000 }, + { 598474602406721, 1468128276358244, 1191923149557635, 1501376424093216, 1281662691293476 } + }, + { + { 1721138489890707, 1264336102277790, 433064545421287, 1359988423149466, 1561871293409447 }, + { 719520245587143, 393380711632345, 132350400863381, 1543271270810729, 1819543295798660 }, + { 396397949784152, 1811354474471839, 1362679985304303, 2117033964846756, 498041172552279 } + }, + { + { 1812471844975748, 1856491995543149, 126579494584102, 1036244859282620, 1975108050082550 }, + { 650623932407995, 1137551288410575, 2125223403615539, 1725658013221271, 2134892965117796 }, + { 522584000310195, 1241762481390450, 1743702789495384, 2227404127826575, 1686746002148897 } + } +}, +{ /* 7/31 */ + { + { 427904865186312, 1703211129693455, 1585368107547509, 1436984488744336, 761188534613978 }, + { 318101947455002, 248138407995851, 1481904195303927, 309278454311197, 1258516760217879 }, + { 1275068538599310, 513726919533379, 349926553492294, 688428871968420, 1702400196000666 } + }, + { + { 1061864036265233, 961611260325381, 321859632700838, 1045600629959517, 1985130202504038 }, + { 1558816436882417, 1962896332636523, 1337709822062152, 1501413830776938, 294436165831932 }, + { 818359826554971, 1862173000996177, 626821592884859, 573655738872376, 1749691246745455 } + }, + { + { 1988022651432119, 1082111498586040, 1834020786104821, 1454826876423687, 692929915223122 }, + { 2146513703733331, 584788900394667, 464965657279958, 2183973639356127, 238371159456790 }, + { 1129007025494441, 2197883144413266, 265142755578169, 971864464758890, 1983715884903702 } + }, + { + { 1291366624493075, 381456718189114, 1711482489312444, 1815233647702022, 892279782992467 }, + { 444548969917454, 1452286453853356, 2113731441506810, 645188273895859, 810317625309512 }, + { 2242724082797924, 1373354730327868, 1006520110883049, 2147330369940688, 1151816104883620 } + }, + { + { 1745720200383796, 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794250831877809 }, + { 77571826285752, 999304298101753, 487841111777762, 1038031143212339, 339066367948762 } + } +}, +{ /* 8/31 */ + { + { 674994775520533, 266035846330789, 826951213393478, 1405007746162285, 1781791018620876 }, + { 1001412661522686, 348196197067298, 1666614366723946, 888424995032760, 580747687801357 }, + { 1939560076207777, 1409892634407635, 552574736069277, 383854338280405, 190706709864139 } + }, + { + { 2177087163428741, 1439255351721944, 1208070840382793, 2230616362004769, 1396886392021913 }, + { 676962063230039, 1880275537148808, 2046721011602706, 888463247083003, 1318301552024067 }, + { 1466980508178206, 617045217998949, 652303580573628, 757303753529064, 207583137376902 } + }, + { + { 1511056752906902, 105403126891277, 493434892772846, 1091943425335976, 1802717338077427 }, + { 1853982405405128, 1878664056251147, 1528011020803992, 1019626468153565, 1128438412189035 }, + { 1963939888391106, 293456433791664, 697897559513649, 985882796904380, 796244541237972 } + }, + 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2218619146419342, 70688125792186 } + }, + { + { 1299739417079761, 1438616663452759, 1536729078504412, 2053896748919838, 1008421032591246 }, + { 2040723824657366, 399555637875075, 632543375452995, 872649937008051, 1235394727030233 }, + { 2211311599327900, 2139787259888175, 938706616835350, 12609661139114, 2081897930719789 } + }, + { + { 1324994503390450, 336982330582631, 1183998925654177, 1091654665913274, 48727673971319 }, + { 1845522914617879, 1222198248335542, 150841072760134, 1927029069940982, 1189913404498011 }, + { 1079559557592645, 2215338383666441, 1903569501302605, 49033973033940, 305703433934152 } + }, + { + { 94653405416909, 1386121349852999, 1062130477891762, 36553947479274, 833669648948846 }, + { 1432015813136298, 440364795295369, 1395647062821501, 1976874522764578, 934452372723352 }, + { 1296625309219774, 2068273464883862, 1858621048097805, 1492281814208508, 2235868981918946 } + }, + { + { 1490330266465570, 1858795661361448, 1436241134969763, 294573218899647, 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672344594801910, 1320437969700239 }, + { 1508590048271766, 1131769479776094, 101550868699323, 428297785557897, 561791648661744 } + } +}, +{ /* 11/31 */ + { + { 756417570499462, 237882279232602, 2136263418594016, 1701968045454886, 703713185137472 }, + { 1781187809325462, 1697624151492346, 1381393690939988, 175194132284669, 1483054666415238 }, + { 2175517777364616, 708781536456029, 955668231122942, 1967557500069555, 2021208005604118 } + }, + { + { 1115135966606887, 224217372950782, 915967306279222, 593866251291540, 561747094208006 }, + { 1443163092879439, 391875531646162, 2180847134654632, 464538543018753, 1594098196837178 }, + { 850858855888869, 319436476624586, 327807784938441, 740785849558761, 17128415486016 } + }, + { + { 2132756334090067, 536247820155645, 48907151276867, 608473197600695, 1261689545022784 }, + { 1525176236978354, 974205476721062, 293436255662638, 148269621098039, 137961998433963 }, + { 1121075518299410, 2071745529082111, 1265567917414828, 1648196578317805, 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1949315551096831, 1069003344994464, 1939165033499916, 1548227205730856, 1933767655861407 }, + { 1730519386931635, 1393284965610134, 1597143735726030, 416032382447158, 1429665248828629 } + }, + { + { 360275475604565, 547835731063078, 215360904187529, 596646739879007, 332709650425085 }, + { 47602113726801, 1522314509708010, 437706261372925, 814035330438027, 335930650933545 }, + { 1291597595523886, 1058020588994081, 402837842324045, 1363323695882781, 2105763393033193 } + } +}, +{ /* 12/31 */ + { + { 109521982566564, 1715257748585139, 1112231216891516, 2046641005101484, 134249157157013 }, + { 2156991030936798, 2227544497153325, 1869050094431622, 754875860479115, 1754242344267058 }, + { 1846089562873800, 98894784984326, 1412430299204844, 171351226625762, 1100604760929008 } + }, + { + { 84172382130492, 499710970700046, 425749630620778, 1762872794206857, 612842602127960 }, + { 868309334532756, 1703010512741873, 1952690008738057, 4325269926064, 2071083554962116 }, + { 523094549451158, 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923808779163088, 664390074196579 }, + { 1323460699404750, 1262690757880991, 871777133477900, 1060078894988977, 1712236889662886 }, + { 1696163952057966, 1391710137550823, 608793846867416, 1034391509472039, 1780770894075012 } + }, + { + { 1367603834210841, 2131988646583224, 890353773628144, 1908908219165595, 270836895252891 }, + { 597536315471731, 40375058742586, 1942256403956049, 1185484645495932, 312666282024145 }, + { 1919411405316294, 1234508526402192, 1066863051997083, 1008444703737597, 1348810787701552 } + } +}, +{ /* 15/31 */ + { + { 2102881477513865, 1570274565945361, 1573617900503708, 18662635732583, 2232324307922098 }, + { 1853931367696942, 8107973870707, 350214504129299, 775206934582587, 1752317649166792 }, + { 1417148368003523, 721357181628282, 505725498207811, 373232277872983, 261634707184480 } + }, + { + { 2186733281493267, 2250694917008620, 1014829812957440, 479998161452389, 83566193876474 }, + { 1268116367301224, 560157088142809, 802626839600444, 2210189936605713, 1129993785579988 }, + { 615183387352312, 917611676109240, 878893615973325, 978940963313282, 938686890583575 } + }, + { + { 522024729211672, 1045059315315808, 1892245413707790, 1907891107684253, 2059998109500714 }, + { 1799679152208884, 912132775900387, 25967768040979, 432130448590461, 274568990261996 }, + { 98698809797682, 2144627600856209, 1907959298569602, 811491302610148, 1262481774981493 } + }, + { + { 1791451399743152, 1713538728337276, 118349997257490, 1882306388849954, 158235232210248 }, + { 1217809823321928, 2173947284933160, 1986927836272325, 1388114931125539, 12686131160169 }, + { 1650875518872272, 1136263858253897, 1732115601395988, 734312880662190, 1252904681142109 } + }, + { + { 372986456113865, 525430915458171, 2116279931702135, 501422713587815, 1907002872974925 }, + { 803147181835288, 868941437997146, 316299302989663, 943495589630550, 571224287904572 }, + { 227742695588364, 1776969298667369, 628602552821802, 457210915378118, 2041906378111140 } + }, + { + { 815000523470260, 913085688728307, 1052060118271173, 1345536665214223, 541623413135555 }, + { 1580216071604333, 1877997504342444, 857147161260913, 703522726778478, 2182763974211603 }, + { 1870080310923419, 71988220958492, 1783225432016732, 615915287105016, 1035570475990230 } + }, + { + { 730987750830150, 857613889540280, 1083813157271766, 1002817255970169, 1719228484436074 }, + { 377616581647602, 1581980403078513, 804044118130621, 2034382823044191, 643844048472185 }, + { 176957326463017, 1573744060478586, 528642225008045, 1816109618372371, 1515140189765006 } + }, + { + { 1888911448245718, 1387110895611080, 1924503794066429, 1731539523700949, 2230378382645454 }, + { 443392177002051, 233793396845137, 2199506622312416, 1011858706515937, 974676837063129 }, + { 1846351103143623, 1949984838808427, 671247021915253, 1946756846184401, 1929296930380217 } + } +}, +{ /* 16/31 */ + { + { 849646212452002, 1410198775302919, 73767886183695, 1641663456615812, 762256272452411 }, + { 692017667358279, 723305578826727, 1638042139863265, 748219305990306, 334589200523901 }, + { 22893968530686, 2235758574399251, 1661465835630252, 925707319443452, 1203475116966621 } + }, + { + { 801299035785166, 1733292596726131, 1664508947088596, 467749120991922, 1647498584535623 }, + { 903105258014366, 427141894933047, 561187017169777, 1884330244401954, 1914145708422219 }, + { 1344191060517578, 1960935031767890, 1518838929955259, 1781502350597190, 1564784025565682 } + }, + { + { 673723351748086, 1979969272514923, 1175287312495508, 1187589090978666, 1881897672213940 }, + { 1917185587363432, 1098342571752737, 5935801044414, 2000527662351839, 1538640296181569 }, + { 2495540013192, 678856913479236, 224998292422872, 219635787698590, 1972465269000940 } + }, + { + { 271413961212179, 1353052061471651, 344711291283483, 2014925838520662, 2006221033113941 }, + { 194583029968109, 514316781467765, 829677956235672, 1676415686873082, 810104584395840 }, + { 1980510813313589, 1948645276483975, 152063780665900, 129968026417582, 256984195613935 } + }, + { + { 1860190562533102, 1936576191345085, 461100292705964, 1811043097042830, 957486749306835 }, + { 796664815624365, 1543160838872951, 1500897791837765, 1667315977988401, 599303877030711 }, + { 1151480509533204, 2136010406720455, 738796060240027, 319298003765044, 1150614464349587 } + }, + { + { 1731069268103150, 735642447616087, 1364750481334268, 417232839982871, 927108269127661 }, + { 1017222050227968, 1987716148359, 2234319589635701, 621282683093392, 2132553131763026 }, + { 1567828528453324, 1017807205202360, 565295260895298, 829541698429100, 307243822276582 } + }, + { + { 249079270936248, 1501514259790706, 947909724204848, 944551802437487, 552658763982480 }, + { 2089966982947227, 1854140343916181, 2151980759220007, 2139781292261749, 158070445864917 }, + { 1338766321464554, 1906702607371284, 1519569445519894, 115384726262267, 1393058953390992 } + }, + { + { 1364621558265400, 1512388234908357, 1926731583198686, 2041482526432505, 920401122333774 }, + { 1884844597333588, 601480070269079, 620203503079537, 1079527400117915, 1202076693132015 }, + { 840922919763324, 727955812569642, 1303406629750194, 522898432152867, 294161410441865 } + } +}, +{ /* 17/31 */ + { + { 353760790835310, 1598361541848743, 1122905698202299, 1922533590158905, 419107700666580 }, + { 359856369838236, 180914355488683, 861726472646627, 218807937262986, 575626773232501 }, + { 755467689082474, 909202735047934, 730078068932500, 936309075711518, 2007798262842972 } + }, + { + { 1609384177904073, 362745185608627, 1335318541768201, 800965770436248, 547877979267412 }, + { 984339177776787, 815727786505884, 1645154585713747, 1659074964378553, 1686601651984156 }, + { 1697863093781930, 599794399429786, 1104556219769607, 830560774794755, 12812858601017 } + }, + { + { 1168737550514982, 897832437380552, 463140296333799, 302564600022547, 2008360505135501 }, + { 1856930662813910, 678090852002597, 1920179140755167, 1259527833759868, 55540971895511 }, + { 1158643631044921, 476554103621892, 178447851439725, 1305025542653569, 103433927680625 } + }, + { + { 2176793111709008, 1576725716350391, 2009350167273523, 2012390194631546, 2125297410909580 }, + { 825403285195098, 2144208587560784, 1925552004644643, 1915177840006985, 1015952128947864 }, + { 1807108316634472, 1534392066433717, 347342975407218, 1153820745616376, 7375003497471 } + }, + { + { 983061001799725, 431211889901241, 2201903782961093, 817393911064341, 2214616493042167 }, + { 228567918409756, 865093958780220, 358083886450556, 159617889659320, 1360637926292598 }, + { 234147501399755, 2229469128637390, 2175289352258889, 1397401514549353, 1885288963089922 } + }, + { + { 1111762412951562, 252849572507389, 1048714233823341, 146111095601446, 1237505378776770 }, + { 1113790697840279, 1051167139966244, 1045930658550944, 2011366241542643, 1686166824620755 }, + { 1054097349305049, 1872495070333352, 182121071220717, 1064378906787311, 100273572924182 } + }, + { + { 1306410853171605, 1627717417672447, 50983221088417, 1109249951172250, 870201789081392 }, + { 104233794644221, 1548919791188248, 2224541913267306, 2054909377116478, 1043803389015153 }, + { 216762189468802, 707284285441622, 190678557969733, 973969342604308, 1403009538434867 } + }, + { + { 1279024291038477, 344776835218310, 273722096017199, 1834200436811442, 634517197663804 }, + { 343805853118335, 1302216857414201, 566872543223541, 2051138939539004, 321428858384280 }, + { 470067171324852, 1618629234173951, 2000092177515639, 7307679772789, 1117521120249968 } + } +}, +{ /* 18/31 */ + { + { 278151578291475, 1810282338562947, 1771599529530998, 1383659409671631, 685373414471841 }, + { 577009397403102, 1791440261786291, 2177643735971638, 174546149911960, 1412505077782326 }, + { 893719721537457, 1201282458018197, 1522349501711173, 58011597740583, 1130406465887139 } + }, + { + { 412607348255453, 1280455764199780, 2233277987330768, 14180080401665, 331584698417165 }, + { 262483770854550, 990511055108216, 526885552771698, 571664396646158, 354086190278723 }, + { 1820352417585487, 24495617171480, 1547899057533253, 10041836186225, 480457105094042 } + }, + { + { 2023310314989233, 637905337525881, 2106474638900687, 557820711084072, 1687858215057826 }, + { 1144168702609745, 604444390410187, 1544541121756138, 1925315550126027, 626401428894002 }, + { 1922168257351784, 2018674099908659, 1776454117494445, 956539191509034, 36031129147635 } + }, + { + { 544644538748041, 1039872944430374, 876750409130610, 710657711326551, 1216952687484972 }, + { 58242421545916, 2035812695641843, 2118491866122923, 1191684463816273, 46921517454099 }, + { 272268252444639, 1374166457774292, 2230115177009552, 1053149803909880, 1354288411641016 } + }, + { + { 1857910905368338, 1754729879288912, 885945464109877, 1516096106802166, 1602902393369811 }, + { 1193437069800958, 901107149704790, 999672920611411, 477584824802207, 364239578697845 }, + { 886299989548838, 1538292895758047, 1590564179491896, 1944527126709657, 837344427345298 } + }, + { + { 754558365378305, 1712186480903618, 1703656826337531, 750310918489786, 518996040250900 }, + { 1309847803895382, 1462151862813074, 211370866671570, 1544595152703681, 1027691798954090 }, + { 803217563745370, 1884799722343599, 1357706345069218, 2244955901722095, 730869460037413 } + }, + { + { 689299471295966, 1831210565161071, 1375187341585438, 1106284977546171, 1893781834054269 }, + { 696351368613042, 1494385251239250, 738037133616932, 636385507851544, 927483222611406 }, + { 1949114198209333, 1104419699537997, 783495707664463, 1747473107602770, 2002634765788641 } + }, + { + { 1607325776830197, 530883941415333, 1451089452727895, 1581691157083423, 496100432831154 }, + { 1068900648804224, 2006891997072550, 1134049269345549, 1638760646180091, 2055396084625778 }, + { 2222475519314561, 1870703901472013, 1884051508440561, 1344072275216753, 1318025677799069 } + } +}, +{ /* 19/31 */ + { + { 155711679280656, 681100400509288, 389811735211209, 2135723811340709, 408733211204125 }, + { 7813206966729, 194444201427550, 2071405409526507, 1065605076176312, 1645486789731291 }, + { 16625790644959, 1647648827778410, 1579910185572704, 436452271048548, 121070048451050 } + }, + { + { 1037263028552531, 568385780377829, 297953104144430, 1558584511931211, 2238221839292471 }, + { 190565267697443, 672855706028058, 338796554369226, 337687268493904, 853246848691734 }, + { 1763863028400139, 766498079432444, 1321118624818005, 69494294452268, 858786744165651 } + }, + { + { 1292056768563024, 1456632109855638, 1100631247050184, 1386133165675321, 1232898350193752 }, + { 366253102478259, 525676242508811, 1449610995265438, 1183300845322183, 185960306491545 }, + { 28315355815982, 460422265558930, 1799675876678724, 1969256312504498, 1051823843138725 } + }, + { + { 156914999361983, 1606148405719949, 1665208410108430, 317643278692271, 1383783705665320 }, + { 54684536365732, 2210010038536222, 1194984798155308, 535239027773705, 1516355079301361 }, + { 1484387703771650, 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2224911448949390, 964352058245223 }, + { 1730194207717538, 431790042319772, 1831515233279467, 1372080552768581, 1074513929381760 }, + { 1450880638731607, 1019861580989005, 1229729455116861, 1174945729836143, 826083146840706 } + } +}, +{ /* 20/31 */ + { + { 1899935429242705, 1602068751520477, 940583196550370, 82431069053859, 1540863155745696 }, + { 2136688454840028, 2099509000964294, 1690800495246475, 1217643678575476, 828720645084218 }, + { 765548025667841, 462473984016099, 998061409979798, 546353034089527, 2212508972466858 } + }, + { + { 46575283771160, 892570971573071, 1281983193144090, 1491520128287375, 75847005908304 }, + { 1801436127943107, 1734436817907890, 1268728090345068, 167003097070711, 2233597765834956 }, + { 1997562060465113, 1048700225534011, 7615603985628, 1855310849546841, 2242557647635213 } + }, + { + { 1161017320376250, 492624580169043, 2169815802355237, 976496781732542, 1770879511019629 }, + { 1357044908364776, 729130645262438, 1762469072918979, 1365633616878458, 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984292135520292, 135138246951259, 2220652137473167, 1722843421165029, 190482558012909 }, + { 298845952651262, 1166086588952562, 1179896526238434, 1347812759398693, 1412945390096208 }, + { 1143239552672925, 906436640714209, 2177000572812152, 2075299936108548, 325186347798433 } + }, + { + { 721024854374772, 684487861263316, 1373438744094159, 2193186935276995, 1387043709851261 }, + { 418098668140962, 715065997721283, 1471916138376055, 2168570337288357, 937812682637044 }, + { 1043584187226485, 2143395746619356, 2209558562919611, 482427979307092, 847556718384018 } + } +}, +{ /* 21/31 */ + { + { 1248731221520759, 1465200936117687, 540803492710140, 52978634680892, 261434490176109 }, + { 1057329623869501, 620334067429122, 461700859268034, 2012481616501857, 297268569108938 }, + { 1055352180870759, 1553151421852298, 1510903185371259, 1470458349428097, 1226259419062731 } + }, + { + { 1492988790301668, 790326625573331, 1190107028409745, 1389394752159193, 1620408196604194 }, + { 47000654413729, 1004754424173864, 1868044813557703, 173236934059409, 588771199737015 }, + { 30498470091663, 1082245510489825, 576771653181956, 806509986132686, 1317634017056939 } + }, + { + { 420308055751555, 1493354863316002, 165206721528088, 1884845694919786, 2065456951573059 }, + { 1115636332012334, 1854340990964155, 83792697369514, 1972177451994021, 457455116057587 }, + { 1698968457310898, 1435137169051090, 1083661677032510, 938363267483709, 340103887207182 } + }, + { + { 1995325341336574, 911500251774648, 164010755403692, 855378419194762, 1573601397528842 }, + { 241719380661528, 310028521317150, 1215881323380194, 1408214976493624, 2141142156467363 }, + { 1315157046163473, 727368447885818, 1363466668108618, 1668921439990361, 1398483384337907 } + }, + { + { 75029678299646, 1015388206460473, 1849729037055212, 1939814616452984, 444404230394954 }, + { 2053597130993710, 2024431685856332, 2233550957004860, 2012407275509545, 872546993104440 }, + { 1217269667678610, 599909351968693, 1390077048548598, 1471879360694802, 739586172317596 } + }, + { + { 1718318639380794, 1560510726633958, 904462881159922, 1418028351780052, 94404349451937 }, + { 2132502667405250, 214379346175414, 1502748313768060, 1960071701057800, 1353971822643138 }, + { 319394212043702, 2127459436033571, 717646691535162, 663366796076914, 318459064945314 } + }, + { + { 405989424923593, 1960452633787083, 667349034401665, 1492674260767112, 1451061489880787 }, + { 947085906234007, 323284730494107, 1485778563977200, 728576821512394, 901584347702286 }, + { 1575783124125742, 2126210792434375, 1569430791264065, 1402582372904727, 1891780248341114 } + }, + { + { 838432205560695, 1997703511451664, 1018791879907867, 1662001808174331, 78328132957753 }, + { 739152638255629, 2074935399403557, 505483666745895, 1611883356514088, 628654635394878 }, + { 1822054032121349, 643057948186973, 7306757352712, 577249257962099, 284735863382083 } + } +}, +{ /* 22/31 */ + { + { 1366558556363930, 1448606567552086, 1478881020944768, 165803179355898, 1115718458123498 }, + { 204146226972102, 1630511199034723, 2215235214174763, 174665910283542, 956127674017216 }, + { 1562934578796716, 1070893489712745, 11324610642270, 958989751581897, 2172552325473805 } + }, + { + { 1770564423056027, 735523631664565, 1326060113795289, 1509650369341127, 65892421582684 }, + { 623682558650637, 1337866509471512, 990313350206649, 1314236615762469, 1164772974270275 }, + { 223256821462517, 723690150104139, 1000261663630601, 933280913953265, 254872671543046 } + }, + { + { 1969087237026041, 624795725447124, 1335555107635969, 2069986355593023, 1712100149341902 }, + { 1236103475266979, 1837885883267218, 1026072585230455, 1025865513954973, 1801964901432134 }, + { 1115241013365517, 1712251818829143, 2148864332502771, 2096001471438138, 2235017246626125 } + }, + { + { 1299268198601632, 2047148477845621, 2165648650132450, 1612539282026145, 514197911628890 }, + { 118352772338543, 1067608711804704, 1434796676193498, 1683240170548391, 230866769907437 }, + { 1850689576796636, 1601590730430274, 1139674615958142, 1954384401440257, 76039205311 } + }, + { + { 1723387471374172, 997301467038410, 533927635123657, 20928644693965, 1756575222802513 }, + { 2146711623855116, 503278928021499, 625853062251406, 1109121378393107, 1033853809911861 }, + { 571005965509422, 2005213373292546, 1016697270349626, 56607856974274, 914438579435146 } + }, + { + { 1346698876211176, 2076651707527589, 1084761571110205, 265334478828406, 1068954492309671 }, + { 1769967932677654, 1695893319756416, 1151863389675920, 1781042784397689, 400287774418285 }, + { 1851867764003121, 403841933237558, 820549523771987, 761292590207581, 1743735048551143 } + }, + { + { 410915148140008, 2107072311871739, 1004367461876503, 99684895396761, 1180818713503224 }, + { 285945406881439, 648174397347453, 1098403762631981, 1366547441102991, 1505876883139217 }, + { 672095903120153, 1675918957959872, 636236529315028, 1569297300327696, 2164144194785875 } + }, + { + { 1902708175321798, 1035343530915438, 1178560808893263, 301095684058146, 1280977479761118 }, + { 1615357281742403, 404257611616381, 2160201349780978, 1160947379188955, 1578038619549541 }, + { 2013087639791217, 822734930507457, 1785668418619014, 1668650702946164, 389450875221715 } + } +}, +{ /* 23/31 */ + { + { 453918449698368, 106406819929001, 2072540975937135, 308588860670238, 1304394580755385 }, + { 1295082798350326, 2091844511495996, 1851348972587817, 3375039684596, 789440738712837 }, + { 2083069137186154, 848523102004566, 993982213589257, 1405313299916317, 1532824818698468 } + }, + { + { 1495961298852430, 1397203457344779, 1774950217066942, 139302743555696, 66603584342787 }, + { 1782411379088302, 1096724939964781, 27593390721418, 542241850291353, 1540337798439873 }, + { 693543956581437, 171507720360750, 1557908942697227, 1074697073443438, 1104093109037196 } + }, + { + { 345288228393419, 1099643569747172, 134881908403743, 1740551994106740, 248212179299770 }, + { 231429562203065, 1526290236421172, 2021375064026423, 1520954495658041, 806337791525116 }, + { 1079623667189886, 872403650198613, 766894200588288, 2163700860774109, 2023464507911816 } + }, + { + { 854645372543796, 1936406001954827, 151460662541253, 825325739271555, 1554306377287556 }, + { 1497138821904622, 1044820250515590, 1742593886423484, 1237204112746837, 849047450816987 }, + { 667962773375330, 1897271816877105, 1399712621683474, 1143302161683099, 2081798441209593 } + }, + { + { 127147851567005, 1936114012888110, 1704424366552046, 856674880716312, 716603621335359 }, + { 1072409664800960, 2146937497077528, 1508780108920651, 935767602384853, 1112800433544068 }, + { 333549023751292, 280219272863308, 2104176666454852, 1036466864875785, 536135186520207 } + }, + { + { 373666279883137, 146457241530109, 304116267127857, 416088749147715, 1258577131183391 }, + { 1186115062588401, 2251609796968486, 1098944457878953, 1153112761201374, 1791625503417267 }, + { 1870078460219737, 2129630962183380, 852283639691142, 292865602592851, 401904317342226 } + }, + { + { 1361070124828035, 815664541425524, 1026798897364671, 1951790935390647, 555874891834790 }, + { 1546301003424277, 459094500062839, 1097668518375311, 1780297770129643, 720763293687608 }, + { 1212405311403990, 1536693382542438, 61028431067459, 1863929423417129, 1223219538638038 } + }, + { + { 1294303766540260, 1183557465955093, 882271357233093, 63854569425375, 2213283684565087 }, + { 339050984211414, 601386726509773, 413735232134068, 966191255137228, 1839475899458159 }, + { 235605972169408, 2174055643032978, 1538335001838863, 1281866796917192, 1815940222628465 } + } +}, +{ /* 24/31 */ + { + { 1632352921721536, 1833328609514701, 2092779091951987, 1923956201873226, 2210068022482919 }, + { 35271216625062, 1712350667021807, 983664255668860, 98571260373038, 1232645608559836 }, + { 1998172393429622, 1798947921427073, 784387737563581, 1589352214827263, 1589861734168180 } + }, + { + { 1733739258725305, 31715717059538, 201969945218860, 992093044556990, 1194308773174556 }, + { 846415389605137, 746163495539180, 829658752826080, 592067705956946, 957242537821393 }, + { 1758148849754419, 619249044817679, 168089007997045, 1371497636330523, 1867101418880350 } + }, + { + { 326633984209635, 261759506071016, 1700682323676193, 1577907266349064, 1217647663383016 }, + { 1714182387328607, 1477856482074168, 574895689942184, 2159118410227270, 1555532449716575 }, + { 853828206885131, 998498946036955, 1835887550391235, 207627336608048, 258363815956050 } + }, + { + { 141141474651677, 1236728744905256, 643101419899887, 1646615130509173, 1208239602291765 }, + { 1501663228068911, 1354879465566912, 1444432675498247, 897812463852601, 855062598754348 }, + { 714380763546606, 1032824444965790, 1774073483745338, 1063840874947367, 1738680636537158 } + }, + { + { 1640635546696252, 633168953192112, 2212651044092396, 30590958583852, 368515260889378 }, + { 1171650314802029, 1567085444565577, 1453660792008405, 757914533009261, 1619511342778196 }, + { 420958967093237, 971103481109486, 2169549185607107, 1301191633558497, 1661514101014240 } + }, + { + { 907123651818302, 1332556122804146, 1824055253424487, 1367614217442959, 1982558335973172 }, + { 1121533090144639, 1021251337022187, 110469995947421, 1511059774758394, 2110035908131662 }, + { 303213233384524, 2061932261128138, 352862124777736, 40828818670255, 249879468482660 } + }, + { + { 856559257852200, 508517664949010, 1378193767894916, 1723459126947129, 1962275756614521 }, + { 1445691340537320, 40614383122127, 402104303144865, 485134269878232, 1659439323587426 }, + { 20057458979482, 1183363722525800, 2140003847237215, 2053873950687614, 2112017736174909 } + }, + { + { 2228654250927986, 1483591363415267, 1368661293910956, 1076511285177291, 526650682059608 }, + { 709481497028540, 531682216165724, 316963769431931, 1814315888453765, 258560242424104 }, + { 1053447823660455, 1955135194248683, 1010900954918985, 1182614026976701, 1240051576966610 } + } +}, +{ /* 25/31 */ + { + { 1957943897155497, 1788667368028035, 137692910029106, 1039519607062, 826404763313028 }, + { 1848942433095597, 1582009882530495, 1849292741020143, 1068498323302788, 2001402229799484 }, + { 1528282417624269, 2142492439828191, 2179662545816034, 362568973150328, 1591374675250271 } + }, + { + { 160026679434388, 232341189218716, 2149181472355545, 598041771119831, 183859001910173 }, + { 2013278155187349, 662660471354454, 793981225706267, 411706605985744, 804490933124791 }, + { 2051892037280204, 488391251096321, 2230187337030708, 930221970662692, 679002758255210 } + }, + { + { 1530723630438670, 875873929577927, 341560134269988, 449903119530753, 1055551308214179 }, + { 1461835919309432, 1955256480136428, 180866187813063, 1551979252664528, 557743861963950 }, + { 359179641731115, 1324915145732949, 902828372691474, 294254275669987, 1887036027752957 } + }, + { + { 2043271609454323, 2038225437857464, 1317528426475850, 1398989128982787, 2027639881006861 }, + { 2072902725256516, 312132452743412, 309930885642209, 996244312618453, 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2014540178270324, 192672779514432, 213877182641530, 2194819933853411, 1716422829364835 }, + { 1540769606609725, 2148289943846077, 1597804156127445, 1230603716683868, 815423458809453 }, + { 1738560251245018, 1779576754536888, 1783765347671392, 1880170990446751, 1088225159617541 } + } +}, +{ /* 26/31 */ + { + { 659303913929492, 1956447718227573, 1830568515922666, 841069049744408, 1669607124206368 }, + { 1143465490433355, 1532194726196059, 1093276745494697, 481041706116088, 2121405433561163 }, + { 1686424298744462, 1451806974487153, 266296068846582, 1834686947542675, 1720762336132256 } + }, + { + { 889217026388959, 1043290623284660, 856125087551909, 1669272323124636, 1603340330827879 }, + { 1206396181488998, 333158148435054, 1402633492821422, 1120091191722026, 1945474114550509 }, + { 766720088232571, 1512222781191002, 1189719893490790, 2091302129467914, 2141418006894941 } + }, + { + { 419663647306612, 1998875112167987, 1426599870253707, 1154928355379510, 486538532138187 }, + { 938160078005954, 1421776319053174, 1941643234741774, 180002183320818, 1414380336750546 }, + { 398001940109652, 1577721237663248, 1012748649830402, 1540516006905144, 1011684812884559 } + }, + { + { 1653276489969630, 6081825167624, 1921777941170836, 1604139841794531, 861211053640641 }, + { 996661541407379, 1455877387952927, 744312806857277, 139213896196746, 1000282908547789 }, + { 1450817495603008, 1476865707053229, 1030490562252053, 620966950353376, 1744760161539058 } + }, + { + { 559728410002599, 37056661641185, 2038622963352006, 1637244893271723, 1026565352238948 }, + { 962165956135846, 1116599660248791, 182090178006815, 1455605467021751, 196053588803284 }, + { 796863823080135, 1897365583584155, 420466939481601, 2165972651724672, 932177357788289 } + }, + { + { 877047233620632, 1375632631944375, 643773611882121, 660022738847877, 19353932331831 }, + { 2216943882299338, 394841323190322, 2222656898319671, 558186553950529, 1077236877025190 }, + { 801118384953213, 1914330175515892, 574541023311511, 1471123787903705, 1526158900256288 } + }, + { + { 949617889087234, 2207116611267331, 912920039141287, 501158539198789, 62362560771472 }, + { 1474518386765335, 1760793622169197, 1157399790472736, 1622864308058898, 165428294422792 }, + { 1961673048027128, 102619413083113, 1051982726768458, 1603657989805485, 1941613251499678 } + }, + { + { 1401939116319266, 335306339903072, 72046196085786, 862423201496006, 850518754531384 }, + { 1234706593321979, 1083343891215917, 898273974314935, 1640859118399498, 157578398571149 }, + { 1143483057726416, 1992614991758919, 674268662140796, 1773370048077526, 674318359920189 } + } +}, +{ /* 27/31 */ + { + { 1835401379538542, 173900035308392, 818247630716732, 1762100412152786, 1021506399448291 }, + { 1506632088156630, 2127481795522179, 513812919490255, 140643715928370, 442476620300318 }, + { 2056683376856736, 219094741662735, 2193541883188309, 1841182310235800, 556477468664293 } + }, + { + { 1315019427910827, 1049075855992603, 2066573052986543, 266904467185534, 2040482348591520 }, + { 94096246544434, 922482381166992, 24517828745563, 2139430508542503, 2097139044231004 }, + { 537697207950515, 1399352016347350, 1563663552106345, 2148749520888918, 549922092988516 } + }, + { + { 1747985413252434, 680511052635695, 1809559829982725, 594274250930054, 201673170745982 }, + { 323583936109569, 1973572998577657, 1192219029966558, 79354804385273, 1374043025560347 }, + { 213277331329947, 416202017849623, 1950535221091783, 1313441578103244, 2171386783823658 } + }, + { + { 189088804229831, 993969372859110, 895870121536987, 1547301535298256, 1477373024911350 }, + { 1620578418245010, 541035331188469, 2235785724453865, 2154865809088198, 1974627268751826 }, + { 1346805451740245, 1350981335690626, 942744349501813, 2155094562545502, 1012483751693409 } + }, + { + { 2107080134091762, 1132567062788208, 1824935377687210, 769194804343737, 1857941799971888 }, + { 1074666112436467, 249279386739593, 1174337926625354, 1559013532006480, 1472287775519121 }, + { 1872620123779532, 1892932666768992, 1921559078394978, 1270573311796160, 1438913646755037 } + }, + { + { 837390187648199, 1012253300223599, 989780015893987, 1351393287739814, 328627746545550 }, + { 1028328827183114, 1711043289969857, 1350832470374933, 1923164689604327, 1495656368846911 }, + { 1900828492104143, 430212361082163, 687437570852799, 832514536673512, 1685641495940794 } + }, + { + { 842632847936398, 605670026766216, 290836444839585, 163210774892356, 2213815011799645 }, + { 1176336383453996, 1725477294339771, 12700622672454, 678015708818208, 162724078519879 }, + { 1448049969043497, 1789411762943521, 385587766217753, 90201620913498, 832999441066823 } + }, + { + { 516086333293313, 2240508292484616, 1351669528166508, 1223255565316488, 750235824427138 }, + { 1263624896582495, 1102602401673328, 526302183714372, 2152015839128799, 1483839308490010 }, + { 442991718646863, 1599275157036458, 1925389027579192, 899514691371390, 350263251085160 } + } +}, +{ /* 28/31 */ + { + { 1689713572022143, 593854559254373, 978095044791970, 1985127338729499, 1676069120347625 }, + { 1557207018622683, 340631692799603, 1477725909476187, 614735951619419, 2033237123746766 }, + { 968764929340557, 1225534776710944, 662967304013036, 1155521416178595, 791142883466590 } + }, + { + { 1487081286167458, 993039441814934, 1792378982844640, 698652444999874, 2153908693179754 }, + { 1123181311102823, 685575944875442, 507605465509927, 1412590462117473, 568017325228626 }, + { 560258797465417, 2193971151466401, 1824086900849026, 579056363542056, 1690063960036441 } + }, + { + { 1918407319222416, 353767553059963, 1930426334528099, 1564816146005724, 1861342381708096 }, + { 2131325168777276, 1176636658428908, 1756922641512981, 1390243617176012, 1966325177038383 }, + { 2063958120364491, 2140267332393533, 699896251574968, 273268351312140, 375580724713232 } + }, + { + { 2024297515263178, 416959329722687, 1079014235017302, 171612225573183, 1031677520051053 }, + { 2033900009388450, 1744902869870788, 2190580087917640, 1949474984254121, 231049754293748 }, + { 343868674606581, 550155864008088, 1450580864229630, 481603765195050, 896972360018042 } + }, + { + { 2151139328380127, 314745882084928, 59756825775204, 1676664391494651, 2048348075599360 }, + { 1528930066340597, 1605003907059576, 1055061081337675, 1458319101947665, 1234195845213142 }, + { 830430507734812, 1780282976102377, 1425386760709037, 362399353095425, 2168861579799910 } + }, + { + { 1155762232730333, 980662895504006, 2053766700883521, 490966214077606, 510405877041357 }, + { 1683750316716132, 652278688286128, 1221798761193539, 1897360681476669, 319658166027343 }, + { 618808732869972, 72755186759744, 2060379135624181, 1730731526741822, 48862757828238 } + }, + { + { 1463171970593505, 1143040711767452, 614590986558883, 1409210575145591, 1882816996436803 }, + { 2230133264691131, 563950955091024, 2042915975426398, 827314356293472, 672028980152815 }, + { 264204366029760, 1654686424479449, 2185050199932931, 2207056159091748, 506015669043634 } + }, + { + { 1784446333136569, 1973746527984364, 334856327359575, 1156769775884610, 1023950124675478 }, + { 2065270940578383, 31477096270353, 306421879113491, 181958643936686, 1907105536686083 }, + { 1496516440779464, 1748485652986458, 872778352227340, 818358834654919, 97932669284220 } + } +}, +{ /* 29/31 */ + { + { 471636015770351, 672455402793577, 1804995246884103, 1842309243470804, 1501862504981682 }, + { 1013216974933691, 538921919682598, 1915776722521558, 1742822441583877, 1886550687916656 }, + { 2094270000643336, 303971879192276, 40801275554748, 649448917027930, 1818544418535447 } + }, + { + { 2241737709499165, 549397817447461, 838180519319392, 1725686958520781, 1705639080897747 }, + { 1216074541925116, 50120933933509, 1565829004133810, 721728156134580, 349206064666188 }, + { 948617110470858, 346222547451945, 1126511960599975, 1759386906004538, 493053284802266 } + }, + { + { 1454933046815146, 874696014266362, 1467170975468588, 1432316382418897, 2111710746366763 }, + { 2105387117364450, 1996463405126433, 1303008614294500, 851908115948209, 1353742049788635 }, + { 750300956351719, 1487736556065813, 15158817002104, 1511998221598392, 971739901354129 } + }, + { + { 1874648163531693, 2124487685930551, 1810030029384882, 918400043048335, 586348627300650 }, + { 1235084464747900, 1166111146432082, 1745394857881591, 1405516473883040, 4463504151617 }, + { 1663810156463827, 327797390285791, 1341846161759410, 1964121122800605, 1747470312055380 } + }, + { + { 660005247548233, 2071860029952887, 1358748199950107, 911703252219107, 1014379923023831 }, + { 2206641276178231, 1690587809721504, 1600173622825126, 2156096097634421, 1106822408548216 }, + { 1344788193552206, 1949552134239140, 1735915881729557, 675891104100469, 1834220014427292 } + }, + { + { 1920949492387964, 158885288387530, 70308263664033, 626038464897817, 1468081726101009 }, + { 622221042073383, 1210146474039168, 1742246422343683, 1403839361379025, 417189490895736 }, + { 22727256592983, 168471543384997, 1324340989803650, 1839310709638189, 504999476432775 } + }, + { + { 1313240518756327, 1721896294296942, 52263574587266, 2065069734239232, 804910473424630 }, + { 1337466662091884, 1287645354669772, 2018019646776184, 652181229374245, 898011753211715 }, + { 1969792547910734, 779969968247557, 2011350094423418, 1823964252907487, 1058949448296945 } + }, + { + { 207343737062002, 1118176942430253, 758894594548164, 806764629546266, 1157700123092949 }, + { 1273565321399022, 1638509681964574, 759235866488935, 666015124346707, 897983460943405 }, + { 1717263794012298, 1059601762860786, 1837819172257618, 1054130665797229, 680893204263559 } + } +}, +{ /* 30/31 */ + { + { 2237039662793603, 2249022333361206, 2058613546633703, 149454094845279, 2215176649164582 }, + { 79472182719605, 1851130257050174, 1825744808933107, 821667333481068, 781795293511946 }, + { 755822026485370, 152464789723500, 1178207602290608, 410307889503239, 156581253571278 } + }, + { + { 1418185496130297, 484520167728613, 1646737281442950, 1401487684670265, 1349185550126961 }, + { 1495380034400429, 325049476417173, 46346894893933, 1553408840354856, 828980101835683 }, + { 1280337889310282, 2070832742866672, 1640940617225222, 2098284908289951, 450929509534434 } + }, + { + { 407703353998781, 126572141483652, 286039827513621, 1999255076709338, 2030511179441770 }, + { 1254958221100483, 1153235960999843, 942907704968834, 637105404087392, 1149293270147267 }, + { 894249020470196, 400291701616810, 406878712230981, 1599128793487393, 1145868722604026 } + }, + { + { 1497955250203334, 110116344653260, 1128535642171976, 1900106496009660, 129792717460909 }, + { 452487513298665, 1352120549024569, 1173495883910956, 1999111705922009, 367328130454226 }, + { 1717539401269642, 1475188995688487, 891921989653942, 836824441505699, 1885988485608364 } + }, + { + { 1241784121422547, 187337051947583, 1118481812236193, 428747751936362, 30358898927325 }, + { 2022432361201842, 1088816090685051, 1977843398539868, 1854834215890724, 564238862029357 }, + { 938868489100585, 1100285072929025, 1017806255688848, 1957262154788833, 152787950560442 } + }, + { + { 867319417678923, 620471962942542, 226032203305716, 342001443957629, 1761675818237336 }, + { 1295072362439987, 931227904689414, 1355731432641687, 922235735834035, 892227229410209 }, + { 1680989767906154, 535362787031440, 2136691276706570, 1942228485381244, 1267350086882274 } + }, + { + { 366018233770527, 432660629755596, 126409707644535, 1973842949591662, 645627343442376 }, + { 535509430575217, 546885533737322, 1524675609547799, 2138095752851703, 1260738089896827 }, + { 1159906385590467, 2198530004321610, 714559485023225, 81880727882151, 1484020820037082 } + }, + { + { 1377485731340769, 2046328105512000, 1802058637158797, 62146136768173, 1356993908853901 }, + { 2013612215646735, 1830770575920375, 536135310219832, 609272325580394, 270684344495013 }, + { 1237542585982777, 2228682050256790, 1385281931622824, 593183794882890, 493654978552689 } + } +}, +{ /* 31/31 */ + { + { 47341488007760, 1891414891220257, 983894663308928, 176161768286818, 1126261115179708 }, + { 1694030170963455, 502038567066200, 1691160065225467, 949628319562187, 275110186693066 }, + { 1124515748676336, 1661673816593408, 1499640319059718, 1584929449166988, 558148594103306 } + }, + { + { 1784525599998356, 1619698033617383, 2097300287550715, 258265458103756, 1905684794832758 }, + { 1288941072872766, 931787902039402, 190731008859042, 2006859954667190, 1005931482221702 }, + { 1465551264822703, 152905080555927, 680334307368453, 173227184634745, 666407097159852 } + }, + { + { 2111017076203943, 1378760485794347, 1248583954016456, 1352289194864422, 1895180776543896 }, + { 171348223915638, 662766099800389, 462338943760497, 466917763340314, 656911292869115 }, + { 488623681976577, 866497561541722, 1708105560937768, 1673781214218839, 1506146329818807 } + }, + { + { 160425464456957, 950394373239689, 430497123340934, 711676555398832, 320964687779005 }, + { 988979367990485, 1359729327576302, 1301834257246029, 294141160829308, 29348272277475 }, + { 1434382743317910, 100082049942065, 221102347892623, 186982837860588, 1305765053501834 } + }, + { + { 2205916462268190, 499863829790820, 961960554686616, 158062762756985, 1841471168298305 }, + { 1191737341426592, 1847042034978363, 1382213545049056, 1039952395710448, 788812858896859 }, + { 1346965964571152, 1291881610839830, 2142916164336056, 786821641205979, 1571709146321039 } + }, + { + { 787164375951248, 202869205373189, 1356590421032140, 1431233331032510, 786341368775957 }, + { 492448143532951, 304105152670757, 1761767168301056, 233782684697790, 1981295323106089 }, + { 665807507761866, 1343384868355425, 895831046139653, 439338948736892, 1986828765695105 } + }, + { + { 756096210874553, 1721699973539149, 258765301727885, 1390588532210645, 1212530909934781 }, + { 852891097972275, 1816988871354562, 1543772755726524, 1174710635522444, 202129090724628 }, + { 1205281565824323, 22430498399418, 992947814485516, 1392458699738672, 688441466734558 } + }, + { + { 1050627428414972, 1955849529137135, 2171162376368357, 91745868298214, 447733118757826 }, + { 1287181461435438, 622722465530711, 880952150571872, 741035693459198, 311565274989772 }, + { 1003649078149734, 545233927396469, 1849786171789880, 1318943684880434, 280345687170552 } + } +} diff --git a/src/libsodium/crypto_core/curve25519/ref10/fe_51/base2.h b/src/libsodium/crypto_core/curve25519/ref10/fe_51/base2.h new file mode 100644 index 00000000..d0882416 --- /dev/null +++ b/src/libsodium/crypto_core/curve25519/ref10/fe_51/base2.h @@ -0,0 +1,40 @@ +{ + { 1288382639258501, 245678601348599, 269427782077623, 1462984067271730, 137412439391563 }, + { 62697248952638, 204681361388450, 631292143396476, 338455783676468, 1213667448819585 }, + { 301289933810280, 1259582250014073, 1422107436869536, 796239922652654, 1953934009299142 } +}, +{ + { 1601611775252272, 1720807796594148, 1132070835939856, 1260455018889551, 2147779492816911 }, + { 316559037616741, 2177824224946892, 1459442586438991, 1461528397712656, 751590696113597 }, + { 1850748884277385, 1200145853858453, 1068094770532492, 672251375690438, 1586055907191707 } +}, +{ + { 769950342298419, 132954430919746, 844085933195555, 974092374476333, 726076285546016 }, + { 425251763115706, 608463272472562, 442562545713235, 837766094556764, 374555092627893 }, + { 1086255230780037, 274979815921559, 1960002765731872, 929474102396301, 1190409889297339 } +}, +{ + { 665000864555967, 2065379846933859, 370231110385876, 350988370788628, 1233371373142985 }, + { 2019367628972465, 676711900706637, 110710997811333, 1108646842542025, 517791959672113 }, + { 965130719900578, 247011430587952, 526356006571389, 91986625355052, 2157223321444601 } +}, +{ + { 1802695059465007, 1664899123557221, 593559490740857, 2160434469266659, 927570450755031 }, + { 1725674970513508, 1933645953859181, 1542344539275782, 1767788773573747, 1297447965928905 }, + { 1381809363726107, 1430341051343062, 2061843536018959, 1551778050872521, 2036394857967624 } +}, +{ + { 1970894096313054, 528066325833207, 1619374932191227, 2207306624415883, 1169170329061080 }, + { 2070390218572616, 1458919061857835, 624171843017421, 1055332792707765, 433987520732508 }, + { 893653801273833, 1168026499324677, 1242553501121234, 1306366254304474, 1086752658510815 } +}, +{ + { 213454002618221, 939771523987438, 1159882208056014, 317388369627517, 621213314200687 }, + { 1971678598905747, 338026507889165, 762398079972271, 655096486107477, 42299032696322 }, + { 177130678690680, 1754759263300204, 1864311296286618, 1180675631479880, 1292726903152791 } +}, +{ + { 1913163449625248, 460779200291993, 2193883288642314, 1008900146920800, 1721983679009502 }, + { 1070401523076875, 1272492007800961, 1910153608563310, 2075579521696771, 1191169788841221 }, + { 692896803108118, 500174642072499, 2068223309439677, 1162190621851337, 1426986007309901 } +} diff --git a/src/libsodium/crypto_core/curve25519/ref10/fe_51/fe.h b/src/libsodium/crypto_core/curve25519/ref10/fe_51/fe.h new file mode 100644 index 00000000..4c1b138f --- /dev/null +++ b/src/libsodium/crypto_core/curve25519/ref10/fe_51/fe.h @@ -0,0 +1,569 @@ +/* 37095705934669439343138083508754565189542113879843219016388785533085940283555 */ +static const fe d = { + 929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575 +}; + +/* 2 * d = + * 16295367250680780974490674513165176452449235426866156013048779062215315747161 + */ +static const fe d2 = { + 1859910466990425, 932731440258426, 1072319116312658, 1815898335770999, 633789495995903 +}; + +/* sqrt(-1) */ +static const fe sqrtm1 = { + 1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133 +}; + +/* + h = 0 + */ + +void +fe_0(fe h) +{ + memset(&h[0], 0, 5 * sizeof h[0]); +} + +/* + h = 1 + */ + +void +fe_1(fe h) +{ + h[0] = 1; + memset(&h[1], 0, 4 * sizeof h[0]); +} + +/* + h = f + g + Can overlap h with f or g. + */ + +void +fe_add(fe h, const fe f, const fe g) +{ + uint64_t h0 = f[0] + g[0]; + uint64_t h1 = f[1] + g[1]; + uint64_t h2 = f[2] + g[2]; + uint64_t h3 = f[3] + g[3]; + uint64_t h4 = f[4] + g[4]; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +/* + h = f - g + */ + +void +fe_sub(fe h, const fe f, const fe g) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint64_t h0, h1, h2, h3, h4; + + h0 = g[0]; + h1 = g[1]; + h2 = g[2]; + h3 = g[3]; + h4 = g[4]; + + h1 += h0 >> 51; + h0 &= mask; + h2 += h1 >> 51; + h1 &= mask; + h3 += h2 >> 51; + h2 &= mask; + h4 += h3 >> 51; + h3 &= mask; + h0 += 19ULL * (h4 >> 51); + h4 &= mask; + + h0 = (f[0] + 0xfffffffffffdaULL) - h0; + h1 = (f[1] + 0xffffffffffffeULL) - h1; + h2 = (f[2] + 0xffffffffffffeULL) - h2; + h3 = (f[3] + 0xffffffffffffeULL) - h3; + h4 = (f[4] + 0xffffffffffffeULL) - h4; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +/* + h = -f + */ + +static void +fe_neg(fe h, const fe f) +{ + fe zero; + + fe_0(zero); + fe_sub(h, zero, f); +} + +/* + Replace (f,g) with (g,g) if b == 1; + replace (f,g) with (f,g) if b == 0. + * + Preconditions: b in {0,1}. + */ + +static void +fe_cmov(fe f, const fe g, unsigned int b) +{ + const uint64_t mask = (uint64_t) (-(int64_t) b); + + uint64_t f0 = f[0]; + uint64_t f1 = f[1]; + uint64_t f2 = f[2]; + uint64_t f3 = f[3]; + uint64_t f4 = f[4]; + + uint64_t x0 = f0 ^ g[0]; + uint64_t x1 = f1 ^ g[1]; + uint64_t x2 = f2 ^ g[2]; + uint64_t x3 = f3 ^ g[3]; + uint64_t x4 = f4 ^ g[4]; + + x0 &= mask; + x1 &= mask; + x2 &= mask; + x3 &= mask; + x4 &= mask; + f[0] = f0 ^ x0; + f[1] = f1 ^ x1; + f[2] = f2 ^ x2; + f[3] = f3 ^ x3; + f[4] = f4 ^ x4; +} + +/* + h = f + */ + +void +fe_copy(fe h, const fe f) +{ + uint64_t f0 = f[0]; + uint64_t f1 = f[1]; + uint64_t f2 = f[2]; + uint64_t f3 = f[3]; + uint64_t f4 = f[4]; + + h[0] = f0; + h[1] = f1; + h[2] = f2; + h[3] = f3; + h[4] = f4; +} + +/* + Ignores top bit of h. + */ + +void +fe_frombytes(fe h, const unsigned char *s) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint64_t h0, h1, h2, h3, h4; + + h0 = (LOAD64_LE(s ) ) & mask; + h1 = (LOAD64_LE(s + 6) >> 3) & mask; + h2 = (LOAD64_LE(s + 12) >> 6) & mask; + h3 = (LOAD64_LE(s + 19) >> 1) & mask; + h4 = (LOAD64_LE(s + 24) >> 12) & mask; + + h[0] = h0; + h[1] = h1; + h[2] = h2; + h[3] = h3; + h[4] = h4; +} + +static void +fe_reduce(fe h, const fe f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t t[5]; + + t[0] = f[0]; + t[1] = f[1]; + t[2] = f[2]; + t[3] = f[3]; + t[4] = f[4]; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19 * (t[4] >> 51); + t[4] &= mask; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19 * (t[4] >> 51); + t[4] &= mask; + + /* now t is between 0 and 2^255-1, properly carried. */ + /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */ + + t[0] += 19ULL; + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[0] += 19ULL * (t[4] >> 51); + t[4] &= mask; + + /* now between 19 and 2^255-1 in both cases, and offset by 19. */ + + t[0] += 0x8000000000000 - 19ULL; + t[1] += 0x8000000000000 - 1ULL; + t[2] += 0x8000000000000 - 1ULL; + t[3] += 0x8000000000000 - 1ULL; + t[4] += 0x8000000000000 - 1ULL; + + /* now between 2^255 and 2^256-20, and offset by 2^255. */ + + t[1] += t[0] >> 51; + t[0] &= mask; + t[2] += t[1] >> 51; + t[1] &= mask; + t[3] += t[2] >> 51; + t[2] &= mask; + t[4] += t[3] >> 51; + t[3] &= mask; + t[4] &= mask; + + h[0] = t[0]; + h[1] = t[1]; + h[2] = t[2]; + h[3] = t[3]; + h[4] = t[4]; +} + +void +fe_tobytes(unsigned char *s, const fe h) +{ + fe t; + uint64_t t0, t1, t2, t3; + + fe_reduce(t, h); + t0 = t[0] | (t[1] << 51); + t1 = (t[1] >> 13) | (t[2] << 38); + t2 = (t[2] >> 26) | (t[3] << 25); + t3 = (t[3] >> 39) | (t[4] << 12); + STORE64_LE(s + 0, t0); + STORE64_LE(s + 8, t1); + STORE64_LE(s + 16, t2); + STORE64_LE(s + 24, t3); +} + +/* + return 1 if f is in {1,3,5,...,q-2} + return 0 if f is in {0,2,4,...,q-1} + */ + +static int +fe_isnegative(const fe f) +{ + unsigned char s[32]; + + fe_tobytes(s, f); + + return s[0] & 1; +} + +/* + return 1 if f == 0 + return 0 if f != 0 + */ + +int +fe_iszero(const fe f) +{ + unsigned char s[32]; + + fe_tobytes(s, f); + + return sodium_is_zero(s, 32); +} + +/* + h = f * g + Can overlap h with f or g. + */ + +void +fe_mul(fe h, const fe f, const fe g) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f1_19, f2_19, f3_19, f4_19; + uint64_t g0, g1, g2, g3, g4; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + g0 = g[0]; + g1 = g[1]; + g2 = g[2]; + g3 = g[3]; + g4 = g[4]; + + f1_19 = 19ULL * f1; + f2_19 = 19ULL * f2; + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) g0); + r0 += ((uint128_t) f1_19) * ((uint128_t) g4); + r0 += ((uint128_t) f2_19) * ((uint128_t) g3); + r0 += ((uint128_t) f3_19) * ((uint128_t) g2); + r0 += ((uint128_t) f4_19) * ((uint128_t) g1); + + r1 = ((uint128_t) f0 ) * ((uint128_t) g1); + r1 += ((uint128_t) f1 ) * ((uint128_t) g0); + r1 += ((uint128_t) f2_19) * ((uint128_t) g4); + r1 += ((uint128_t) f3_19) * ((uint128_t) g3); + r1 += ((uint128_t) f4_19) * ((uint128_t) g2); + + r2 = ((uint128_t) f0 ) * ((uint128_t) g2); + r2 += ((uint128_t) f1 ) * ((uint128_t) g1); + r2 += ((uint128_t) f2 ) * ((uint128_t) g0); + r2 += ((uint128_t) f3_19) * ((uint128_t) g4); + r2 += ((uint128_t) f4_19) * ((uint128_t) g3); + + r3 = ((uint128_t) f0 ) * ((uint128_t) g3); + r3 += ((uint128_t) f1 ) * ((uint128_t) g2); + r3 += ((uint128_t) f2 ) * ((uint128_t) g1); + r3 += ((uint128_t) f3 ) * ((uint128_t) g0); + r3 += ((uint128_t) f4_19) * ((uint128_t) g4); + + r4 = ((uint128_t) f0 ) * ((uint128_t) g4); + r4 += ((uint128_t) f1 ) * ((uint128_t) g3); + r4 += ((uint128_t) f2 ) * ((uint128_t) g2); + r4 += ((uint128_t) f3 ) * ((uint128_t) g1); + r4 += ((uint128_t) f4 ) * ((uint128_t) g0); + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} + +/* + h = f * f + Can overlap h with f. + */ + +void +fe_sq(fe h, const fe f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f0_2, f1_2, f1_38, f2_38, f3_38, f3_19, f4_19; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + f0_2 = f0 << 1; + f1_2 = f1 << 1; + + f1_38 = 38ULL * f1; + f2_38 = 38ULL * f2; + f3_38 = 38ULL * f3; + + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) f0); + r0 += ((uint128_t) f1_38) * ((uint128_t) f4); + r0 += ((uint128_t) f2_38) * ((uint128_t) f3); + + r1 = ((uint128_t) f0_2 ) * ((uint128_t) f1); + r1 += ((uint128_t) f2_38) * ((uint128_t) f4); + r1 += ((uint128_t) f3_19) * ((uint128_t) f3); + + r2 = ((uint128_t) f0_2 ) * ((uint128_t) f2); + r2 += ((uint128_t) f1 ) * ((uint128_t) f1); + r2 += ((uint128_t) f3_38) * ((uint128_t) f4); + + r3 = ((uint128_t) f0_2 ) * ((uint128_t) f3); + r3 += ((uint128_t) f1_2 ) * ((uint128_t) f2); + r3 += ((uint128_t) f4_19) * ((uint128_t) f4); + + r4 = ((uint128_t) f0_2 ) * ((uint128_t) f4); + r4 += ((uint128_t) f1_2 ) * ((uint128_t) f3); + r4 += ((uint128_t) f2 ) * ((uint128_t) f2); + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} + +/* + h = 2 * f * f + Can overlap h with f. +*/ + +static void +fe_sq2(fe h, const fe f) +{ + const uint64_t mask = 0x7ffffffffffffULL; + uint128_t r0, r1, r2, r3, r4, carry; + uint64_t f0, f1, f2, f3, f4; + uint64_t f0_2, f1_2, f1_38, f2_38, f3_38, f3_19, f4_19; + uint64_t r00, r01, r02, r03, r04; + + f0 = f[0]; + f1 = f[1]; + f2 = f[2]; + f3 = f[3]; + f4 = f[4]; + + f0_2 = f0 << 1; + f1_2 = f1 << 1; + + f1_38 = 38ULL * f1; + f2_38 = 38ULL * f2; + f3_38 = 38ULL * f3; + + f3_19 = 19ULL * f3; + f4_19 = 19ULL * f4; + + r0 = ((uint128_t) f0 ) * ((uint128_t) f0); + r0 += ((uint128_t) f1_38) * ((uint128_t) f4); + r0 += ((uint128_t) f2_38) * ((uint128_t) f3); + + r1 = ((uint128_t) f0_2 ) * ((uint128_t) f1); + r1 += ((uint128_t) f2_38) * ((uint128_t) f4); + r1 += ((uint128_t) f3_19) * ((uint128_t) f3); + + r2 = ((uint128_t) f0_2 ) * ((uint128_t) f2); + r2 += ((uint128_t) f1 ) * ((uint128_t) f1); + r2 += ((uint128_t) f3_38) * ((uint128_t) f4); + + r3 = ((uint128_t) f0_2 ) * ((uint128_t) f3); + r3 += ((uint128_t) f1_2 ) * ((uint128_t) f2); + r3 += ((uint128_t) f4_19) * ((uint128_t) f4); + + r4 = ((uint128_t) f0_2 ) * ((uint128_t) f4); + r4 += ((uint128_t) f1_2 ) * ((uint128_t) f3); + r4 += ((uint128_t) f2 ) * ((uint128_t) f2); + + r0 <<= 1; + r1 <<= 1; + r2 <<= 1; + r3 <<= 1; + r4 <<= 1; + + r00 = ((uint64_t) r0) & mask; + carry = r0 >> 51; + r1 += carry; + r01 = ((uint64_t) r1) & mask; + carry = r1 >> 51; + r2 += carry; + r02 = ((uint64_t) r2) & mask; + carry = r2 >> 51; + r3 += carry; + r03 = ((uint64_t) r3) & mask; + carry = r3 >> 51; + r4 += carry; + r04 = ((uint64_t) r4) & mask; + carry = r4 >> 51; + r00 += 19ULL * (uint64_t) carry; + carry = r00 >> 51; + r00 &= mask; + r01 += (uint64_t) carry; + carry = r01 >> 51; + r01 &= mask; + r02 += (uint64_t) carry; + + h[0] = r00; + h[1] = r01; + h[2] = r02; + h[3] = r03; + h[4] = r04; +} diff --git a/src/libsodium/include/sodium/private/curve25519_ref10.h b/src/libsodium/include/sodium/private/curve25519_ref10.h index aaf43af5..4088e8ec 100644 --- a/src/libsodium/include/sodium/private/curve25519_ref10.h +++ b/src/libsodium/include/sodium/private/curve25519_ref10.h @@ -5,7 +5,11 @@ #include #define fe crypto_core_curve25519_ref10_fe +#ifdef HAVE_TI_MODE +typedef uint64_t fe[5]; +#else typedef int32_t fe[10]; +#endif /* fe means field element.