diff options
Diffstat (limited to 'comm/third_party/botan/src/lib/pubkey/ed25519/ed25519_fe.cpp')
-rw-r--r-- | comm/third_party/botan/src/lib/pubkey/ed25519/ed25519_fe.cpp | 754 |
1 files changed, 754 insertions, 0 deletions
diff --git a/comm/third_party/botan/src/lib/pubkey/ed25519/ed25519_fe.cpp b/comm/third_party/botan/src/lib/pubkey/ed25519/ed25519_fe.cpp new file mode 100644 index 0000000000..135813d393 --- /dev/null +++ b/comm/third_party/botan/src/lib/pubkey/ed25519/ed25519_fe.cpp @@ -0,0 +1,754 @@ +/* +* Ed25519 field element +* (C) 2017 Ribose Inc +* +* Based on the public domain code from SUPERCOP ref10 by +* Peter Schwabe, Daniel J. Bernstein, Niels Duif, Tanja Lange, Bo-Yin Yang +* +* Botan is released under the Simplified BSD License (see license.txt) +*/ + +#include <botan/internal/ed25519_fe.h> +#include <botan/internal/ed25519_internal.h> + +namespace Botan { + +//static +FE_25519 FE_25519::invert(const FE_25519& z) + { + fe t0; + fe t1; + fe t2; + fe t3; + + fe_sq(t0, z); + fe_sq_iter(t1, t0, 2); + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t2, t0); + fe_mul(t1, t1, t2); + fe_sq_iter(t2, t1, 5); + fe_mul(t1, t2, t1); + fe_sq_iter(t2, t1, 10); + fe_mul(t2, t2, t1); + fe_sq_iter(t3, t2, 20); + fe_mul(t2, t3, t2); + fe_sq_iter(t2, t2, 10); + fe_mul(t1, t2, t1); + fe_sq_iter(t2, t1, 50); + fe_mul(t2, t2, t1); + fe_sq_iter(t3, t2, 100); + fe_mul(t2, t3, t2); + fe_sq_iter(t2, t2, 50); + fe_mul(t1, t2, t1); + fe_sq_iter(t1, t1, 5); + + fe_mul(t0, t1, t0); + return t0; + } + +FE_25519 FE_25519::pow_22523(const fe& z) + { + fe t0; + fe t1; + fe t2; + + fe_sq(t0, z); + fe_sq_iter(t1, t0, 2); + fe_mul(t1, z, t1); + fe_mul(t0, t0, t1); + fe_sq(t0, t0); + fe_mul(t0, t1, t0); + fe_sq_iter(t1, t0, 5); + fe_mul(t0, t1, t0); + fe_sq_iter(t1, t0, 10); + fe_mul(t1, t1, t0); + fe_sq_iter(t2, t1, 20); + fe_mul(t1, t2, t1); + fe_sq_iter(t1, t1, 10); + fe_mul(t0, t1, t0); + fe_sq_iter(t1, t0, 50); + fe_mul(t1, t1, t0); + fe_sq_iter(t2, t1, 100); + fe_mul(t1, t2, t1); + fe_sq_iter(t1, t1, 50); + fe_mul(t0, t1, t0); + fe_sq_iter(t0, t0, 2); + + fe_mul(t0, t0, z); + return t0; + } + +/* +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. +*/ + +//static +FE_25519 FE_25519::mul(const FE_25519& f, const FE_25519& g) + { + const int32_t f0 = f[0]; + const int32_t f1 = f[1]; + const int32_t f2 = f[2]; + const int32_t f3 = f[3]; + const int32_t f4 = f[4]; + const int32_t f5 = f[5]; + const int32_t f6 = f[6]; + const int32_t f7 = f[7]; + const int32_t f8 = f[8]; + const int32_t f9 = f[9]; + + const int32_t g0 = g[0]; + const int32_t g1 = g[1]; + const int32_t g2 = g[2]; + const int32_t g3 = g[3]; + const int32_t g4 = g[4]; + const int32_t g5 = g[5]; + const int32_t g6 = g[6]; + const int32_t g7 = g[7]; + const int32_t g8 = g[8]; + const int32_t g9 = g[9]; + + const int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ + const int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ + const int32_t g3_19 = 19 * g3; + const int32_t g4_19 = 19 * g4; + const int32_t g5_19 = 19 * g5; + const int32_t g6_19 = 19 * g6; + const int32_t g7_19 = 19 * g7; + const int32_t g8_19 = 19 * g8; + const int32_t g9_19 = 19 * g9; + const int32_t f1_2 = 2 * f1; + const int32_t f3_2 = 2 * f3; + const int32_t f5_2 = 2 * f5; + const int32_t f7_2 = 2 * f7; + const int32_t f9_2 = 2 * f9; + + const int64_t f0g0 = f0 * static_cast<int64_t>(g0); + const int64_t f0g1 = f0 * static_cast<int64_t>(g1); + const int64_t f0g2 = f0 * static_cast<int64_t>(g2); + const int64_t f0g3 = f0 * static_cast<int64_t>(g3); + const int64_t f0g4 = f0 * static_cast<int64_t>(g4); + const int64_t f0g5 = f0 * static_cast<int64_t>(g5); + const int64_t f0g6 = f0 * static_cast<int64_t>(g6); + const int64_t f0g7 = f0 * static_cast<int64_t>(g7); + const int64_t f0g8 = f0 * static_cast<int64_t>(g8); + const int64_t f0g9 = f0 * static_cast<int64_t>(g9); + const int64_t f1g0 = f1 * static_cast<int64_t>(g0); + const int64_t f1g1_2 = f1_2 * static_cast<int64_t>(g1); + const int64_t f1g2 = f1 * static_cast<int64_t>(g2); + const int64_t f1g3_2 = f1_2 * static_cast<int64_t>(g3); + const int64_t f1g4 = f1 * static_cast<int64_t>(g4); + const int64_t f1g5_2 = f1_2 * static_cast<int64_t>(g5); + const int64_t f1g6 = f1 * static_cast<int64_t>(g6); + const int64_t f1g7_2 = f1_2 * static_cast<int64_t>(g7); + const int64_t f1g8 = f1 * static_cast<int64_t>(g8); + const int64_t f1g9_38 = f1_2 * static_cast<int64_t>(g9_19); + const int64_t f2g0 = f2 * static_cast<int64_t>(g0); + const int64_t f2g1 = f2 * static_cast<int64_t>(g1); + const int64_t f2g2 = f2 * static_cast<int64_t>(g2); + const int64_t f2g3 = f2 * static_cast<int64_t>(g3); + const int64_t f2g4 = f2 * static_cast<int64_t>(g4); + const int64_t f2g5 = f2 * static_cast<int64_t>(g5); + const int64_t f2g6 = f2 * static_cast<int64_t>(g6); + const int64_t f2g7 = f2 * static_cast<int64_t>(g7); + const int64_t f2g8_19 = f2 * static_cast<int64_t>(g8_19); + const int64_t f2g9_19 = f2 * static_cast<int64_t>(g9_19); + const int64_t f3g0 = f3 * static_cast<int64_t>(g0); + const int64_t f3g1_2 = f3_2 * static_cast<int64_t>(g1); + const int64_t f3g2 = f3 * static_cast<int64_t>(g2); + const int64_t f3g3_2 = f3_2 * static_cast<int64_t>(g3); + const int64_t f3g4 = f3 * static_cast<int64_t>(g4); + const int64_t f3g5_2 = f3_2 * static_cast<int64_t>(g5); + const int64_t f3g6 = f3 * static_cast<int64_t>(g6); + const int64_t f3g7_38 = f3_2 * static_cast<int64_t>(g7_19); + const int64_t f3g8_19 = f3 * static_cast<int64_t>(g8_19); + const int64_t f3g9_38 = f3_2 * static_cast<int64_t>(g9_19); + const int64_t f4g0 = f4 * static_cast<int64_t>(g0); + const int64_t f4g1 = f4 * static_cast<int64_t>(g1); + const int64_t f4g2 = f4 * static_cast<int64_t>(g2); + const int64_t f4g3 = f4 * static_cast<int64_t>(g3); + const int64_t f4g4 = f4 * static_cast<int64_t>(g4); + const int64_t f4g5 = f4 * static_cast<int64_t>(g5); + const int64_t f4g6_19 = f4 * static_cast<int64_t>(g6_19); + const int64_t f4g7_19 = f4 * static_cast<int64_t>(g7_19); + const int64_t f4g8_19 = f4 * static_cast<int64_t>(g8_19); + const int64_t f4g9_19 = f4 * static_cast<int64_t>(g9_19); + const int64_t f5g0 = f5 * static_cast<int64_t>(g0); + const int64_t f5g1_2 = f5_2 * static_cast<int64_t>(g1); + const int64_t f5g2 = f5 * static_cast<int64_t>(g2); + const int64_t f5g3_2 = f5_2 * static_cast<int64_t>(g3); + const int64_t f5g4 = f5 * static_cast<int64_t>(g4); + const int64_t f5g5_38 = f5_2 * static_cast<int64_t>(g5_19); + const int64_t f5g6_19 = f5 * static_cast<int64_t>(g6_19); + const int64_t f5g7_38 = f5_2 * static_cast<int64_t>(g7_19); + const int64_t f5g8_19 = f5 * static_cast<int64_t>(g8_19); + const int64_t f5g9_38 = f5_2 * static_cast<int64_t>(g9_19); + const int64_t f6g0 = f6 * static_cast<int64_t>(g0); + const int64_t f6g1 = f6 * static_cast<int64_t>(g1); + const int64_t f6g2 = f6 * static_cast<int64_t>(g2); + const int64_t f6g3 = f6 * static_cast<int64_t>(g3); + const int64_t f6g4_19 = f6 * static_cast<int64_t>(g4_19); + const int64_t f6g5_19 = f6 * static_cast<int64_t>(g5_19); + const int64_t f6g6_19 = f6 * static_cast<int64_t>(g6_19); + const int64_t f6g7_19 = f6 * static_cast<int64_t>(g7_19); + const int64_t f6g8_19 = f6 * static_cast<int64_t>(g8_19); + const int64_t f6g9_19 = f6 * static_cast<int64_t>(g9_19); + const int64_t f7g0 = f7 * static_cast<int64_t>(g0); + const int64_t f7g1_2 = f7_2 * static_cast<int64_t>(g1); + const int64_t f7g2 = f7 * static_cast<int64_t>(g2); + const int64_t f7g3_38 = f7_2 * static_cast<int64_t>(g3_19); + const int64_t f7g4_19 = f7 * static_cast<int64_t>(g4_19); + const int64_t f7g5_38 = f7_2 * static_cast<int64_t>(g5_19); + const int64_t f7g6_19 = f7 * static_cast<int64_t>(g6_19); + const int64_t f7g7_38 = f7_2 * static_cast<int64_t>(g7_19); + const int64_t f7g8_19 = f7 * static_cast<int64_t>(g8_19); + const int64_t f7g9_38 = f7_2 * static_cast<int64_t>(g9_19); + const int64_t f8g0 = f8 * static_cast<int64_t>(g0); + const int64_t f8g1 = f8 * static_cast<int64_t>(g1); + const int64_t f8g2_19 = f8 * static_cast<int64_t>(g2_19); + const int64_t f8g3_19 = f8 * static_cast<int64_t>(g3_19); + const int64_t f8g4_19 = f8 * static_cast<int64_t>(g4_19); + const int64_t f8g5_19 = f8 * static_cast<int64_t>(g5_19); + const int64_t f8g6_19 = f8 * static_cast<int64_t>(g6_19); + const int64_t f8g7_19 = f8 * static_cast<int64_t>(g7_19); + const int64_t f8g8_19 = f8 * static_cast<int64_t>(g8_19); + const int64_t f8g9_19 = f8 * static_cast<int64_t>(g9_19); + const int64_t f9g0 = f9 * static_cast<int64_t>(g0); + const int64_t f9g1_38 = f9_2 * static_cast<int64_t>(g1_19); + const int64_t f9g2_19 = f9 * static_cast<int64_t>(g2_19); + const int64_t f9g3_38 = f9_2 * static_cast<int64_t>(g3_19); + const int64_t f9g4_19 = f9 * static_cast<int64_t>(g4_19); + const int64_t f9g5_38 = f9_2 * static_cast<int64_t>(g5_19); + const int64_t f9g6_19 = f9 * static_cast<int64_t>(g6_19); + const int64_t f9g7_38 = f9_2 * static_cast<int64_t>(g7_19); + const int64_t f9g8_19 = f9 * static_cast<int64_t>(g8_19); + const int64_t f9g9_38 = f9_2 * static_cast<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 ; + + /* + |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 + */ + carry<26>(h0, h1); + carry<26>(h4, h5); + + /* |h0| <= 2^25 */ + /* |h4| <= 2^25 */ + /* |h1| <= 1.71*2^59 */ + /* |h5| <= 1.71*2^59 */ + + carry<25>(h1, h2); + carry<25>(h5, h6); + + /* |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 */ + + carry<26>(h2, h3); + carry<26>(h6, h7); + /* |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 */ + + carry<25>(h3, h4); + carry<25>(h7, h8); + /* |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 */ + + carry<26>(h4, h5); + carry<26>(h8, h9); + /* |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 */ + + carry<25, 19>(h9, h0); + + /* |h9| <= 2^24; from now on fits into int32 unchanged */ + /* |h0| <= 1.1*2^39 */ + + carry<26>(h0, h1); + /* |h0| <= 2^25; from now on fits into int32 unchanged */ + /* |h1| <= 1.01*2^24 */ + + return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, 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. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +//static +FE_25519 FE_25519::sqr_iter(const FE_25519& f, size_t iter) + { + 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]; + + for(size_t i = 0; i != iter; ++i) + { + const int32_t f0_2 = 2 * f0; + const int32_t f1_2 = 2 * f1; + const int32_t f2_2 = 2 * f2; + const int32_t f3_2 = 2 * f3; + const int32_t f4_2 = 2 * f4; + const int32_t f5_2 = 2 * f5; + const int32_t f6_2 = 2 * f6; + const int32_t f7_2 = 2 * f7; + const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + + const int64_t f0f0 = f0 * static_cast<int64_t>(f0); + const int64_t f0f1_2 = f0_2 * static_cast<int64_t>(f1); + const int64_t f0f2_2 = f0_2 * static_cast<int64_t>(f2); + const int64_t f0f3_2 = f0_2 * static_cast<int64_t>(f3); + const int64_t f0f4_2 = f0_2 * static_cast<int64_t>(f4); + const int64_t f0f5_2 = f0_2 * static_cast<int64_t>(f5); + const int64_t f0f6_2 = f0_2 * static_cast<int64_t>(f6); + const int64_t f0f7_2 = f0_2 * static_cast<int64_t>(f7); + const int64_t f0f8_2 = f0_2 * static_cast<int64_t>(f8); + const int64_t f0f9_2 = f0_2 * static_cast<int64_t>(f9); + const int64_t f1f1_2 = f1_2 * static_cast<int64_t>(f1); + const int64_t f1f2_2 = f1_2 * static_cast<int64_t>(f2); + const int64_t f1f3_4 = f1_2 * static_cast<int64_t>(f3_2); + const int64_t f1f4_2 = f1_2 * static_cast<int64_t>(f4); + const int64_t f1f5_4 = f1_2 * static_cast<int64_t>(f5_2); + const int64_t f1f6_2 = f1_2 * static_cast<int64_t>(f6); + const int64_t f1f7_4 = f1_2 * static_cast<int64_t>(f7_2); + const int64_t f1f8_2 = f1_2 * static_cast<int64_t>(f8); + const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38); + const int64_t f2f2 = f2 * static_cast<int64_t>(f2); + const int64_t f2f3_2 = f2_2 * static_cast<int64_t>(f3); + const int64_t f2f4_2 = f2_2 * static_cast<int64_t>(f4); + const int64_t f2f5_2 = f2_2 * static_cast<int64_t>(f5); + const int64_t f2f6_2 = f2_2 * static_cast<int64_t>(f6); + const int64_t f2f7_2 = f2_2 * static_cast<int64_t>(f7); + const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19); + const int64_t f2f9_38 = f2 * static_cast<int64_t>(f9_38); + const int64_t f3f3_2 = f3_2 * static_cast<int64_t>(f3); + const int64_t f3f4_2 = f3_2 * static_cast<int64_t>(f4); + const int64_t f3f5_4 = f3_2 * static_cast<int64_t>(f5_2); + const int64_t f3f6_2 = f3_2 * static_cast<int64_t>(f6); + const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38); + const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19); + const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38); + const int64_t f4f4 = f4 * static_cast<int64_t>(f4); + const int64_t f4f5_2 = f4_2 * static_cast<int64_t>(f5); + const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19); + const int64_t f4f7_38 = f4 * static_cast<int64_t>(f7_38); + const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19); + const int64_t f4f9_38 = f4 * static_cast<int64_t>(f9_38); + const int64_t f5f5_38 = f5 * static_cast<int64_t>(f5_38); + const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19); + const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38); + const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19); + const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38); + const int64_t f6f6_19 = f6 * static_cast<int64_t>(f6_19); + const int64_t f6f7_38 = f6 * static_cast<int64_t>(f7_38); + const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19); + const int64_t f6f9_38 = f6 * static_cast<int64_t>(f9_38); + const int64_t f7f7_38 = f7 * static_cast<int64_t>(f7_38); + const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19); + const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38); + const int64_t f8f8_19 = f8 * static_cast<int64_t>(f8_19); + const int64_t f8f9_38 = f8 * static_cast<int64_t>(f9_38); + const int64_t f9f9_38 = f9 * static_cast<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; + + carry<26>(h0, h1); + carry<26>(h4, h5); + carry<25>(h1, h2); + carry<25>(h5, h6); + carry<26>(h2, h3); + carry<26>(h6, h7); + + carry<25>(h3, h4); + carry<25>(h7, h8); + + carry<26>(h4, h5); + carry<26>(h8, h9); + carry<25,19>(h9, h0); + carry<26>(h0, h1); + + f0 = static_cast<int32_t>(h0); + f1 = static_cast<int32_t>(h1); + f2 = static_cast<int32_t>(h2); + f3 = static_cast<int32_t>(h3); + f4 = static_cast<int32_t>(h4); + f5 = static_cast<int32_t>(h5); + f6 = static_cast<int32_t>(h6); + f7 = static_cast<int32_t>(h7); + f8 = static_cast<int32_t>(h8); + f9 = static_cast<int32_t>(h9); + } + + return FE_25519(f0, f1, f2, f3, f4, f5, f6, f7, f8, f9); + } + +/* +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. +*/ + +/* +See fe_mul.c for discussion of implementation strategy. +*/ + +//static +FE_25519 FE_25519::sqr2(const FE_25519& f) + { + const int32_t f0 = f[0]; + const int32_t f1 = f[1]; + const int32_t f2 = f[2]; + const int32_t f3 = f[3]; + const int32_t f4 = f[4]; + const int32_t f5 = f[5]; + const int32_t f6 = f[6]; + const int32_t f7 = f[7]; + const int32_t f8 = f[8]; + const int32_t f9 = f[9]; + const int32_t f0_2 = 2 * f0; + const int32_t f1_2 = 2 * f1; + const int32_t f2_2 = 2 * f2; + const int32_t f3_2 = 2 * f3; + const int32_t f4_2 = 2 * f4; + const int32_t f5_2 = 2 * f5; + const int32_t f6_2 = 2 * f6; + const int32_t f7_2 = 2 * f7; + const int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ + const int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ + const int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ + const int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ + const int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ + const int64_t f0f0 = f0 * static_cast<int64_t>(f0); + const int64_t f0f1_2 = f0_2 * static_cast<int64_t>(f1); + const int64_t f0f2_2 = f0_2 * static_cast<int64_t>(f2); + const int64_t f0f3_2 = f0_2 * static_cast<int64_t>(f3); + const int64_t f0f4_2 = f0_2 * static_cast<int64_t>(f4); + const int64_t f0f5_2 = f0_2 * static_cast<int64_t>(f5); + const int64_t f0f6_2 = f0_2 * static_cast<int64_t>(f6); + const int64_t f0f7_2 = f0_2 * static_cast<int64_t>(f7); + const int64_t f0f8_2 = f0_2 * static_cast<int64_t>(f8); + const int64_t f0f9_2 = f0_2 * static_cast<int64_t>(f9); + const int64_t f1f1_2 = f1_2 * static_cast<int64_t>(f1); + const int64_t f1f2_2 = f1_2 * static_cast<int64_t>(f2); + const int64_t f1f3_4 = f1_2 * static_cast<int64_t>(f3_2); + const int64_t f1f4_2 = f1_2 * static_cast<int64_t>(f4); + const int64_t f1f5_4 = f1_2 * static_cast<int64_t>(f5_2); + const int64_t f1f6_2 = f1_2 * static_cast<int64_t>(f6); + const int64_t f1f7_4 = f1_2 * static_cast<int64_t>(f7_2); + const int64_t f1f8_2 = f1_2 * static_cast<int64_t>(f8); + const int64_t f1f9_76 = f1_2 * static_cast<int64_t>(f9_38); + const int64_t f2f2 = f2 * static_cast<int64_t>(f2); + const int64_t f2f3_2 = f2_2 * static_cast<int64_t>(f3); + const int64_t f2f4_2 = f2_2 * static_cast<int64_t>(f4); + const int64_t f2f5_2 = f2_2 * static_cast<int64_t>(f5); + const int64_t f2f6_2 = f2_2 * static_cast<int64_t>(f6); + const int64_t f2f7_2 = f2_2 * static_cast<int64_t>(f7); + const int64_t f2f8_38 = f2_2 * static_cast<int64_t>(f8_19); + const int64_t f2f9_38 = f2 * static_cast<int64_t>(f9_38); + const int64_t f3f3_2 = f3_2 * static_cast<int64_t>(f3); + const int64_t f3f4_2 = f3_2 * static_cast<int64_t>(f4); + const int64_t f3f5_4 = f3_2 * static_cast<int64_t>(f5_2); + const int64_t f3f6_2 = f3_2 * static_cast<int64_t>(f6); + const int64_t f3f7_76 = f3_2 * static_cast<int64_t>(f7_38); + const int64_t f3f8_38 = f3_2 * static_cast<int64_t>(f8_19); + const int64_t f3f9_76 = f3_2 * static_cast<int64_t>(f9_38); + const int64_t f4f4 = f4 * static_cast<int64_t>(f4); + const int64_t f4f5_2 = f4_2 * static_cast<int64_t>(f5); + const int64_t f4f6_38 = f4_2 * static_cast<int64_t>(f6_19); + const int64_t f4f7_38 = f4 * static_cast<int64_t>(f7_38); + const int64_t f4f8_38 = f4_2 * static_cast<int64_t>(f8_19); + const int64_t f4f9_38 = f4 * static_cast<int64_t>(f9_38); + const int64_t f5f5_38 = f5 * static_cast<int64_t>(f5_38); + const int64_t f5f6_38 = f5_2 * static_cast<int64_t>(f6_19); + const int64_t f5f7_76 = f5_2 * static_cast<int64_t>(f7_38); + const int64_t f5f8_38 = f5_2 * static_cast<int64_t>(f8_19); + const int64_t f5f9_76 = f5_2 * static_cast<int64_t>(f9_38); + const int64_t f6f6_19 = f6 * static_cast<int64_t>(f6_19); + const int64_t f6f7_38 = f6 * static_cast<int64_t>(f7_38); + const int64_t f6f8_38 = f6_2 * static_cast<int64_t>(f8_19); + const int64_t f6f9_38 = f6 * static_cast<int64_t>(f9_38); + const int64_t f7f7_38 = f7 * static_cast<int64_t>(f7_38); + const int64_t f7f8_38 = f7_2 * static_cast<int64_t>(f8_19); + const int64_t f7f9_76 = f7_2 * static_cast<int64_t>(f9_38); + const int64_t f8f8_19 = f8 * static_cast<int64_t>(f8_19); + const int64_t f8f9_38 = f8 * static_cast<int64_t>(f9_38); + const int64_t f9f9_38 = f9 * static_cast<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; + + h0 += h0; + h1 += h1; + h2 += h2; + h3 += h3; + h4 += h4; + h5 += h5; + h6 += h6; + h7 += h7; + h8 += h8; + h9 += h9; + + carry<26>(h0, h1); + carry<26>(h4, h5); + + carry<25>(h1, h2); + carry<25>(h5, h6); + + carry<26>(h2, h3); + carry<26>(h6, h7); + + carry<25>(h3, h4); + carry<25>(h7, h8); + carry<26>(h4, h5); + carry<26>(h8, h9); + carry<25,19>(h9, h0); + carry<26>(h0, h1); + + return FE_25519(h0, h1, h2, h3, h4, h5, h6, h7, h8, h9); + } + +/* +Ignores top bit of h. +*/ + +void FE_25519::from_bytes(const uint8_t s[32]) + { + 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) & 0x7fffff) << 2; + + carry<25,19>(h9, h0); + carry<25>(h1, h2); + carry<25>(h3, h4); + carry<25>(h5, h6); + carry<25>(h7, h8); + + carry<26>(h0, h1); + carry<26>(h2, h3); + carry<26>(h4, h5); + carry<26>(h6, h7); + carry<26>(h8, h9); + + m_fe[0] = static_cast<int32_t>(h0); + m_fe[1] = static_cast<int32_t>(h1); + m_fe[2] = static_cast<int32_t>(h2); + m_fe[3] = static_cast<int32_t>(h3); + m_fe[4] = static_cast<int32_t>(h4); + m_fe[5] = static_cast<int32_t>(h5); + m_fe[6] = static_cast<int32_t>(h6); + m_fe[7] = static_cast<int32_t>(h7); + m_fe[8] = static_cast<int32_t>(h8); + m_fe[9] = static_cast<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<y<1. + +Write r=h-pq. +Have 0<=r<=p-1=2^255-20. +Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. + +Write x=r+19(2^-255)r+y. +Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. + +Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) +so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. +*/ + +void FE_25519::to_bytes(uint8_t s[32]) const + { + const int64_t X25 = (1 << 25); + + int32_t h0 = m_fe[0]; + int32_t h1 = m_fe[1]; + int32_t h2 = m_fe[2]; + int32_t h3 = m_fe[3]; + int32_t h4 = m_fe[4]; + int32_t h5 = m_fe[5]; + int32_t h6 = m_fe[6]; + int32_t h7 = m_fe[7]; + int32_t h8 = m_fe[8]; + int32_t h9 = m_fe[9]; + int32_t q; + + q = (19 * h9 + ((static_cast<int32_t>(1) << 24))) >> 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<26>(h0, h1); + carry0<25>(h1, h2); + carry0<26>(h2, h3); + carry0<25>(h3, h4); + carry0<26>(h4, h5); + carry0<25>(h5, h6); + carry0<26>(h6, h7); + carry0<25>(h7, h8); + carry0<26>(h8, h9); + + int32_t carry9 = h9 >> 25; + h9 -= carry9 * X25; + /* 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] = static_cast<uint8_t>(h0 >> 0); + s[1] = static_cast<uint8_t>(h0 >> 8); + s[2] = static_cast<uint8_t>(h0 >> 16); + s[3] = static_cast<uint8_t>((h0 >> 24) | (h1 << 2)); + s[4] = static_cast<uint8_t>(h1 >> 6); + s[5] = static_cast<uint8_t>(h1 >> 14); + s[6] = static_cast<uint8_t>((h1 >> 22) | (h2 << 3)); + s[7] = static_cast<uint8_t>(h2 >> 5); + s[8] = static_cast<uint8_t>(h2 >> 13); + s[9] = static_cast<uint8_t>((h2 >> 21) | (h3 << 5)); + s[10] = static_cast<uint8_t>(h3 >> 3); + s[11] = static_cast<uint8_t>(h3 >> 11); + s[12] = static_cast<uint8_t>((h3 >> 19) | (h4 << 6)); + s[13] = static_cast<uint8_t>(h4 >> 2); + s[14] = static_cast<uint8_t>(h4 >> 10); + s[15] = static_cast<uint8_t>(h4 >> 18); + s[16] = static_cast<uint8_t>(h5 >> 0); + s[17] = static_cast<uint8_t>(h5 >> 8); + s[18] = static_cast<uint8_t>(h5 >> 16); + s[19] = static_cast<uint8_t>((h5 >> 24) | (h6 << 1)); + s[20] = static_cast<uint8_t>(h6 >> 7); + s[21] = static_cast<uint8_t>(h6 >> 15); + s[22] = static_cast<uint8_t>((h6 >> 23) | (h7 << 3)); + s[23] = static_cast<uint8_t>(h7 >> 5); + s[24] = static_cast<uint8_t>(h7 >> 13); + s[25] = static_cast<uint8_t>((h7 >> 21) | (h8 << 4)); + s[26] = static_cast<uint8_t>(h8 >> 4); + s[27] = static_cast<uint8_t>(h8 >> 12); + s[28] = static_cast<uint8_t>((h8 >> 20) | (h9 << 6)); + s[29] = static_cast<uint8_t>(h9 >> 2); + s[30] = static_cast<uint8_t>(h9 >> 10); + s[31] = static_cast<uint8_t>(h9 >> 18); + } + +} |