Ed25519 signatures are under 2ms
Juniper Beatitudes [email protected]
Sun, 04 Jan 2026 08:34:05 -0600
6 files changed,
2306 insertions(+),
4208 deletions(-)
M
meson.build
→
meson.build
@@ -13,7 +13,6 @@
build_args = [ '-Os', '-ffreestanding', - '-pg', ] target = static_library('tinycrypt', sources, c_args: build_args, include_directories: incdir)
A
test.c
@@ -0,0 +1,57 @@
+#include "tinycrypt/ed25519.h" +#include <stdint.h> +#include <stdio.h> + +static uint8_t SK4[] = { + 0x6d, 0xf9, 0x34, 0x0c, 0x13, 0x8c, 0xc1, 0x88, 0xb5, 0xfe, 0x44, + 0x64, 0xeb, 0xaa, 0x3f, 0x7f, 0xc2, 0x06, 0xa2, 0xd5, 0x5c, 0x34, + 0x34, 0x70, 0x7e, 0x74, 0xc9, 0xfc, 0x04, 0xe2, 0x0e, 0xbb, +}; +static uint8_t PK4[] = { + 0xc0, 0xda, 0xc1, 0x02, 0xc4, 0x53, 0x31, 0x86, 0xe2, 0x5d, 0xc4, + 0x31, 0x28, 0x47, 0x23, 0x53, 0xea, 0xab, 0xdb, 0x87, 0x8b, 0x15, + 0x2a, 0xeb, 0x8e, 0x00, 0x1f, 0x92, 0xd9, 0x02, 0x33, 0xa7, +}; +static uint8_t MSG4[] = { + 0x5f, + 0x4c, + 0x89, + 0x89, +}; +static uint8_t SIG4[] = { + 0x12, 0x4f, 0x6f, 0xc6, 0xb0, 0xd1, 0x00, 0x84, 0x27, 0x69, 0xe7, 0x1b, 0xd5, + 0x30, 0x66, 0x4d, 0x88, 0x8d, 0xf8, 0x50, 0x7d, 0xf6, 0xc5, 0x6d, 0xed, 0xfd, + 0xb5, 0x09, 0xae, 0xb9, 0x34, 0x16, 0xe2, 0x6b, 0x91, 0x8d, 0x38, 0xaa, 0x06, + 0x30, 0x5d, 0xf3, 0x09, 0x56, 0x97, 0xc1, 0x8b, 0x2a, 0xa8, 0x32, 0xea, 0xa5, + 0x2e, 0xdc, 0x0a, 0xe4, 0x9f, 0xba, 0xe5, 0xa8, 0x5e, 0x15, 0x0c, 0x07, +}; + +int +main (int argc, char **argv) +{ + uint8_t actual_signature[64]; + uint8_t working_buf[sizeof (MSG4) + 64]; + tct_ed25519_sign (MSG4, sizeof (MSG4), SK4, PK4, working_buf, + actual_signature); + for (unsigned int i = 0; i < 32; ++i) + { + printf ("%02x", SIG4[i]); + } + printf ("\n"); + for (unsigned int i = 0; i < 32; ++i) + { + printf ("%02x", actual_signature[i]); + } + printf ("\n"); + for (unsigned int i = 0; i < 32; ++i) + { + printf ("%02x", SIG4[63 - i]); + } + printf ("\n"); + for (unsigned int i = 0; i < 32; ++i) + { + printf ("%02x", actual_signature[63 - i]); + } + printf ("\n"); + return 0; +}
M
tinycrypt/ed25519.c
→
tinycrypt/ed25519.c
@@ -14,201 +14,188 @@ return (u << 8) | x[0];
} static void -to_le64 (uint64_t u, uint8_t *x) +to_le32 (const uint32_t x, uint8_t *out) { - for (unsigned int i = 0; i < 8; ++i) + for (unsigned int i = 0; i < 4; ++i) { - x[i] = u & 0xFF; - u >>= 8; + out[i] = (x >> (8 * i)) & 0xff; } } static void -add_shifted (uint8_t *h, const uint64_t c, const unsigned int shift) +add_shifted (uint32_t *h, const uint64_t c, const unsigned int shift) { - uint8_t digits[8]; - to_le64 (c, digits); - uint16_t accumulator = 0; + uint32_t digits[2]; + digits[0] = c & 0xffffffff; + digits[1] = (c >> 32) & 0xffffffff; + uint64_t accumulator = 0; unsigned int i; - for (i = shift; i <= shift + 8 && i < 64; ++i) + for (i = shift; i < shift + 2 && i < 16; ++i) { - accumulator += digits[i - shift] + h[i]; - h[i] = accumulator & 0xFF; - accumulator >>= 8; + accumulator += (uint64_t)digits[i - shift] + (uint64_t)h[i]; + h[i] = accumulator & 0xffffffff; + accumulator >>= 32; } - while (i < 64) + while (i < 16) { - accumulator += h[i]; - h[i] = accumulator & 0xFF; - accumulator >>= 8; + accumulator += (uint64_t)h[i]; + h[i] = accumulator & 0xffffffff; + accumulator >>= 32; ++i; } } static void -mult256 (const uint8_t *a, const uint8_t *b, uint8_t *out) +mult256 (const uint32_t *a, const uint32_t *b, uint32_t *out) { // Literal long multiplication - for (unsigned int i = 0; i < 64; ++i) + for (unsigned int i = 0; i < 16; ++i) { out[i] = 0x0; - } - uint32_t a_digits[8]; - uint32_t b_digits[8]; - for (unsigned int i = 0; i < 8; ++i) - { - a_digits[i] = from_le32 (a + i * 4); - b_digits[i] = from_le32 (b + i * 4); } for (unsigned int i = 0; i < 8; ++i) { for (unsigned int j = 0; j < 8; ++j) { - uint64_t prod = (uint64_t)a_digits[i] * (uint64_t)b_digits[j]; - add_shifted (out, prod, i * 4 + j * 4); + uint64_t prod = (uint64_t)a[i] * (uint64_t)b[j]; + add_shifted (out, prod, i + j); } } } -static void -mult264 (const uint8_t *a, const uint8_t *b, uint8_t *out) +static bool +iszero256 (const uint32_t *a) { - for (unsigned int i = 0; i < 64; ++i) - { - out[i] = 0x0; - } - uint32_t a_digits[9]; - uint32_t b_digits[9]; + uint32_t dummy = 0x0; for (unsigned int i = 0; i < 8; ++i) { - a_digits[i] = from_le32 (a + i * 4); - b_digits[i] = from_le32 (b + i * 4); + dummy |= a[i]; } - a_digits[8] = a[32]; - b_digits[8] = b[32]; - for (unsigned int i = 0; i < 9; ++i) - { - for (unsigned int j = 0; j < 9; ++j) - { - uint64_t prod = (uint64_t)a_digits[i] * (uint64_t)b_digits[j]; - add_shifted (out, prod, i * 4 + j * 4); - } - } + return !dummy; } static void -shr512_by_255 (const uint8_t *in, uint8_t *out) +sub288 (uint32_t *h, const uint32_t *c) { - for (unsigned int i = 0; i < 32; ++i) + uint64_t acc = 0; + for (unsigned int i = 0; i < 9; ++i) { - out[i] = (in[i + 31] >> 7) | (in[i + 32] << 1); + acc += (uint64_t)(0xffffffff - h[i]) + (uint64_t)c[i]; + h[i] = 0xffffffff - (acc & 0xffffffff); + acc >>= 32; } - out[32] = in[63] >> 7; } static bool -iszero256 (const uint8_t *a) +greater288 (const uint32_t *a, const uint32_t *b) { - uint8_t dummy = 0x0; - for (unsigned int i = 0; i < 32; ++i) + uint32_t buf[9]; + for (unsigned int i = 0; i < 9; ++i) { - dummy |= a[i]; + buf[i] = a[i]; } - return !dummy; + sub288 (buf, b); + + return !(buf[8] & (1 << 31)); } static void -sub264 (uint8_t *h, const uint8_t *c) +sub256 (uint32_t *h, const uint32_t *c) { - uint16_t acc = 0; - for (unsigned int i = 0; i < 33; ++i) + uint64_t acc = 0; + for (unsigned int i = 0; i < 8; ++i) { - acc += (255 - h[i]) + c[i]; - h[i] = 255 - (acc & 0xFF); - acc >>= 8; + acc += (uint64_t)(0xffffffff - h[i]) + (uint64_t)c[i]; + h[i] = 0xffffffff - (acc & 0xffffffff); + acc >>= 32; } } static bool -greater264 (const uint8_t *a, const uint8_t *b) +greater256 (const uint32_t *a, const uint32_t *b) { - uint8_t buf[33]; - for (unsigned int i = 0; i < 33; ++i) + uint32_t buf[8]; + for (unsigned int i = 0; i < 8; ++i) { buf[i] = a[i]; } - sub264 (buf, b); + sub256 (buf, b); - return !(buf[32] & (1 << 7)); + return !(buf[7] & (1 << 31)); } static void -add512 (uint8_t *h, const uint8_t *c) +add512 (uint32_t *h, const uint32_t *c) { - uint16_t acc = 0; - for (unsigned int i = 0; i < 64; ++i) + uint64_t acc = 0; + for (unsigned int i = 0; i < 16; ++i) { - acc += h[i] + c[i]; - h[i] = acc & 0xFF; - acc >>= 8; + acc += (uint64_t)h[i] + (uint64_t)c[i]; + h[i] = acc & 0xffffffff; + acc >>= 32; } } static void -sub512 (uint8_t *h, const uint8_t *c) +sub512 (uint32_t *h, const uint32_t *c) { - uint16_t acc = 0; - for (unsigned int i = 0; i < 64; ++i) + uint64_t acc = 0; + for (unsigned int i = 0; i < 16; ++i) { - acc += (255 - h[i]) + c[i]; - h[i] = 255 - (acc & 0xFF); - acc >>= 8; + acc += (uint64_t)(0xffffffff - h[i]) + (uint64_t)c[i]; + h[i] = 0xffffffff - (acc & 0xffffffff); + acc >>= 32; } } static void -sub520 (uint8_t *h, const uint8_t *c) +sub534 (uint32_t *h, const uint32_t *c) { - uint16_t acc = 0; - for (unsigned int i = 0; i < 65; ++i) + uint64_t acc = 0; + for (unsigned int i = 0; i < 17; ++i) { - acc += (255 - h[i]) + c[i]; - h[i] = 255 - (acc & 0xFF); - acc >>= 8; + acc += (uint64_t)(0xffffffff - h[i]) + (uint64_t)c[i]; + h[i] = 0xffffffff - (acc & 0xffffffff); + acc >>= 32; } } static bool -greater512_unsigned (const uint8_t *a, const uint8_t *b) +greater512_unsigned (const uint32_t *a, const uint32_t *b) { - uint8_t a_int[65], b_int[65]; - for (unsigned int i = 0; i < 64; ++i) + uint32_t a_int[17], b_int[17]; + for (unsigned int i = 0; i < 16; ++i) { a_int[i] = a[i]; b_int[i] = b[i]; } - a_int[64] = 0x0; - b_int[64] = 0x0; - sub520 (a_int, b_int); + a_int[16] = 0x0; + b_int[16] = 0x0; + sub534 (a_int, b_int); - return !(a_int[64] & (1 << 7)); + return !(a_int[16] & (1 << 31)); } static void -modp512 (const uint8_t *in, uint8_t *out) +modp512 (const uint32_t *in, uint32_t *out) { - const uint8_t P[64] = { - 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, 0x00, - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, + uint32_t P[16] = { + 0xffffffed, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, + 0xffffffff, 0x7fffffff, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, }; - uint8_t approx_quotient[33]; - uint8_t approx_dividend[64]; - uint8_t accumulator[64]; - for (unsigned int i = 0; i < 64; ++i) + uint32_t P2[16] = { + 0xffffffda, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, + 0xffffffff, 0xffffffff, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, + }; + uint32_t ZERO[16] = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + }; + uint32_t approx_dividend[16]; + uint32_t accumulator[16]; + for (unsigned int i = 0; i < 16; ++i) { accumulator[i] = in[i]; }@@ -216,41 +203,37 @@ // Handle negatives properly
add512 (accumulator, P); for (unsigned int i = 0; i < 2; ++i) { - shr512_by_255 (accumulator, approx_quotient); - mult264 (P, approx_quotient, approx_dividend); + mult256 (P2, accumulator + 8, approx_dividend); sub512 (accumulator, approx_dividend); } - uint8_t dummy_buf[64]; - uint8_t dummy_val = (greater264 (accumulator, P)) ? 0x1 : 0x0; - for (unsigned int i = 0; i < 64; ++i) - { - dummy_buf[i] = P[i] * dummy_val; - } - sub512 (accumulator, dummy_buf); - for (unsigned int i = 0; i < 32; ++i) + uint32_t *dummy = (greater288 (accumulator, P2)) ? P2 : ZERO; + sub512 (accumulator, dummy); + dummy = greater256 (accumulator, P) ? P : ZERO; + sub256 (accumulator, dummy); + for (unsigned int i = 0; i < 8; ++i) { out[i] = accumulator[i]; } } static void -mult256_modp (const uint8_t *a, const uint8_t *b, uint8_t *out) +mult256_modp (const uint32_t *a, const uint32_t *b, uint32_t *out) { - uint8_t intermediate[64]; + uint32_t intermediate[16]; mult256 (a, b, intermediate); modp512 (intermediate, out); } static void -sub256_modp (const uint8_t *a, const uint8_t *b, uint8_t *out) +sub256_modp (const uint32_t *a, const uint32_t *b, uint32_t *out) { - uint8_t intermediates[2][64]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t intermediates[2][16]; + for (unsigned int i = 0; i < 8; ++i) { intermediates[0][i] = a[i]; intermediates[1][i] = b[i]; } - for (unsigned int i = 32; i < 64; ++i) + for (unsigned int i = 8; i < 16; ++i) { intermediates[0][i] = 0x0; intermediates[1][i] = 0x0;@@ -260,15 +243,15 @@ modp512 (intermediates[0], out);
} static void -add256_modp (const uint8_t *a, const uint8_t *b, uint8_t *out) +add256_modp (const uint32_t *a, const uint32_t *b, uint32_t *out) { - uint8_t intermediates[2][64]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t intermediates[2][16]; + for (unsigned int i = 0; i < 8; ++i) { intermediates[0][i] = a[i]; intermediates[1][i] = b[i]; } - for (unsigned int i = 32; i < 64; ++i) + for (unsigned int i = 8; i < 16; ++i) { intermediates[0][i] = 0x0; intermediates[1][i] = 0x0;@@ -278,51 +261,40 @@ modp512 (intermediates[0], out);
} static void -inv256_modp (const uint8_t *x, uint8_t *out) +inv256_modp (const uint32_t *x, uint32_t *out) { - uint8_t buf[64]; - uint8_t *i0 = buf; - uint8_t *i1 = buf + 32; - for (unsigned int i = 0; i < 32; ++i) + uint32_t buf[16]; + uint32_t *i0 = buf; + uint32_t *i1 = buf + 8; + for (unsigned int i = 0; i < 8; ++i) { i0[i] = x[i]; } for (unsigned int i = 0; i < 254; ++i) { mult256_modp (i0, i0, i1); - uint8_t *t1 = i1; + uint32_t *t1 = i1; i1 = i0; i0 = t1; if (i != 251 && i != 249) { mult256_modp (i0, x, i1); - uint8_t *t0 = i1; + uint32_t *t0 = i1; i1 = i0; i0 = t0; } } - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 8; ++i) { out[i] = i0[i]; } } static void -swap256 (unsigned int do_swap, uint8_t *a, uint8_t *b) -{ - for (unsigned int i = 0; i < 32; ++i) - { - uint8_t dummy = (a[i] ^ b[i]) & ((do_swap) ? 0xFF : 0x0); - a[i] = a[i] ^ dummy; - b[i] = b[i] ^ dummy; - } -} - -static void -pow256_2523_modp (const uint8_t *in, uint8_t *out) +pow256_2523_modp (const uint32_t *in, uint32_t *out) { - uint8_t i0[32]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t i0[8]; + for (unsigned int i = 0; i < 8; ++i) { i0[i] = in[i]; }@@ -334,34 +306,31 @@ {
mult256_modp (i0, in, i0); } } - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 8; ++i) { out[i] = i0[i]; } } static bool -decode256 (const uint8_t *point, uint8_t *x, uint8_t *y) +decode256 (const uint8_t *point, uint32_t *x, uint32_t *y) { bool x0 = (point[31] & 0x80) != 0; - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 8; ++i) { - y[i] = point[i]; + y[i] = from_le32 (point + 4 * i); } - y[31] &= 0x7F; - const uint8_t D[32] = { - 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, 0xab, 0xd8, 0x41, - 0x41, 0x4d, 0x0a, 0x70, 0x00, 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, - 0xc7, 0x8c, 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52, + y[7] &= 0x7fffffff; + const uint32_t D[8] = { + 0x135978a3, 0x75eb4dca, 0x4141d8ab, 0x00700a4d, + 0x7779e898, 0x8cc74079, 0x2b6ffe73, 0x52036cee, }; - const uint8_t ONE[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + const uint32_t ONE[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t v[32]; - uint8_t u[32]; - uint8_t i0[32], i1[32]; + uint32_t v[8]; + uint32_t u[8]; + uint32_t i0[8], i1[8]; mult256_modp (y, y, u); mult256_modp (y, y, v); sub256_modp (u, ONE, u);@@ -381,16 +350,14 @@
mult256_modp (x, x, i0); mult256_modp (i0, v, i0); sub256_modp (i0, u, i0); - const uint8_t *mask; - const uint8_t KMULT[32] = { - 0xb0, 0xa0, 0x0e, 0x4a, 0x27, 0x1b, 0xee, 0xc4, 0x78, 0xe4, 0x2f, - 0xad, 0x06, 0x18, 0x43, 0x2f, 0xa7, 0xd7, 0xfb, 0x3d, 0x99, 0x00, - 0x4d, 0x2b, 0x0b, 0xdf, 0xc1, 0x4f, 0x80, 0x24, 0x83, 0x2b, + const uint32_t *mask; + const uint32_t KMULT[8] = { + 0x4a0ea0b0, 0xc4ee1b27, 0xad2fe478, 0x2f431806, + 0x3dfbd7a7, 0x2b4d0099, 0x4fc1df0b, 0x2b832480, }; - const uint8_t P[32] = { - 0xed, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, - 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7f, + uint32_t P[8] = { + 0xffffffed, 0xffffffff, 0xffffffff, 0xffffffff, + 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff, }; if (iszero256 (i0))@@ -421,22 +388,19 @@ return true;
} static void -addpoints (const uint8_t *x1, const uint8_t *y1, const uint8_t *z1, - const uint8_t *t1, const uint8_t *x2, const uint8_t *y2, - const uint8_t *z2, const uint8_t *t2, uint8_t *x3, uint8_t *y3, - uint8_t *z3, uint8_t *t3) +addpoints (const uint32_t *x1, const uint32_t *y1, const uint32_t *z1, + const uint32_t *t1, const uint32_t *x2, const uint32_t *y2, + const uint32_t *z2, const uint32_t *t2, uint32_t *x3, uint32_t *y3, + uint32_t *z3, uint32_t *t3) { - const uint8_t TWO[32] = { - 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + const uint32_t TWO[8] = { + 0x2, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - const uint8_t D[32] = { - 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75, 0xab, 0xd8, 0x41, - 0x41, 0x4d, 0x0a, 0x70, 0x00, 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, - 0xc7, 0x8c, 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52, + const uint32_t D[8] = { + 0x135978a3, 0x75eb4dca, 0x4141d8ab, 0x00700a4d, + 0x7779e898, 0x8cc74079, 0x2b6ffe73, 0x52036cee, }; - uint8_t intermediates[8][32]; + uint32_t intermediates[8][8]; sub256_modp (y1, x1, intermediates[0]); sub256_modp (y2, x2, intermediates[1]); mult256_modp (intermediates[0], intermediates[1], intermediates[0]);@@ -459,11 +423,11 @@ mult256_modp (intermediates[3], intermediates[6], t3);
} static bool -points_eq (const uint8_t *x1, const uint8_t *y1, const uint8_t *z1, - const uint8_t *t1, const uint8_t *x2, const uint8_t *y2, - const uint8_t *z2, const uint8_t *t2) +points_eq (const uint32_t *x1, const uint32_t *y1, const uint32_t *z1, + const uint32_t *t1, const uint32_t *x2, const uint32_t *y2, + const uint32_t *z2, const uint32_t *t2) { - uint8_t i0[32], i1[32]; + uint32_t i0[8], i1[8]; mult256_modp (x1, z2, i0); mult256_modp (x2, z1, i1); sub256_modp (i0, i1, i0);@@ -482,58 +446,53 @@ return true;
} static void -scalarmult (const uint8_t *k, const uint8_t *x_in, const uint8_t *y_in, - uint8_t *x_out, uint8_t *y_out, uint8_t *z_out, uint8_t *t_out) +scalarmult (const uint32_t *k, const uint32_t *x_in, const uint32_t *y_in, + uint32_t *x_out, uint32_t *y_out, uint32_t *z_out, uint32_t *t_out) { - uint8_t x1[32], y1[32], t1[32]; - for (unsigned int i = 0; i < 32; ++i) - { - x1[i] = x_in[i]; - y1[i] = y_in[i]; - } - mult256_modp (x1, y1, t1); - uint8_t z1[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t t_in[8]; + mult256_modp (x_in, y_in, t_in); + uint32_t z_in[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t z2[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t z2[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t x2[32] = { - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t x2[8] = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t y2[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t y2[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t t2[32] = { - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t t2[8] = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - for (int i = 253; i >= 0; --i) + uint32_t lut[16][4][8]; + for (unsigned int i = 0; i < 8; ++i) { - unsigned int swap = (k[i / 8] >> (i % 8)) & 1; - swap256 (swap, x1, x2); - swap256 (swap, y1, y2); - swap256 (swap, z1, z2); - swap256 (swap, t1, t2); - - addpoints (x1, y1, z1, t1, x2, y2, z2, t2, x1, y1, z1, t1); + lut[0][0][i] = 0x0; + lut[0][1][i] = 0x0; + lut[0][2][i] = 0x0; + lut[0][3][i] = 0x0; + } + lut[0][1][0] = 0x1; + lut[0][2][0] = 0x1; + for (unsigned int i = 1; i < 16; ++i) + { + addpoints (lut[i - 1][0], lut[i - 1][1], lut[i - 1][2], lut[i - 1][3], + x_in, y_in, z_in, t_in, lut[i][0], lut[i][1], lut[i][2], + lut[i][3]); + } + for (int i = 63; i >= 0; --i) + { + addpoints (x2, y2, z2, t2, x2, y2, z2, t2, x2, y2, z2, t2); + addpoints (x2, y2, z2, t2, x2, y2, z2, t2, x2, y2, z2, t2); + addpoints (x2, y2, z2, t2, x2, y2, z2, t2, x2, y2, z2, t2); addpoints (x2, y2, z2, t2, x2, y2, z2, t2, x2, y2, z2, t2); - - swap256 (swap, x1, x2); - swap256 (swap, y1, y2); - swap256 (swap, z1, z2); - swap256 (swap, t1, t2); + uint8_t ind = (k[i / 8] >> (4 * (i % 8))) & 0xf; + addpoints (lut[ind][0], lut[ind][1], lut[ind][2], lut[ind][3], x2, y2, + z2, t2, x2, y2, z2, t2); } - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 8; ++i) { x_out[i] = x2[i]; y_out[i] = y2[i];@@ -543,110 +502,104 @@ }
} static void -shl512 (const uint8_t *in, const uint64_t shift, uint8_t *out) +shl512 (const uint32_t *in, const uint64_t shift, uint32_t *out) { - for (uint64_t i = 0; i < 64; ++i) + for (uint64_t i = 0; i < 16; ++i) { out[i] = 0x0; } - uint64_t shift_amt = shift % 8; - for (uint64_t i = 0; i < 64 - shift / 8; ++i) + uint64_t shift_amt = shift % 32; + for (uint64_t i = 0; i < 16 - shift / 32; ++i) { - out[i + shift / 8] = in[i] << shift_amt; - if (i > 0) + out[i + shift / 32] = in[i] << shift_amt; + if (i > 0 && shift_amt != 0) { - out[i + shift / 8] |= in[i - 1] >> (8 - shift_amt); + out[i + shift / 32] |= in[i - 1] >> (32 - shift_amt); } } } static void -modl512 (const uint8_t *x, uint8_t *out) +modl512 (const uint32_t *x, uint32_t *out) { - uint8_t L[64] = { - 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58, 0xd6, 0x9c, 0xf7, - 0xa2, 0xde, 0xf9, 0xde, 0x14, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, - 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t L[16] = { + 0x5cf5d3ed, 0x5812631a, 0xa2f79cd6, 0x14def9de, 0x00000000, 0x00000000, + 0x00000000, 0x10000000, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, }; - uint8_t LMULT[64]; - uint8_t ZERO[64] = { - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t LMULT[16]; + uint32_t ZERO[16] = { + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t i0[64]; - for (unsigned int i = 0; i < 64; ++i) + uint32_t i0[16]; + for (unsigned int i = 0; i < 16; ++i) { i0[i] = x[i]; } for (int i = 259; i >= 0; --i) { shl512 (L, i, LMULT); - uint8_t *dummy = greater512_unsigned (i0, LMULT) ? LMULT : ZERO; + uint32_t *dummy = greater512_unsigned (i0, LMULT) ? LMULT : ZERO; sub512 (i0, dummy); dummy = greater512_unsigned (i0, LMULT) ? LMULT : ZERO; sub512 (i0, dummy); } - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 8; ++i) { out[i] = i0[i]; } } static void -xB_lowmem (const uint8_t *k, uint8_t *x, uint8_t *y, uint8_t *z, uint8_t *t) +xB_lowmem (const uint32_t *k, uint32_t *x, uint32_t *y, uint32_t *z, + uint32_t *t) { - const uint8_t BX[32] = { - 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, - 0x95, 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, - 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, + const uint32_t BX[8] = { + 0x8f25d51a, 0xc9562d60, 0x9525a7b2, 0x692cc760, + 0xfdd6dc5c, 0xc0a4e231, 0xcd6e53fe, 0x216936d3, }; - const uint8_t BY[32] = { - 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, - 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, - 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, + const uint32_t BY[8] = { + 0x66666658, 0x66666666, 0x66666666, 0x66666666, + 0x66666666, 0x66666666, 0x66666666, 0x66666666, }; scalarmult (k, BX, BY, x, y, z, t); } void -tct_ed25519_pctable_gen (uint8_t *out) +tct_ed25519_pctable_gen (uint32_t *out) { - uint8_t a[64], b[64]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t a[16], b[16]; + for (unsigned int i = 0; i < 8; ++i) { a[i] = 0x0; - a[32 + i] = 0x0; + a[8 + i] = 0x0; } - a[0] = 0x1; - uint8_t t[32], z[32]; + a[0] = b[0] = 0x1; + uint32_t t[8], z[8]; for (unsigned int i = 0; i < 64; ++i) { modl512 (a, a); modl512 (a, b); - if (iszero256 (a) && iszero256 (a + 32)) + if (iszero256 (a) && iszero256 (a + 8)) { a[0] = b[0] = 0x1; } - for (unsigned int j = 32; j < 64; ++j) + for (unsigned int j = 8; j < 16; ++j) { a[j] = b[j] = 0x0; } for (unsigned int j = 0; j < 15; ++j) { // We don't need `t` where we're going - uint8_t *x_out = &(out[15 * 32 * 2 * i + 32 * 2 * j]); - uint8_t *y_out = &(out[15 * 32 * 2 * i + 32 * 2 * j + 32]); + uint32_t *x_out = &(out[15 * 8 * 2 * i + 8 * 2 * j]); + uint32_t *y_out = &(out[15 * 8 * 2 * i + 8 * 2 * j + 8]); xB_lowmem (a, x_out, y_out, z, t); - inv256_modp (z, z); - mult256_modp (x_out, z, x_out); - mult256_modp (y_out, z, y_out); + uint32_t z_inv[8]; + inv256_modp (z, z_inv); + mult256_modp (x_out, z_inv, x_out); + mult256_modp (y_out, z_inv, y_out); add512 (a, b); } }@@ -657,12 +610,10 @@
#include "tinycrypt/ed25519_precompute.h" static void -xB (const uint8_t *k, uint8_t *x, uint8_t *y, uint8_t *z, uint8_t *t) +xB (const uint32_t *k, uint32_t *x, uint32_t *y, uint32_t *z, uint32_t *t) { - const uint8_t ONE[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + const uint32_t ONE[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; for (unsigned int i = 0; i < 32; ++i) {@@ -670,37 +621,19 @@ x[i] = y[i] = z[i] = t[i] = 0x0;
} y[0] = 1; z[0] = 1; - for (unsigned int i = 0; i < 32; ++i) + for (unsigned int i = 0; i < 64; ++i) { - uint8_t ri0 = k[i] & 0xf; - uint8_t ri1 = (k[i] & 0xf0) >> 4; - uint8_t t0[32]; - uint8_t t1[32]; - if (ri0 != 0) + uint32_t ri = (k[i / 8] >> (4 * (i % 8))) & 0xf; + uint32_t t0[8]; + if (ri != 0) { mult256_modp ( - &PRECOMPUTE_TABLE[2 * i * 15 * 32 * 2 + (ri0 - 1) * 32 * 2], - &PRECOMPUTE_TABLE[2 * i * 15 * 32 * 2 + (ri0 - 1) * 32 * 2 + 32], - t0); - addpoints ( - x, y, z, t, - &PRECOMPUTE_TABLE[2 * i * 15 * 32 * 2 + (ri0 - 1) * 32 * 2], - &PRECOMPUTE_TABLE[2 * i * 15 * 32 * 2 + (ri0 - 1) * 32 * 2 + 32], - ONE, t0, x, y, z, t); - } - if (ri1 != 0) - { - mult256_modp (&PRECOMPUTE_TABLE[(2 * i + 1) * 15 * 32 * 2 - + (ri1 - 1) * 32 * 2], - &PRECOMPUTE_TABLE[(2 * i + 1) * 15 * 32 * 2 - + (ri1 - 1) * 32 * 2 + 32], - t1); + &PRECOMPUTE_TABLE[i * 15 * 8 * 2 + (ri - 1) * 8 * 2], + &PRECOMPUTE_TABLE[i * 15 * 8 * 2 + (ri - 1) * 8 * 2 + 8], t0); addpoints (x, y, z, t, - &PRECOMPUTE_TABLE[(2 * i + 1) * 15 * 32 * 2 - + (ri1 - 1) * 32 * 2], - &PRECOMPUTE_TABLE[(2 * i + 1) * 15 * 32 * 2 - + (ri1 - 1) * 32 * 2 + 32], - ONE, t1, x, y, z, t); + &PRECOMPUTE_TABLE[i * 15 * 8 * 2 + (ri - 1) * 8 * 2], + &PRECOMPUTE_TABLE[i * 15 * 8 * 2 + (ri - 1) * 8 * 2 + 8], + ONE, t0, x, y, z, t); } } }@@ -708,7 +641,7 @@
#else static void -xB (const uint8_t *k, uint8_t *x, uint8_t *y, uint8_t *z, uint8_t *t) +xB (const uint32_t *k, uint32_t *x, uint32_t *y, uint32_t *z, uint32_t *t) { xB_lowmem (k, x, y, z, t); }@@ -723,15 +656,25 @@ tct_sha512 (privkey, 32, digest);
digest[0] &= 0b11111000; digest[31] &= 0b01111111; digest[31] |= 0b01000000; - uint8_t z[32]; - uint8_t t[32]; - uint8_t x[32]; - xB (digest, x, pubkey, z, t); + uint32_t k[16]; + for (unsigned int i = 0; i < 16; ++i) + { + k[i] = from_le32 (digest + 4 * i); + } + uint32_t y[8]; + uint32_t z[8]; + uint32_t t[8]; + uint32_t x[8]; + xB (k, x, y, z, t); inv256_modp (z, z); mult256_modp (x, z, x); - mult256_modp (pubkey, z, pubkey); + mult256_modp (y, z, y); + for (unsigned int i = 0; i < 8; ++i) + { + to_le32 (y[i], pubkey + 4 * i); + } pubkey[31] &= 0b01111111; - pubkey[31] |= x[0] << 7; + pubkey[31] |= x[0] << 31; } void@@ -740,7 +683,7 @@ const uint8_t *privkey, const uint8_t *pubkey,
uint8_t *working_buf, uint8_t *signature) { uint8_t digest[64]; - uint8_t s[64]; + uint32_t s[8]; tct_sha512 (privkey, 32, digest); digest[0] &= 0b11111000; digest[31] &= 0b01111111;@@ -748,23 +691,35 @@ digest[31] |= 0b01000000;
for (unsigned int i = 0; i < 32; ++i) { working_buf[i] = digest[32 + i]; - s[i] = digest[i]; + } + for (unsigned int i = 0; i < 8; ++i) + { + s[i] = from_le32 (digest + i * 4); } for (uint64_t i = 32; i < msg_len + 32; ++i) { working_buf[i] = msg[i - 32]; } tct_sha512 (working_buf, msg_len + 32, digest); - uint8_t r[32]; - modl512 (digest, r); - uint8_t rBx[32]; - uint8_t rBy[32]; - uint8_t rBz[32]; - uint8_t rBt[32]; + uint32_t r[8]; + uint32_t chunked[16]; + for (unsigned int i = 0; i < 16; ++i) + { + chunked[i] = from_le32 (digest + i * 4); + } + modl512 (chunked, r); + uint32_t rBx[8]; + uint32_t rBy[8]; + uint32_t rBz[8]; + uint32_t rBt[8]; xB (r, rBx, rBy, rBz, rBt); inv256_modp (rBz, rBz); mult256_modp (rBz, rBx, rBx); - mult256_modp (rBz, rBy, signature); + mult256_modp (rBz, rBy, chunked); + for (unsigned int i = 0; i < 8; ++i) + { + to_le32 (chunked[i], signature + 4 * i); + } signature[31] &= 0b01111111; signature[31] |= (rBx[0] & 1) << 7; for (unsigned int i = 0; i < 32; ++i)@@ -777,20 +732,24 @@ {
working_buf[i] = msg[i - 64]; } tct_sha512 (working_buf, msg_len + 64, digest); - uint8_t k[32]; - modl512 (digest, k); - mult256 (k, s, working_buf); - uint8_t big_r[64]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t k[8]; + for (unsigned int i = 0; i < 16; ++i) + { + chunked[i] = from_le32 (digest + 4 * i); + } + modl512 (chunked, k); + mult256 (k, s, chunked); + uint32_t big_r[16]; + for (unsigned int i = 0; i < 8; ++i) { big_r[i] = r[i]; - big_r[32 + i] = 0x0; + big_r[8 + i] = 0x0; } - add512 (working_buf, big_r); - modl512 (working_buf, working_buf); - for (unsigned int i = 0; i < 32; ++i) + add512 (chunked, big_r); + modl512 (chunked, chunked); + for (unsigned int i = 0; i < 8; ++i) { - signature[32 + i] = working_buf[i]; + to_le32 (chunked[i], 32 + signature + 4 * i); } }@@ -799,20 +758,18 @@ tct_ed25519_verify (const uint8_t *pubkey, const uint8_t *msg,
const uint64_t msg_len, uint8_t *working_buf, const uint8_t *signature) { - uint8_t Ax[32]; - uint8_t Ay[32]; + uint32_t Ax[8]; + uint32_t Ay[8]; if (!decode256 (pubkey, Ax, Ay)) { return false; } - uint8_t Rx[32]; - uint8_t Ry[32]; - uint8_t Rz[32] = { - 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, - 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, + uint32_t Rx[8]; + uint32_t Ry[8]; + uint32_t Rz[8] = { + 0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, }; - uint8_t Rt[32]; + uint32_t Rt[8]; if (!decode256 (signature, Rx, Ry)) { return false;@@ -835,24 +792,29 @@ working_buf[i] = msg[i - 64];
} } tct_sha512 (working_buf, 64 + msg_len, h); - modl512 (h, h); - uint8_t sBx[32]; - uint8_t sBy[32]; - uint8_t sBz[32]; - uint8_t sBt[32]; - uint8_t hAx[32]; - uint8_t hAy[32]; - uint8_t hAz[32]; - uint8_t hAt[32]; - uint8_t sigk[64]; - for (unsigned int i = 0; i < 32; ++i) + uint32_t chunked[16]; + for (unsigned int i = 0; i < 16; ++i) { - sigk[i] = signature[32 + i]; - sigk[32 + i] = 0x0; + chunked[i] = from_le32 (h + i * 4); + } + modl512 (chunked, chunked); + uint32_t sBx[8]; + uint32_t sBy[8]; + uint32_t sBz[8]; + uint32_t sBt[8]; + uint32_t hAx[8]; + uint32_t hAy[8]; + uint32_t hAz[8]; + uint32_t hAt[8]; + uint32_t sigk[16]; + for (unsigned int i = 0; i < 8; ++i) + { + sigk[i] = from_le32 (signature + 32 + 4 * i); + sigk[8 + i] = 0x0; } modl512 (sigk, sigk); xB (sigk, sBx, sBy, sBz, sBt); - scalarmult (h, Ax, Ay, hAx, hAy, hAz, hAt); + scalarmult (chunked, Ax, Ay, hAx, hAy, hAz, hAt); addpoints (Rx, Ry, Rz, Rt, hAx, hAy, hAz, hAt, hAx, hAy, hAz, hAt); return points_eq (sBx, sBy, sBz, sBt, hAx, hAy, hAz, hAt); }
M
tinycrypt/ed25519.h
→
tinycrypt/ed25519.h
@@ -23,6 +23,6 @@
/// Constructs a memory-speed-tradeoff lookup table for use in Ed25519 /// verifications, similar (but larger by ~2x) to the method described in /// https://ed25519.cr.yp.to/ed25519-20110926.pdf. -void tct_ed25519_pctable_gen (uint8_t *out); +void tct_ed25519_pctable_gen (uint32_t *out); #endif
M
tinycrypt/ed25519_precompute.h
→
tinycrypt/ed25519_precompute.h
@@ -1,3843 +1,1923 @@
#include <stdint.h> -const static uint8_t PRECOMPUTE_TABLE[61440] = { - 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69, - 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, - 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, - 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, - 0x0e, 0xce, 0x43, 0x28, 0x4e, 0xa1, 0xc5, 0x83, 0x5f, 0xa4, 0xd7, 0x15, 0x45, 0x8e, 0x0d, 0x08, - 0xac, 0xe7, 0x33, 0x18, 0x7d, 0x3b, 0x04, 0x3d, 0x6c, 0x04, 0x5a, 0x9f, 0x4c, 0x38, 0xab, 0x36, - 0xc9, 0xa3, 0xf8, 0x6a, 0xae, 0x46, 0x5f, 0x0e, 0x56, 0x51, 0x38, 0x64, 0x51, 0x0f, 0x39, 0x97, - 0x56, 0x1f, 0xa2, 0xc9, 0xe8, 0x5e, 0xa2, 0x1d, 0xc2, 0x29, 0x23, 0x09, 0xf3, 0xcd, 0x60, 0x22, - 0x5c, 0xe2, 0xf8, 0xd3, 0x5f, 0x48, 0x62, 0xac, 0x86, 0x48, 0x62, 0x81, 0x19, 0x98, 0x43, 0x63, - 0x3a, 0xc8, 0xda, 0x3e, 0x74, 0xae, 0xf4, 0x1f, 0x49, 0x8f, 0x92, 0x22, 0x4a, 0x9c, 0xae, 0x67, - 0xd4, 0xb4, 0xf5, 0x78, 0x48, 0x68, 0xc3, 0x02, 0x04, 0x03, 0x24, 0x67, 0x17, 0xec, 0x16, 0x9f, - 0xf7, 0x9e, 0x26, 0x60, 0x8e, 0xa1, 0x26, 0xa1, 0xab, 0x69, 0xee, 0x77, 0xd1, 0xb1, 0x67, 0x12, - 0x70, 0xf8, 0xc9, 0xc4, 0x57, 0xa6, 0x3a, 0x49, 0x47, 0x15, 0xce, 0x93, 0xc1, 0x9e, 0x73, 0x1a, - 0xf9, 0x20, 0x35, 0x7a, 0xb8, 0xd4, 0x25, 0x83, 0x46, 0xf1, 0xcf, 0x56, 0xdb, 0xa8, 0x3d, 0x20, - 0x2f, 0x11, 0x32, 0xca, 0x61, 0xab, 0x38, 0xdf, 0xf0, 0x0f, 0x2f, 0xea, 0x32, 0x28, 0xf2, 0x4c, - 0x6c, 0x71, 0xd5, 0x80, 0x85, 0xb8, 0x0e, 0x47, 0xe1, 0x95, 0x15, 0xcb, 0x27, 0xe8, 0xd0, 0x47, - 0x33, 0xf2, 0x2e, 0x32, 0xc0, 0x9c, 0x40, 0x91, 0xa5, 0xe1, 0x1b, 0x3e, 0xf9, 0x19, 0x28, 0x5c, - 0xde, 0xa5, 0x2d, 0xd1, 0xf7, 0x7c, 0xef, 0xfc, 0x7b, 0x58, 0xe3, 0xad, 0x3e, 0xa7, 0xfd, 0x49, - 0xed, 0xc8, 0x76, 0xd6, 0x83, 0x1f, 0xd2, 0x10, 0x5d, 0x0b, 0x43, 0x89, 0xca, 0x2e, 0x28, 0x31, - 0x66, 0x46, 0x92, 0x89, 0x14, 0x6e, 0x2c, 0xe0, 0x6f, 0xae, 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0xe1, 0x42, 0x67, - 0xb4, 0xb9, 0x37, 0xfc, 0xa9, 0x5b, 0x2f, 0x1e, 0x93, 0xe4, 0x1e, 0x62, 0xfc, 0x3c, 0x78, 0x81, - 0x8f, 0xf3, 0x8a, 0x66, 0x09, 0x6f, 0xad, 0x6e, 0x79, 0x73, 0xe5, 0xc9, 0x00, 0x06, 0xd3, 0x21, - 0x5c, 0x71, 0x85, 0x51, 0x06, 0x23, 0xe0, 0xd3, 0x94, 0x02, 0x4e, 0x2e, 0x5c, 0x0e, 0xd8, 0x86, - 0xb8, 0x22, 0x94, 0x6f, 0xe0, 0x36, 0xf3, 0x1b, 0x65, 0x71, 0x00, 0xc8, 0x70, 0xc9, 0x7c, 0x35, - 0xc0, 0xf1, 0x22, 0x55, 0x84, 0x44, 0x4e, 0xc7, 0x30, 0x44, 0x6e, 0x23, 0x13, 0x90, 0x78, 0x1f, - 0xfd, 0xd2, 0xf2, 0x56, 0xe9, 0xfc, 0xbe, 0xb2, 0xf4, 0x0d, 0xdd, 0xc2, 0xc2, 0x23, 0x3d, 0x7f, - 0x4f, 0xf9, 0x77, 0x48, 0x22, 0x1f, 0x95, 0x44, 0x14, 0xf8, 0x36, 0xd8, 0x4e, 0x8e, 0x7e, 0x20, - 0x77, 0x86, 0xbc, 0xd2, 0x0e, 0xb6, 0x70, 0x44, 0x75, 0x6d, 0xca, 0x30, 0x7e, 0x79, 0x2c, 0x60, - 0x2c, 0x7b, 0xe8, 0x6a, 0xb0, 0x74, 0x88, 0xba, 0x43, 0xe8, 0xe0, 0x3d, 0x85, 0xa6, 0x76, 0x25, - 0xcf, 0xbf, 0x98, 0xc8, 0x54, 0x4d, 0xe4, 0xc8, 0x77, 0x24, 0x1b, 0x7a, 0xaa, 0xfc, 0x7f, 0x63, - 0xcb, 0xf3, 0x7c, 0x20, 0xc1, 0xd2, 0x2f, 0xff, 0x52, 0xd5, 0x93, 0xc5, 0xb2, 0xa5, 0x81, 0xd3, - 0x38, 0x24, 0x71, 0xd6, 0x8d, 0x07, 0xcf, 0xb6, 0x17, 0xe4, 0x4b, 0x15, 0xb1, 0x28, 0xe5, 0x14, - 0x13, 0x37, 0x03, 0x6a, 0xc3, 0x2d, 0x8f, 0x30, 0xd4, 0x58, 0x9c, 0x3c, 0x1c, 0x59, 0x58, 0x12, - 0xce, 0x0f, 0xff, 0x40, 0xe3, 0x7c, 0x6f, 0x5a, 0x97, 0xab, 0x21, 0x3f, 0x31, 0x82, 0x90, 0x2d, - 0x2d, 0x90, 0xf0, 0x78, 0x66, 0xfe, 0x62, 0xae, 0x42, 0x3b, 0xc1, 0x85, 0x23, 0xbf, 0x95, 0x32, - 0xdb, 0x49, 0xa2, 0x0c, 0xe0, 0x70, 0xcf, 0x5e, 0x35, 0x5d, 0x6e, 0x01, 0x7e, 0xe1, 0x19, 0x47, - 0xf9, 0xe4, 0x2d, 0x2e, 0xdc, 0x81, 0xd2, 0x33, 0x67, 0x96, 0x73, 0x52, 0xb4, 0x7e, 0x48, 0x56, - 0xb8, 0x25, 0x78, 0x63, 0x4e, 0x6c, 0x1d, 0xe7, 0x22, 0x80, 0xce, 0x8b, 0x60, 0xce, 0x70, 0x40, - 0xed, 0x5f, 0xc0, 0xb7, 0x73, 0xe0, 0x80, 0x37, 0xb8, 0xb7, 0x22, 0x8d, 0xe8, 0xe3, 0x43, 0x88, - 0x4f, 0x30, 0x2d, 0x28, 0xf0, 0xad, 0x33, 0xdb, 0xcc, 0x66, 0xf3, 0xd5, 0xe0, 0x27, 0x74, 0x10, - 0x80, 0x1f, 0x40, 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0x19, 0x8b, 0x0c, 0x6a, - 0xb8, 0x42, 0x1c, 0x03, 0xad, 0x2c, 0x03, 0x8e, 0xac, 0xd7, 0x98, 0x29, 0x13, 0xc6, 0x02, 0x29, - 0xb5, 0xd4, 0xe7, 0xcf, 0xcc, 0x8b, 0x83, 0xec, 0x35, 0xc7, 0x9c, 0x74, 0xb7, 0xad, 0x85, 0x5f, - 0x78, 0x84, 0xe1, 0x56, 0x45, 0x69, 0x68, 0x5a, 0x4f, 0xb8, 0xb1, 0x29, 0xff, 0x33, 0x03, 0x31, - 0xb7, 0xcb, 0x96, 0x25, 0xe6, 0xe6, 0x41, 0x98, 0x1a, 0xbb, 0x03, 0x56, 0xf2, 0xb2, 0x91, 0x34, - 0x2c, 0x6c, 0xf7, 0x66, 0xa4, 0x62, 0x6b, 0x39, 0xb3, 0xba, 0x65, 0xd3, 0x1c, 0xf8, 0x11, 0xaa, - 0xbe, 0xdc, 0x80, 0x59, 0x87, 0xf5, 0x7b, 0xe5, 0xe3, 0xb3, 0x3e, 0x39, 0xda, 0xbe, 0x88, 0x09, - 0x8b, 0xf1, 0xa0, 0xf5, 0xdc, 0x29, 0xb4, 0xe2, 0x07, 0xc6, 0x7a, 0x00, 0xd0, 0x89, 0x17, 0x51, - 0xd4, 0xbb, 0xd4, 0x22, 0xea, 0x7e, 0x7d, 0x7c, 0x24, 0xea, 0xf2, 0xe8, 0x22, 0x12, 0x95, 0x06, - 0xda, 0x7c, 0xa4, 0x0c, 0xf4, 0xba, 0x6e, 0xe1, 0x89, 0xb5, 0x59, 0xca, 0xf1, 0xc0, 0x29, 0x36, - 0x09, 0x44, 0xe2, 0x7f, 0xd1, 0x63, 0x15, 0x99, 0xea, 0x25, 0xcf, 0x0c, 0x9d, 0xc0, 0x44, 0x6f, +const static uint32_t PRECOMPUTE_TABLE[15360] = { + 0x8f25d51a, 0xc9562d60, 0x9525a7b2, 0x692cc760, 0xfdd6dc5c, 0xc0a4e231, 0xcd6e53fe, 0x216936d3, + 0x66666658, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, + 0x2843ce0e, 0x83c5a14e, 0x15d7a45f, 0x80d8e45, 0x1833e7ac, 0x3d043b7d, 0x9f5a046c, 0x36ab384c, + 0x6af8a3c9, 0xe5f46ae, 0x64385156, 0x97390f51, 0xc9a21f56, 0x1da25ee8, 0x92329c2, 0x2260cdf3, + 0xd3f8e25c, 0xac62485f, 0x81624886, 0x63439819, 0x3edac83a, 0x1ff4ae74, 0x22928f49, 0x67ae9c4a, + 0x78f5b4d4, 0x2c36848, 0x67240304, 0x9f16ec17, 0x60269ef7, 0xa126a18e, 0x77ee69ab, 0x1267b1d1, + 0xc4c9f870, 0x493aa657, 0x93ce1547, 0x1a739ec1, 0x7a3520f9, 0x8325d4b8, 0x56cff146, 0x203da8db, + 0xca32112f, 0xdf38ab61, 0xea2f0ff0, 0x4cf22832, 0x80d5716c, 0x470eb885, 0xcb1595e1, 0x47d0e827, + 0x322ef233, 0x91409cc0, 0x3e1be1a5, 0x5c2819f9, 0xd12da5de, 0xfcef7cf7, 0xade3587b, 0x49fda73e, + 0xd676c8ed, 0x10d21f83, 0x89430b5d, 0x31282eca, 0x89924666, 0xe02c6e14, 0x98feae6f, 0x5f4825b2, + 0x7dcbf23d, 0x783a741a, 0x6c7b4427, 0xa1e59982, 0xdd0a29be, 0x62aeacc0, 0x7a45601c, 0x4c9797ba, + 0xf9497ef4, 0xc1d27ad0, 0x944d6b60, 0xf9417c06, 0xfd4f7d77, 0x1db709a7, 0x2886d8a1, 0x54de3fc, + 0xf50e4107, 0x5855981a, 0xbbf1ce95, 0x83e809f3, 0x4b1d8107, 0xe9e3ee19, 0xfcf4bd4e, 0x14568685, + 0x9f4062b8, 0x12c4c4b5, 0xf7abf23d, 0xf0882b46, 0xdd36ad41, 0x87ce6468, 0x2b47d52f, 0x31c563e3, + 0x8a584c8, 0x3b87fdbc, 0x80698b99, 0xeb3ac67b, 0xf84ecf93, 0x42862d5c, 0x97d771b6, 0x6742e15f, + 0xfc37b9b4, 0x1e2f5ba9, 0x621ee493, 0x81783cfc, 0x668af38f, 0x6ead6f09, 0xc9e57379, 0x21d30600, + 0x5185715c, 0xd3e02306, 0x2e4e0294, 0x86d80e5c, 0x6f9422b8, 0x1bf336e0, 0xc8007165, 0x357cc970, + 0x5522f1c0, 0xc74e4484, 0x236e4430, 0x1f789013, 0x56f2d2fd, 0xb2befce9, 0xc2dd0df4, 0x7f3d23c2, + 0x4877f94f, 0x44951f22, 0xd836f814, 0x207e8e4e, 0xd2bc8677, 0x4470b60e, 0x30ca6d75, 0x602c797e, + 0x6ae87b2c, 0xba8874b0, 0x3de0e843, 0x2576a685, 0xc898bfcf, 0xc8e44d54, 0x7a1b2477, 0x637ffcaa, + 0x207cf3cb, 0xff2fd2c1, 0xc593d552, 0xd381a5b2, 0xd6712438, 0xb6cf078d, 0x154be417, 0x14e528b1, + 0x6a033713, 0x308f2dc3, 0x3c9c58d4, 0x1258591c, 0x40ff0fce, 0x5a6f7ce3, 0x3f21ab97, 0x2d908231, + 0x78f0902d, 0xae62fe66, 0x85c13b42, 0x3295bf23, 0xca249db, 0x5ecf70e0, 0x16e5d35, 0x4719e17e, + 0x2e2de4f9, 0x33d281dc, 0x52739667, 0x56487eb4, 0x637825b8, 0xe71d6c4e, 0x8bce8022, 0x4070ce60, + 0xb7c05fed, 0x3780e073, 0x8d22b7b8, 0x8843e3e8, 0x282d304f, 0xdb33adf0, 0xd5f366cc, 0x107427e0, + 0xea401f80, 0x87efe1ae, 0x289a2723, 0x3740cfb2, 0xd2da89b8, 0x78466022, 0xed538b74, 0x12dbb00d, + 0xb58515b9, 0xa38e7353, 0x3e39832a, 0xd8dee6d8, 0x5ccabb15, 0x48c7a89, 0xf5884aaf, 0x205f3b42, + 0x899c2839, 0x8369fd98, 0x19b6265c, 0xa74898e8, 0xcbb702bf, 0x15bad17a, 0x50c4cb81, 0x4e50256f, + 0x66a18dc1, 0x90617f3e, 0x770189cb, 0xd9631374, 0x5d20419e, 0xdc5ac6f9, 0xec2ec435, 0x4f162dea, + 0xad2e5cdf, 0x946d4cc4, 0xa19a9aa1, 0xace5af18, 0x64d29331, 0x5162f701, 0x4ff22f5, 0x12cbfb2d, + 0x6c28f9f8, 0x59b2596d, 0xe7bf2374, 0x9578d33, 0x8249c91, 0xb8e22b15, 0x27e53aee, 0x23a48606, + 0xc16727eb, 0xd87aab37, 0x8e079c27, 0xb06a11ff, 0x3aad6e78, 0x9f980f2e, 0x827fc372, 0x709696f2, + 0x977e4f26, 0x4fdd40f6, 0xf97852fc, 0xe6033190, 0xb39567d, 0x8582561d, 0x17421af9, 0x39cf6c69, + 0x3a06d269, 0xf92d394f, 0x4c8c4038, 0xb41205e7, 0xc0f88b78, 0x7ade93ec, 0xe12cce6b, 0x4434a90e, + 0x7ba4d779, 0xcf2d0f6f, 0x27bd0f58, 0x2e8a41ae, 0x13770453, 0x9f148a93, 0x26dec7d0, 0x4d6204a5, + 0xa206df11, 0x8745ea7b, 0x882b44a3, 0x8be67387, 0x141fd21a, 0xa89784e2, 0x6d32aaa4, 0x65433072, + 0xb03ca40b, 0xf1517a0f, 0x6ad9d678, 0xb8e846fd, 0x871d79a8, 0x9cf290f9, 0xbf82913, 0x5fa6420, + 0x17da0926, 0xfbd695af, 0x6e0d196a, 0x99f1125e, 0x6fa8aa4c, 0x72f48679, 0xf9260028, 0x3d199eea, + 0xf6425311, 0x3cdfe8d7, 0x29152a1, 0x1912c615, 0xe5a56e1a, 0x514edd21, 0xbc020e13, 0x78b43cc5, + 0xd2fb4db9, 0x7e188d0c, 0x6f27d6ac, 0xa01fbc92, 0xf215646, 0x2f876296, 0x2e64b36e, 0x75358a78, + 0xc15b1416, 0xccf56d4f, 0xfdb7e632, 0x159c0b57, 0x1ebf38f0, 0xcbdd2da2, 0x2e0d4cb9, 0x3b5c6a, + 0xfc243d1e, 0x93449fba, 0xe41bc813, 0x6aedbdda, 0x68d98473, 0x13486397, 0x46acb57c, 0x1bd90068, + 0x3e48f8ea, 0xd7e3380b, 0xd91ecfa3, 0x867b24f2, 0x8f67d336, 0xdc7dab33, 0xa7d69cb9, 0x384bd69c, + 0xdec0a6e5, 0x703124b6, 0xf30a0841, 0xbeba9c9f, 0xb8bcaaca, 0xa46a16b1, 0x9352d734, 0x121351d7, + 0xf0cfdd87, 0x5da2495b, 0x26237a40, 0x8a837aa4, 0x1ad28bb7, 0x2402eabf, 0xa97b5f08, 0x379dbeb1, + 0x84b86fc, 0xfda0e7ee, 0x34094521, 0x233261c1, 0x48559bfc, 0x63f79953, 0x1ce99d0, 0x28eb9fe0, + 0x853166d0, 0x1fe22c8f, 0x7d86f2fb, 0x13092015, 0x2540b5c6, 0x5a45dc81, 0x3f69a0b6, 0x2a15b6f0, + 0xec89df9c, 0x1474b2e4, 0xb08a4e52, 0x85abf729, 0x2cbf29c4, 0x2dc30146, 0xccbeca98, 0x721c3cbb, + 0xf5e111e0, 0x3e142cad, 0xa70046b0, 0x4338a504, 0xeedf9d46, 0x36201356, 0x217bd35a, 0x3609e119, + 0xbca36be2, 0x751d1e78, 0x4cd0e1c2, 0xddbdc510, 0x548cd9b3, 0x54ad97ef, 0x36519c0d, 0x5b7a7411, + 0xed7fda0d, 0xa302a78e, 0x8123b93e, 0x395fa1c, 0x5886c04e, 0x5572e276, 0xc7dfae6b, 0x1624fefe, + 0xbba393cb, 0xc902d581, 0x2d44c6e9, 0x52ed8a90, 0x4461a5a1, 0xad880847, 0x6057a53d, 0x60e4e54d, + 0x5aabfc47, 0x5685f017, 0x2086303a, 0x448e4b28, 0x26e3a74, 0x9f8f32f1, 0xe935083f, 0x6e5f16ca, + 0x651c591c, 0x9a4345d, 0x709c13cd, 0xc52ab17d, 0x600baf88, 0x8d349fc7, 0xea7fb7d6, 0x778d6578, + 0x741b790c, 0x1637083f, 0x7a5df9f2, 0x76cc4c8c, 0x9037b29a, 0x96f3107f, 0x8ddda595, 0x1d19e9b7, + 0xa0c1537b, 0x84fe2b43, 0x4a977e12, 0x12711390, 0x65f92d50, 0xcb8b105c, 0xca0facf7, 0x5cbac182, + 0x1dd31544, 0x42f30f06, 0x655251c7, 0x94979e03, 0x69944d4d, 0xfd5517da, 0x79664378, 0x63c96147, + 0xb9730bb4, 0x6a25a019, 0xa5d3fedc, 0x68f73542, 0x90541ac7, 0x7cf1f4c7, 0x8c2523ed, 0x77472dca, + 0x9304bcd0, 0x767cba15, 0x26c6256d, 0x730e4a5f, 0x72371ae, 0xdb1c00d, 0x8071433a, 0x31875374, + 0x28a2274b, 0x159fa11a, 0xffa0c5b0, 0x5b250826, 0x51784e3a, 0x5eeecf69, 0x4140ad2c, 0x3e65ac8d, + 0xcc2a556, 0x20b8bcdd, 0xb561576d, 0xd4b578fb, 0x26905449, 0xe6e9cbc1, 0x4e1decbf, 0x5e7e07ed, + 0x566cf6c7, 0xe142031, 0xc127d9a8, 0x7d1b3d9a, 0x81d3260e, 0x6bf5ebaa, 0x51f10279, 0xf55755c, + 0x82cd340a, 0x5409333c, 0x303961d2, 0x21effd9b, 0xfa70d426, 0x3331f9ee, 0xb3d08473, 0x2eecbf81, + 0x8b93e8, 0xb89cf764, 0x49e6e074, 0x484d4d48, 0x40a119b6, 0x4132d9b7, 0xa137827c, 0x54d2dc2d, + 0x14cc93bb, 0x4566cef3, 0xa53d51b9, 0x57eadd2a, 0x79cd8dbe, 0xa5aa7b18, 0x7463be28, 0x70b22514, + 0xb18d9c02, 0x5b9e7392, 0x4dd9160a, 0x14793400, 0xf94d609a, 0xc2606727, 0xd32ff401, 0x244980de, + 0x5b4a2b68, 0x9151c7d5, 0x4b2ae11d, 0xbcf147c4, 0xc8cbb37a, 0x90ac7cb6, 0xf9f3fd05, 0x6b113a52, + 0xf327c13d, 0x90954359, 0xf57996c5, 0x296595f4, 0x5519c06, 0x2eb8da18, 0x59697e79, 0x1aeb0171, + 0xe9a95bd2, 0x19c2fde6, 0x3fe64287, 0x1e057ee8, 0x39904059, 0xad6a11dd, 0x7abbc179, 0x661b7575, + 0x2a7b09be, 0x497d97e4, 0xd6db12ae, 0xd10c9557, 0x4f807c07, 0xf0ce022f, 0xb5d4bb12, 0x5da1ae1, + 0xb6490615, 0x2fea3c8a, 0xc3142034, 0x2cafd6aa, 0x2065bd3e, 0x3b4b4de2, 0xc34a9feb, 0x603ba4ad, + 0xc0e658bc, 0x812a2a95, 0xd2f37a9a, 0xbc48be06, 0xe046c50c, 0xfacd46a, 0x3482ccd9, 0x1fdbaf2c, + 0xb391d99, 0x369d4031, 0xd12c1693, 0xebd6a85b, 0x3af9e330, 0x5d1e15af, 0x4bf2d3a4, 0x3d718e64, + 0xa23600f9, 0xa88e3bf5, 0x7f1f7280, 0x5f902ac7, 0x3a22a892, 0x2f228811, 0xbba3f414, 0x320d055d, + 0xbd1317f7, 0xecd2bcfb, 0x3115b345, 0x8482afe9, 0xfcc6283d, 0xb541f511, 0x7612d38b, 0x3c1ae752, + 0x711364e, 0x512015a2, 0x62c32ac4, 0xa67f5e8b, 0x8545f90f, 0xb786116c, 0xf9d7e57e, 0x51c91c3, + 0x3a67a694, 0x5291ff82, 0xdc237ed4, 0x9b5c9d91, 0x361952ee, 0x2eadaa56, 0xe93c59ad, 0x1afdaf17, + 0x2b212fcb, 0x3e8ee70a, 0x2e94f72f, 0x9679cbaf, 0x1d136c01, 0xc16bdbc7, 0x53596b9d, 0x36f6ead7, + 0xa3f91fc6, 0x2e622da2, 0x506ef138, 0xa260d0e2, 0xfd156ea2, 0xb41b378d, 0x7c5f770c, 0x5602e63d, + 0x1643df95, 0x87b95a7b, 0x13bbfffe, 0xdc5b47de, 0xa7efd83, 0xed5e4de1, 0x4b202573, 0xaeba9f7, + 0xa6d0c442, 0x7a537923, 0x43757b11, 0x7f5bab51, 0x89b220c2, 0xbba1e5bd, 0xcca041e2, 0x1ef44c94, + 0x1c34f176, 0x5320a230, 0xed07ed09, 0xdda4ef95, 0xd1037859, 0xf03f7ca9, 0x859ec35b, 0x47ab50af, + 0xaecdd56a, 0x2b5923c4, 0xd3b833f5, 0x252673b1, 0x96027691, 0xb83f395, 0x15ddad5, 0x41191323, + 0x7c8c2739, 0xa6e984a5, 0xd02b97f9, 0x7866c90d, 0x9246dc11, 0x2238e17e, 0xa1f3f7f6, 0x84879c0, + 0xcfd34b9, 0xfc4b7e2a, 0xdc938499, 0x90ecf62f, 0x5bedfbc, 0x24298dd7, 0x13c33657, 0x19ecfb1e, + 0x2917be45, 0xb3a5e1fa, 0x9b2d8889, 0x5e9a8a90, 0x7f2c9496, 0x7a01dc50, 0x606662e4, 0x1b54f5a4, + 0x2cd2b480, 0xc3f7d550, 0x2e9e1dcb, 0xc5eb0b35, 0x8d437473, 0xecbea4e4, 0xbab8bced, 0x3eb39148, + 0x448c6526, 0xd10e1d50, 0x541f5809, 0x5df7a288, 0x8cc47027, 0x231bf388, 0x72ebcb21, 0x23e13220, + 0x84818ddc, 0x515a2cc8, 0xc564171e, 0xa5cd0505, 0x846daef4, 0xe7beae34, 0xa5d28cff, 0x23ebab94, + 0x6c2982c2, 0xe0cbf042, 0xf00139aa, 0x5f7d1b10, 0x6d006cce, 0x723e6f7c, 0x955f2f36, 0x114c9f62, + 0x29ded6ea, 0x2b9003a, 0xc426cb59, 0x97b199ba, 0x92008e2f, 0xeb524f26, 0x8b891b47, 0x7d13c024, + 0x805b20d5, 0x952080a6, 0x8e9fe9c3, 0x9e1e9e87, 0x75ccc77a, 0x91f1a56c, 0x2c01a81a, 0x59a976ab, + 0x31b1c9de, 0x35aa1610, 0xb5d46a14, 0xd2718234, 0x1f9a5d4a, 0xe53c2653, 0x7f338d8e, 0x17d5a9ff, + 0xa4f6af89, 0xe010d564, 0x44efad1d, 0xac83dabd, 0x1cf0a87a, 0x43c3f907, 0xd3b73f6c, 0x73022287, + 0x13491d64, 0x69ec712f, 0xee42d087, 0xede3ec13, 0xbdbf7b56, 0x7b7d2f8c, 0x8eec289d, 0x86f2f76, + 0x4d5ff522, 0x4efcef15, 0x89360357, 0x915bebf0, 0x1cae2d6, 0xec52eea5, 0x338f3ca0, 0x72945a90, + 0x38e74b8a, 0xb0c2dabc, 0xfe4ae185, 0xcb84442d, 0xbf2d6b20, 0xbed79c11, 0xbf5f3ed3, 0x7a8bc68, + 0x22288901, 0x29aa786a, 0x9574c803, 0xbddc3e03, 0xa2a81307, 0x18b32d20, 0x7afd4270, 0x7249d7c4, + 0x77d92bc3, 0x3f9d7eb8, 0x4e448ce2, 0xc0bf2565, 0xed487322, 0x919c5ba, 0x777a6c85, 0x4026046d, + 0x1eda97c1, 0xda6a253c, 0x4109984f, 0x510f84b3, 0xba2ca8cd, 0x747ad31a, 0xd9136c1b, 0x59c711b1, + 0x16d2c34d, 0xee2b9efb, 0xe115a57f, 0xb8ec996a, 0xe5464af3, 0xf177ed7c, 0x5f88733d, 0x34f4c8c3, + 0x9e07bd96, 0xe8a3ae0f, 0x171ada60, 0xc95ba4db, 0xc92952b0, 0x138864ec, 0x3d6f143c, 0x677b89cd, + 0xccfef7f9, 0xf713ad74, 0xcacaa197, 0x9022280b, 0x388b160b, 0x957c7f03, 0x724e5652, 0x43aee427, + 0xf18d16bc, 0x94cb7244, 0x183f60ea, 0x7098bfed, 0x74e13960, 0xb3e71a1a, 0xeba89fb7, 0x4356a646, + 0x2b32ff02, 0x3254935c, 0x1a5457e8, 0x6560338b, 0xc1a467d3, 0x34a4c426, 0xa9a79b1f, 0x5b4fd9f4, + 0x33b08d46, 0x685b2654, 0xecc5bbdf, 0x5a3cf9c2, 0x278ec137, 0x5a49aa47, 0x468fbf8, 0x40ebd123, + 0x86ed4487, 0x7865572a, 0xaf8d9579, 0xd82b432b, 0x924f7c88, 0x3cc65c2a, 0xb65fe757, 0x46ccc8ca, + 0x333635d, 0x7180675e, 0xa5fec4e3, 0xc3abb2a0, 0x1d05b1fb, 0xa13253de, 0xf317da75, 0x4aa14888, + 0x8a9b4a11, 0x25399155, 0xd6b9fc1c, 0x7c723533, 0x6b570c70, 0x847d094, 0x3e2a8434, 0x7fe40f21, + 0x7227c0ed, 0x7515add4, 0xa78896c2, 0xe72f6ca6, 0xbe6ba0ae, 0xfd072c6e, 0x54b3e4fc, 0xabbd1ff, + 0x3482e958, 0x7690e02b, 0x152a37ff, 0xe7c42426, 0x19da5bc4, 0xac8b0007, 0xcd82462, 0x742f517d, + 0x95de6c32, 0xc077d22, 0x8ff7823f, 0xf09c5e16, 0x3d79d311, 0x66b6c9ff, 0x704a314, 0x545f1fcf, + 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0xa5b708c2, 0x4c53cf42, + 0x8ef6bba7, 0x90f7ddad, 0x89935fdd, 0xe63704ae, 0xc0e8b79a, 0xbf2a16df, 0x413c3ac4, 0x5a7289d5, + 0x56be1087, 0x152f5e3e, 0xf6bfb297, 0xe5ebbac, 0xdb572ff5, 0x9dac1193, 0xec584fff, 0x612699cf, + 0x8d29247d, 0x6773f535, 0x2f4c7ed6, 0x6126cd64, 0xf4c99baf, 0xdbed4b5d, 0x31a1e858, 0x12e74956, + 0x76a1aeb7, 0xa6113d8c, 0xfe165f1f, 0x2bedbc6e, 0xe881be39, 0xf997c8df, 0x39afb1db, 0x42fd325f, + 0x96af4565, 0x32d51953, 0x8b50b022, 0xd3b3d950, 0x134ac24f, 0x9571c292, 0x5feafdb1, 0x74ca5bbb, + 0xbd5222c9, 0xc3461811, 0xc93405f7, 0x3b915540, 0xdd114ded, 0xb6bb658b, 0xef969fbe, 0x68ecdd3, + 0xb98df4bd, 0xcb432810, 0x5b67994e, 0x53f7bf8f, 0xcdc1becc, 0x395f4731, 0x126d2343, 0x81ebb1d, + 0x34ff961f, 0xcb21132c, 0xbe85890a, 0x1e9e70b3, 0x96af97de, 0x8948f730, 0xf1078d40, 0x5830f025, + 0x5793d41e, 0x9de717e2, 0x3553cab, 0xdb2b2f82, 0x2e301e56, 0xe66e4724, 0x2c2433ff, 0x67d45175, + 0xa1d9062b, 0xd1f4e15d, 0xc69a3c1e, 0x13132b29, 0x16d8c078, 0xa99e2d17, 0xab5779c9, 0x19929124, + 0x9ca1fb69, 0x7d4975a6, 0x42407360, 0x950a13c4, 0x83041e79, 0x1e9b9994, 0x541fe80c, 0x52c0cbef, + 0x2c76158f, 0x439b720f, 0x2cc5bc27, 0xd15e0aea, 0xc5962bd, 0x3d99ab97, 0xaf64eb25, 0x633198a5, + 0x4a7b0c18, 0x4dc40de6, 0x307cbbc, 0xf1ec273d, 0x40c28268, 0x8f208447, 0xda049e76, 0x888e9e9, + 0xa1738914, 0x7a6a8737, 0x2ed91dcf, 0x74ed671a, 0x339cf0c0, 0xbf08dfdd, 0xda66d17b, 0x849c9e6, + 0x555edde9, 0x21de0ab0, 0xd42e5a4c, 0x92573a80, 0x2cc4f17a, 0xc92faf40, 0x5ae50392, 0x9f4dcbc, + 0xfd1e41bf, 0xc8a5cd31, 0xdafe8685, 0x396596ec, 0x88d03907, 0xed11b25b, 0xd05b2cdd, 0x1deb18e4, + 0xf604fd5f, 0x3a820912, 0x59fe6990, 0x10348f21, 0x6a0a8072, 0x96a3f4bb, 0xcb78e441, 0x4ac1d5c8, + 0x7c2be1f3, 0x93808605, 0x8fb4ad4a, 0xfd0c997e, 0xffd1efcd, 0x1334692c, 0x3bcf6441, 0x1e0990d0, + 0x80d6459d, 0xf4aa45e6, 0x345caa15, 0x8ca29987, 0x7d628426, 0x52c029b6, 0x1881f5ea, 0xea9350f, + 0x9791b943, 0xf22bd3fb, 0xa5574c60, 0x65763a1e, 0x486de95c, 0x56fd58d2, 0x1d8d48c4, 0x1cb7a40c, + 0xc67ef776, 0x383edbae, 0x49acce48, 0x137a6952, 0x61ccecc3, 0x2041a2a5, 0x89be911d, 0x28350196, + 0x7c7220e7, 0x525f946d, 0xf1e35444, 0x4636b0b2, 0xe892ae0f, 0x796e9d70, 0xa937adb1, 0x3dec05f, + 0xc6375515, 0x6d1c271c, 0xa4ca4f14, 0x462588c4, 0xe55afc39, 0x691129fe, 0x4d8472f5, 0x15949f78, + 0x762f52c7, 0x96bdd2e7, 0x3c163339, 0xaa4479f3, 0x27d55b75, 0x571d4fc0, 0xef453c6e, 0x759eead8, + 0x9b19ca0, 0x244bf613, 0x7098341b, 0x2411a84d, 0x9aecbf8c, 0x91bcc0f, 0x483b976f, 0x580c0ccf, + 0x869c3b2e, 0x101fe8e3, 0xbbbf4b17, 0x63e003eb, 0xb30a6b2e, 0xcf5c8617, 0xd3d6565d, 0x64de090c, + 0xa07eb4fe, 0x1a81958e, 0x36691fa2, 0xd539880e, 0x19e0a874, 0x3452b403, 0x88b67e3e, 0xb9840bc, + 0x176913e9, 0xbeba3645, 0xa964241d, 0xf2d6faa7, 0x54f34127, 0x189aac98, 0x24254848, 0x2901dec1, + 0x83dbfde2, 0x1a18b2a2, 0xb0cff2a9, 0x10be0213, 0x6a52976, 0xf34b53f3, 0x85cc7195, 0x7df3164c, + 0x1d730313, 0x787fb44f, 0x560d6d5b, 0x7197db77, 0x29833679, 0x7375a496, 0xb1ae9dec, 0x71009a1a, + 0xebcc0328, 0xdfd76c5d, 0x8b0b1f3a, 0x179bcaf3, 0xb555c85e, 0x3b0781aa, 0x3383ef21, 0x3a2f8063, + 0x85f1909f, 0x5d6d75a5, 0xecf802cc, 0x8ed61372, 0xc0a41d, 0xd4083076, 0xd4f5ae98, 0x335cbd0f, + 0xc73d2a3a, 0xe7047387, 0xdbbbb749, 0x763d0dbf, 0x36c2540a, 0x51857e5, 0x243ab578, 0x551a44b0, + 0x686327a1, 0x33050832, 0xf83656da, 0x8a1d8f6, 0x4fb14a4b, 0x632326a0, 0x3c2ae351, 0x2c518788, + 0x6d0a2a6f, 0xfbb063cf, 0x50be022a, 0xafaab7e0, 0x345c8b3f, 0x14a192ff, 0xd17addbd, 0x4a9df2b1, + 0x16bb308a, 0x2498f793, 0xbb89761a, 0x27a0823c, 0x399a77f, 0xf6742f3f, 0x6f9d053c, 0x838c5d4, + 0xed72268d, 0xb02d644b, 0xda36c530, 0xe6da79c1, 0x4ac7bc1f, 0xd0b49fcd, 0xf5864700, 0x1852a83f, + 0x57ffd3ec, 0xdcb2b00b, 0x12e24ff8, 0x6bbe36d5, 0xa36d4309, 0xb82d904d, 0x4571e874, 0x6a0c8b19, + 0x31c42b8, 0x8e032cad, 0x2998d7ac, 0x2902c613, 0xcfe7d4b5, 0xec838bcc, 0x749cc735, 0x5f85adb7, + 0x56e18478, 0x5a686945, 0x29b1b84f, 0x310333ff, 0x2596cbb7, 0x9841e6e6, 0x5603bb1a, 0x3491b2f2, + 0x66f76c2c, 0x396b62a4, 0xd365bab3, 0xaa11f81c, 0x5980dcbe, 0xe57bf587, 0x393eb3e3, 0x988beda, + 0xf5a0f18b, 0xe2b429dc, 0x7ac607, 0x511789d0, 0x22d4bbd4, 0x7c7d7eea, 0xe8f2ea24, 0x6951222, + 0xca47cda, 0xe16ebaf4, 0xca59b589, 0x3629c0f1, 0x7fe24409, 0x991563d1, 0xccf25ea, 0x6f44c09d, + 0xcf4e861d, 0x251037f7, 0x19fb128f, 0x10ede0fb, 0x75f5e2c8, 0x96c033b1, 0x6c15fb0d, 0x55f070d, + 0x97473e69, 0x7c52af2c, 0x1bad8378, 0x22f8239, 0x2adb476f, 0x9991e1b0, 0x3a99b855, 0x511144a0, + 0xf71f1ccc, 0xb7c04555, 0x16393641, 0x915f38d4, 0xb1efa412, 0x853a5e4d, 0xd900049d, 0x1c1d4afd, + 0xc7e0eb8f, 0x7bc0c4cd, 0xd0fdc93a, 0x1e6f598a, 0x30597ec2, 0xb8268823, 0x7696017d, 0x75b15373, + 0xcbc71630, 0x448b908d, 0x967c6efa, 0x64f10d3b, 0x28070819, 0x7006bf79, 0xe38b5bc4, 0x53135b15, + 0xc822ebfe, 0xfa6a4387, 0x78547fdb, 0xf7cbb466, 0xdf312472, 0x1fcb8f55, 0x234d85e9, 0x1c90d397, + 0x7d28174c, 0x4252424d, 0xa0deef76, 0x513d9015, 0x9e278cb9, 0xd2b9562d, 0x4686eccd, 0x1f5e6757, + 0xe0296477, 0xc4b2004a, 0xd864701, 0x198fc6b2, 0xfa32eaaa, 0x2de92355, 0x9e8b795d, 0x320988a3, + 0x7cfadf6c, 0xeeebb383, 0x2961513b, 0xe1a03917, 0x6b7b5664, 0xddade06b, 0x1499d7d1, 0x11f54017, + 0xa4944b6e, 0x8cbda81c, 0x9ae688e, 0xee53e970, 0xeb4b82a2, 0xfd2c6901, 0xe0251682, 0x418b827f, + 0x5362b889, 0xa871e1a3, 0x8636f528, 0xe84188a1, 0x135280a6, 0x703d3b01, 0xc8017653, 0x7e80126f, + 0xf7bf47e8, 0x5406ef3, 0x64ad414c, 0x9068b4a6, 0x91742806, 0x796f8362, 0x28f9076f, 0x6666a33b, + 0xef3cb304, 0x45a95ff8, 0x20db136, 0xb099591e, 0x635117c1, 0x7d4c8948, 0x6cf324c0, 0x1d5f21c4, + 0x4dfb39b6, 0x4dce57b0, 0xcdfe606a, 0xce186eaa, 0xd7f5a0a4, 0x4a36216, 0xcf2bed0a, 0x606d9cb7, + 0x609415c1, 0x1fdf7aab, 0x29751f15, 0xef765635, 0x863e99b9, 0xe1ba0537, 0xd007904a, 0x42626609, + 0xe138f8c9, 0xb95461b0, 0x482ea7f9, 0x4ed462a0, 0x82f4945f, 0x3d73cbe2, 0x9c77e621, 0x7086d6c3, + 0xd5587862, 0x5695cad1, 0x7f3a3802, 0xbcf3cca3, 0x13c7761a, 0x4807728b, 0xcf71c977, 0x4f571bfc, + 0x28fff766, 0x47ccc22f, 0x4c6285db, 0x6aab7f47, 0xdab82575, 0xdebec4d6, 0xe0e160c7, 0x4e73bd13, + 0x11bfc2fd, 0x375703cf, 0x5600c4e1, 0xf54e59b8, 0x91e70a09, 0xd2fe0424, 0xfccd8698, 0x27795476, + 0x42cd2c6a, 0x72a812e1, 0x4f87d03c, 0x22da245f, 0x5b02b0b2, 0xc360111b, 0xdccf62c9, 0x6d7045b6, + 0x59c595c1, 0x688f7839, 0xd9b8602b, 0x7e3d2ff6, 0xc6c8c5b4, 0x274d8dd7, 0x73e6237b, 0x445f44b5, + 0x6faa2636, 0x9f77cce4, 0xec96e963, 0x2c005e12, 0xa3825a68, 0x53f4e5c5, 0xba5dfcbf, 0x5f620162, + 0xb5ff6500, 0x322bc891, 0x856edb4, 0xb50fbc29, 0xfad9aa95, 0x37aa9031, 0x37d572e1, 0x60de407e, + 0x835fd1e5, 0x8c560530, 0xb80df327, 0xa8d3367b, 0x4f469943, 0x3aae2c3, 0xf68559d1, 0x42c8c4c1, };
M
tinycrypt/pctablegen.c
→
tinycrypt/pctablegen.c
@@ -5,14 +5,14 @@
int main (int argc, const char **argv) { - uint8_t lut[61440]; + uint32_t lut[15360]; tct_ed25519_pctable_gen (lut); printf ("#include <stdint.h>\n"); - printf ("const static uint8_t PRECOMPUTE_TABLE[61440] = {\n "); - for (unsigned int i = 0; i < 61440; ++i) + printf ("const static uint32_t PRECOMPUTE_TABLE[15360] = {\n "); + for (unsigned int i = 0; i < 15360; ++i) { - printf ("0x%02x, ", lut[i]); - if (i % 16 == 15) + printf ("0x%x, ", lut[i]); + if (i % 8 == 7) { printf ("\n "); }