1493 lines
38 KiB
C
1493 lines
38 KiB
C
#include "fixedint.h"
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#include "fe.h"
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#ifndef ED25519_LOAD_BYTES
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#define ED25519_LOAD_BYTES
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/*
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helper functions
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*/
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static uint64_t load_3(const unsigned char *in) {
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uint64_t result;
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result = (uint64_t) in[0];
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result |= ((uint64_t) in[1]) << 8;
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result |= ((uint64_t) in[2]) << 16;
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return result;
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}
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static uint64_t load_4(const unsigned char *in) {
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uint64_t result;
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result = (uint64_t) in[0];
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result |= ((uint64_t) in[1]) << 8;
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result |= ((uint64_t) in[2]) << 16;
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result |= ((uint64_t) in[3]) << 24;
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return result;
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}
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#endif
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/*
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h = 0
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*/
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void fe_0(fe h) {
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h[0] = 0;
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h[1] = 0;
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h[2] = 0;
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h[3] = 0;
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h[4] = 0;
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h[5] = 0;
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h[6] = 0;
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h[7] = 0;
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h[8] = 0;
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h[9] = 0;
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}
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/*
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h = 1
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*/
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void fe_1(fe h) {
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h[0] = 1;
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h[1] = 0;
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h[2] = 0;
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h[3] = 0;
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h[4] = 0;
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h[5] = 0;
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h[6] = 0;
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h[7] = 0;
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h[8] = 0;
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h[9] = 0;
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}
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/*
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h = f + g
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Can overlap h with f or g.
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Preconditions:
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|f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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|g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
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Postconditions:
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|h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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*/
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void fe_add(fe h, const fe f, const fe g) {
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int32_t f0 = f[0];
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int32_t f1 = f[1];
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int32_t f2 = f[2];
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int32_t f3 = f[3];
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int32_t f4 = f[4];
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int32_t f5 = f[5];
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int32_t f6 = f[6];
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int32_t f7 = f[7];
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int32_t f8 = f[8];
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int32_t f9 = f[9];
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int32_t g0 = g[0];
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int32_t g1 = g[1];
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int32_t g2 = g[2];
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int32_t g3 = g[3];
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int32_t g4 = g[4];
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int32_t g5 = g[5];
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int32_t g6 = g[6];
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int32_t g7 = g[7];
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int32_t g8 = g[8];
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int32_t g9 = g[9];
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int32_t h0 = f0 + g0;
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int32_t h1 = f1 + g1;
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int32_t h2 = f2 + g2;
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int32_t h3 = f3 + g3;
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int32_t h4 = f4 + g4;
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int32_t h5 = f5 + g5;
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int32_t h6 = f6 + g6;
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int32_t h7 = f7 + g7;
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int32_t h8 = f8 + g8;
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int32_t h9 = f9 + g9;
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h[0] = h0;
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h[1] = h1;
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h[2] = h2;
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h[3] = h3;
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h[4] = h4;
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h[5] = h5;
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h[6] = h6;
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h[7] = h7;
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h[8] = h8;
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h[9] = h9;
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}
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/*
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Replace (f,g) with (g,g) if b == 1;
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replace (f,g) with (f,g) if b == 0.
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Preconditions: b in {0,1}.
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*/
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void fe_cmov(fe f, const fe g, unsigned int b) {
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int32_t f0 = f[0];
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int32_t f1 = f[1];
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int32_t f2 = f[2];
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int32_t f3 = f[3];
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int32_t f4 = f[4];
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int32_t f5 = f[5];
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int32_t f6 = f[6];
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int32_t f7 = f[7];
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int32_t f8 = f[8];
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int32_t f9 = f[9];
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int32_t g0 = g[0];
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int32_t g1 = g[1];
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int32_t g2 = g[2];
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int32_t g3 = g[3];
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int32_t g4 = g[4];
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int32_t g5 = g[5];
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int32_t g6 = g[6];
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int32_t g7 = g[7];
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int32_t g8 = g[8];
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int32_t g9 = g[9];
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int32_t x0 = f0 ^ g0;
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int32_t x1 = f1 ^ g1;
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int32_t x2 = f2 ^ g2;
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int32_t x3 = f3 ^ g3;
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int32_t x4 = f4 ^ g4;
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int32_t x5 = f5 ^ g5;
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int32_t x6 = f6 ^ g6;
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int32_t x7 = f7 ^ g7;
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int32_t x8 = f8 ^ g8;
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int32_t x9 = f9 ^ g9;
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b = (unsigned int) (- (int) b); /* silence warning */
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x0 &= b;
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x1 &= b;
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x2 &= b;
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x3 &= b;
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x4 &= b;
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x5 &= b;
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x6 &= b;
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x7 &= b;
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x8 &= b;
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x9 &= b;
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f[0] = f0 ^ x0;
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f[1] = f1 ^ x1;
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f[2] = f2 ^ x2;
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f[3] = f3 ^ x3;
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f[4] = f4 ^ x4;
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f[5] = f5 ^ x5;
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f[6] = f6 ^ x6;
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f[7] = f7 ^ x7;
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f[8] = f8 ^ x8;
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f[9] = f9 ^ x9;
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}
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/*
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Replace (f,g) with (g,f) if b == 1;
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replace (f,g) with (f,g) if b == 0.
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Preconditions: b in {0,1}.
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*/
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void fe_cswap(fe f,fe g,unsigned int b) {
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int32_t f0 = f[0];
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int32_t f1 = f[1];
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int32_t f2 = f[2];
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int32_t f3 = f[3];
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int32_t f4 = f[4];
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int32_t f5 = f[5];
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int32_t f6 = f[6];
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int32_t f7 = f[7];
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int32_t f8 = f[8];
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int32_t f9 = f[9];
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int32_t g0 = g[0];
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int32_t g1 = g[1];
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int32_t g2 = g[2];
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int32_t g3 = g[3];
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int32_t g4 = g[4];
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int32_t g5 = g[5];
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int32_t g6 = g[6];
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int32_t g7 = g[7];
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int32_t g8 = g[8];
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int32_t g9 = g[9];
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int32_t x0 = f0 ^ g0;
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int32_t x1 = f1 ^ g1;
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int32_t x2 = f2 ^ g2;
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int32_t x3 = f3 ^ g3;
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int32_t x4 = f4 ^ g4;
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int32_t x5 = f5 ^ g5;
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int32_t x6 = f6 ^ g6;
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int32_t x7 = f7 ^ g7;
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int32_t x8 = f8 ^ g8;
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int32_t x9 = f9 ^ g9;
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b = -b;
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x0 &= b;
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x1 &= b;
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x2 &= b;
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x3 &= b;
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x4 &= b;
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x5 &= b;
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x6 &= b;
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x7 &= b;
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x8 &= b;
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x9 &= b;
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f[0] = f0 ^ x0;
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f[1] = f1 ^ x1;
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f[2] = f2 ^ x2;
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f[3] = f3 ^ x3;
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f[4] = f4 ^ x4;
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f[5] = f5 ^ x5;
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f[6] = f6 ^ x6;
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f[7] = f7 ^ x7;
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f[8] = f8 ^ x8;
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f[9] = f9 ^ x9;
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g[0] = g0 ^ x0;
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g[1] = g1 ^ x1;
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g[2] = g2 ^ x2;
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g[3] = g3 ^ x3;
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g[4] = g4 ^ x4;
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g[5] = g5 ^ x5;
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g[6] = g6 ^ x6;
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g[7] = g7 ^ x7;
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g[8] = g8 ^ x8;
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g[9] = g9 ^ x9;
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}
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/*
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h = f
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*/
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void fe_copy(fe h, const fe f) {
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int32_t f0 = f[0];
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int32_t f1 = f[1];
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int32_t f2 = f[2];
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int32_t f3 = f[3];
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int32_t f4 = f[4];
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int32_t f5 = f[5];
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int32_t f6 = f[6];
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int32_t f7 = f[7];
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int32_t f8 = f[8];
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int32_t f9 = f[9];
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h[0] = f0;
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h[1] = f1;
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h[2] = f2;
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h[3] = f3;
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h[4] = f4;
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h[5] = f5;
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h[6] = f6;
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h[7] = f7;
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h[8] = f8;
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h[9] = f9;
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}
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/*
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Ignores top bit of h.
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*/
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void fe_frombytes(fe h, const unsigned char *s) {
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int64_t h0 = load_4(s);
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int64_t h1 = load_3(s + 4) << 6;
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int64_t h2 = load_3(s + 7) << 5;
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int64_t h3 = load_3(s + 10) << 3;
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int64_t h4 = load_3(s + 13) << 2;
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int64_t h5 = load_4(s + 16);
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int64_t h6 = load_3(s + 20) << 7;
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int64_t h7 = load_3(s + 23) << 5;
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int64_t h8 = load_3(s + 26) << 4;
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int64_t h9 = (load_3(s + 29) & 8388607) << 2;
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int64_t carry0;
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int64_t carry1;
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int64_t carry2;
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int64_t carry3;
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int64_t carry4;
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int64_t carry5;
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int64_t carry6;
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int64_t carry7;
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int64_t carry8;
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int64_t carry9;
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carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
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h0 += carry9 * 19;
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h9 -= carry9 << 25;
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carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
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h2 += carry1;
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h1 -= carry1 << 25;
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carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
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h4 += carry3;
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h3 -= carry3 << 25;
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carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
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h6 += carry5;
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h5 -= carry5 << 25;
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carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
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h8 += carry7;
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h7 -= carry7 << 25;
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carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
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h1 += carry0;
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h0 -= carry0 << 26;
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carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
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h3 += carry2;
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h2 -= carry2 << 26;
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carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
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h5 += carry4;
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h4 -= carry4 << 26;
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carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
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h7 += carry6;
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h6 -= carry6 << 26;
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carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
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h9 += carry8;
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h8 -= carry8 << 26;
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h[0] = (int32_t) h0;
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h[1] = (int32_t) h1;
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h[2] = (int32_t) h2;
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h[3] = (int32_t) h3;
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h[4] = (int32_t) h4;
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h[5] = (int32_t) h5;
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h[6] = (int32_t) h6;
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h[7] = (int32_t) h7;
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h[8] = (int32_t) h8;
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h[9] = (int32_t) h9;
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}
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void fe_invert(fe out, const fe z) {
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fe t0;
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fe t1;
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fe t2;
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fe t3;
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int i;
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fe_sq(t0, z);
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for (i = 1; i < 1; ++i) {
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fe_sq(t0, t0);
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}
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fe_sq(t1, t0);
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for (i = 1; i < 2; ++i) {
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fe_sq(t1, t1);
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}
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fe_mul(t1, z, t1);
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fe_mul(t0, t0, t1);
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fe_sq(t2, t0);
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for (i = 1; i < 1; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t1, t1, t2);
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fe_sq(t2, t1);
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for (i = 1; i < 5; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t1, t2, t1);
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fe_sq(t2, t1);
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for (i = 1; i < 10; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t2, t2, t1);
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fe_sq(t3, t2);
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for (i = 1; i < 20; ++i) {
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fe_sq(t3, t3);
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}
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fe_mul(t2, t3, t2);
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fe_sq(t2, t2);
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for (i = 1; i < 10; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t1, t2, t1);
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fe_sq(t2, t1);
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for (i = 1; i < 50; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t2, t2, t1);
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fe_sq(t3, t2);
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for (i = 1; i < 100; ++i) {
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fe_sq(t3, t3);
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}
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fe_mul(t2, t3, t2);
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fe_sq(t2, t2);
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for (i = 1; i < 50; ++i) {
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fe_sq(t2, t2);
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}
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fe_mul(t1, t2, t1);
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fe_sq(t1, t1);
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for (i = 1; i < 5; ++i) {
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fe_sq(t1, t1);
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}
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fe_mul(out, t1, t0);
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}
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/*
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return 1 if f is in {1,3,5,...,q-2}
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return 0 if f is in {0,2,4,...,q-1}
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Preconditions:
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|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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*/
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int fe_isnegative(const fe f) {
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unsigned char s[32];
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fe_tobytes(s, f);
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return s[0] & 1;
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}
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/*
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return 1 if f == 0
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return 0 if f != 0
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Preconditions:
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|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
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*/
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int fe_isnonzero(const fe f) {
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unsigned char s[32];
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unsigned char r;
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fe_tobytes(s, f);
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r = s[0];
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#define F(i) r |= s[i]
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F(1);
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F(2);
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F(3);
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F(4);
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F(5);
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F(6);
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F(7);
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F(8);
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F(9);
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F(10);
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F(11);
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F(12);
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F(13);
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F(14);
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F(15);
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F(16);
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F(17);
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F(18);
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F(19);
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F(20);
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F(21);
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F(22);
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F(23);
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F(24);
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F(25);
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F(26);
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F(27);
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F(28);
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F(29);
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F(30);
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F(31);
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#undef F
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return r != 0;
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}
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/*
|
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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;
|
|
|
|
carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
|
|
carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
|
|
h2 += carry1;
|
|
h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
|
|
h6 += carry5;
|
|
h5 -= carry5 << 25;
|
|
|
|
carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
|
|
h3 += carry2;
|
|
h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
|
|
h7 += carry6;
|
|
h6 -= carry6 << 26;
|
|
|
|
carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
|
|
h4 += carry3;
|
|
h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
|
|
h8 += carry7;
|
|
h7 -= carry7 << 25;
|
|
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
|
|
h9 += carry8;
|
|
h8 -= carry8 << 26;
|
|
|
|
carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
|
|
h0 += carry9 * 19;
|
|
h9 -= carry9 << 25;
|
|
|
|
carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 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 = f * 121666
|
|
Can overlap h with f.
|
|
|
|
Preconditions:
|
|
|f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
|
|
|
|
Postconditions:
|
|
|h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
|
|
*/
|
|
|
|
void fe_mul121666(fe h, 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];
|
|
int64_t h0 = f0 * (int64_t) 121666;
|
|
int64_t h1 = f1 * (int64_t) 121666;
|
|
int64_t h2 = f2 * (int64_t) 121666;
|
|
int64_t h3 = f3 * (int64_t) 121666;
|
|
int64_t h4 = f4 * (int64_t) 121666;
|
|
int64_t h5 = f5 * (int64_t) 121666;
|
|
int64_t h6 = f6 * (int64_t) 121666;
|
|
int64_t h7 = f7 * (int64_t) 121666;
|
|
int64_t h8 = f8 * (int64_t) 121666;
|
|
int64_t h9 = f9 * (int64_t) 121666;
|
|
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) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
|
|
carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
|
|
carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
|
|
carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
|
|
carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
|
|
|
|
carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
|
|
carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
|
|
carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
|
|
carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
|
|
carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
|
|
|
|
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.
|
|
*/
|
|
|
|
void fe_neg(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 h0 = -f0;
|
|
int32_t h1 = -f1;
|
|
int32_t h2 = -f2;
|
|
int32_t h3 = -f3;
|
|
int32_t h4 = -f4;
|
|
int32_t h5 = -f5;
|
|
int32_t h6 = -f6;
|
|
int32_t h7 = -f7;
|
|
int32_t h8 = -f8;
|
|
int32_t h9 = -f9;
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
void fe_pow22523(fe out, const fe z) {
|
|
fe t0;
|
|
fe t1;
|
|
fe t2;
|
|
int i;
|
|
fe_sq(t0, z);
|
|
|
|
for (i = 1; i < 1; ++i) {
|
|
fe_sq(t0, t0);
|
|
}
|
|
|
|
fe_sq(t1, t0);
|
|
|
|
for (i = 1; i < 2; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t1, z, t1);
|
|
fe_mul(t0, t0, t1);
|
|
fe_sq(t0, t0);
|
|
|
|
for (i = 1; i < 1; ++i) {
|
|
fe_sq(t0, t0);
|
|
}
|
|
|
|
fe_mul(t0, t1, t0);
|
|
fe_sq(t1, t0);
|
|
|
|
for (i = 1; i < 5; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t0, t1, t0);
|
|
fe_sq(t1, t0);
|
|
|
|
for (i = 1; i < 10; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t1, t1, t0);
|
|
fe_sq(t2, t1);
|
|
|
|
for (i = 1; i < 20; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
|
|
fe_mul(t1, t2, t1);
|
|
fe_sq(t1, t1);
|
|
|
|
for (i = 1; i < 10; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t0, t1, t0);
|
|
fe_sq(t1, t0);
|
|
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t1, t1, t0);
|
|
fe_sq(t2, t1);
|
|
|
|
for (i = 1; i < 100; ++i) {
|
|
fe_sq(t2, t2);
|
|
}
|
|
|
|
fe_mul(t1, t2, t1);
|
|
fe_sq(t1, t1);
|
|
|
|
for (i = 1; i < 50; ++i) {
|
|
fe_sq(t1, t1);
|
|
}
|
|
|
|
fe_mul(t0, t1, t0);
|
|
fe_sq(t0, t0);
|
|
|
|
for (i = 1; i < 2; ++i) {
|
|
fe_sq(t0, t0);
|
|
}
|
|
|
|
fe_mul(out, t0, z);
|
|
return;
|
|
}
|
|
|
|
|
|
/*
|
|
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.
|
|
*/
|
|
|
|
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) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
|
|
h2 += carry1;
|
|
h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
|
|
h6 += carry5;
|
|
h5 -= carry5 << 25;
|
|
carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
|
|
h3 += carry2;
|
|
h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
|
|
h7 += carry6;
|
|
h6 -= carry6 << 26;
|
|
carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
|
|
h4 += carry3;
|
|
h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
|
|
h8 += carry7;
|
|
h7 -= carry7 << 25;
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
|
|
h9 += carry8;
|
|
h8 -= carry8 << 26;
|
|
carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
|
|
h0 += carry9 * 19;
|
|
h9 -= carry9 << 25;
|
|
carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 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.
|
|
*/
|
|
|
|
/*
|
|
See fe_mul.c for discussion of implementation strategy.
|
|
*/
|
|
|
|
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) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 26;
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry1 = (h1 + (int64_t) (1 << 24)) >> 25;
|
|
h2 += carry1;
|
|
h1 -= carry1 << 25;
|
|
carry5 = (h5 + (int64_t) (1 << 24)) >> 25;
|
|
h6 += carry5;
|
|
h5 -= carry5 << 25;
|
|
carry2 = (h2 + (int64_t) (1 << 25)) >> 26;
|
|
h3 += carry2;
|
|
h2 -= carry2 << 26;
|
|
carry6 = (h6 + (int64_t) (1 << 25)) >> 26;
|
|
h7 += carry6;
|
|
h6 -= carry6 << 26;
|
|
carry3 = (h3 + (int64_t) (1 << 24)) >> 25;
|
|
h4 += carry3;
|
|
h3 -= carry3 << 25;
|
|
carry7 = (h7 + (int64_t) (1 << 24)) >> 25;
|
|
h8 += carry7;
|
|
h7 -= carry7 << 25;
|
|
carry4 = (h4 + (int64_t) (1 << 25)) >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry8 = (h8 + (int64_t) (1 << 25)) >> 26;
|
|
h9 += carry8;
|
|
h8 -= carry8 << 26;
|
|
carry9 = (h9 + (int64_t) (1 << 24)) >> 25;
|
|
h0 += carry9 * 19;
|
|
h9 -= carry9 << 25;
|
|
carry0 = (h0 + (int64_t) (1 << 25)) >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 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 = 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 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 h0 = f0 - g0;
|
|
int32_t h1 = f1 - g1;
|
|
int32_t h2 = f2 - g2;
|
|
int32_t h3 = f3 - g3;
|
|
int32_t h4 = f4 - g4;
|
|
int32_t h5 = f5 - g5;
|
|
int32_t h6 = f6 - g6;
|
|
int32_t h7 = f7 - g7;
|
|
int32_t h8 = f8 - g8;
|
|
int32_t h9 = f9 - g9;
|
|
|
|
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;
|
|
}
|
|
|
|
|
|
|
|
/*
|
|
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_tobytes(unsigned char *s, const fe h) {
|
|
int32_t h0 = h[0];
|
|
int32_t h1 = h[1];
|
|
int32_t h2 = h[2];
|
|
int32_t h3 = h[3];
|
|
int32_t h4 = h[4];
|
|
int32_t h5 = h[5];
|
|
int32_t h6 = h[6];
|
|
int32_t h7 = h[7];
|
|
int32_t h8 = h[8];
|
|
int32_t h9 = h[9];
|
|
int32_t q;
|
|
int32_t carry0;
|
|
int32_t carry1;
|
|
int32_t carry2;
|
|
int32_t carry3;
|
|
int32_t carry4;
|
|
int32_t carry5;
|
|
int32_t carry6;
|
|
int32_t carry7;
|
|
int32_t carry8;
|
|
int32_t carry9;
|
|
q = (19 * h9 + (((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 = h0 >> 26;
|
|
h1 += carry0;
|
|
h0 -= carry0 << 26;
|
|
carry1 = h1 >> 25;
|
|
h2 += carry1;
|
|
h1 -= carry1 << 25;
|
|
carry2 = h2 >> 26;
|
|
h3 += carry2;
|
|
h2 -= carry2 << 26;
|
|
carry3 = h3 >> 25;
|
|
h4 += carry3;
|
|
h3 -= carry3 << 25;
|
|
carry4 = h4 >> 26;
|
|
h5 += carry4;
|
|
h4 -= carry4 << 26;
|
|
carry5 = h5 >> 25;
|
|
h6 += carry5;
|
|
h5 -= carry5 << 25;
|
|
carry6 = h6 >> 26;
|
|
h7 += carry6;
|
|
h6 -= carry6 << 26;
|
|
carry7 = h7 >> 25;
|
|
h8 += carry7;
|
|
h7 -= carry7 << 25;
|
|
carry8 = h8 >> 26;
|
|
h9 += carry8;
|
|
h8 -= carry8 << 26;
|
|
carry9 = h9 >> 25;
|
|
h9 -= carry9 << 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] = (unsigned char) (h0 >> 0);
|
|
s[1] = (unsigned char) (h0 >> 8);
|
|
s[2] = (unsigned char) (h0 >> 16);
|
|
s[3] = (unsigned char) ((h0 >> 24) | (h1 << 2));
|
|
s[4] = (unsigned char) (h1 >> 6);
|
|
s[5] = (unsigned char) (h1 >> 14);
|
|
s[6] = (unsigned char) ((h1 >> 22) | (h2 << 3));
|
|
s[7] = (unsigned char) (h2 >> 5);
|
|
s[8] = (unsigned char) (h2 >> 13);
|
|
s[9] = (unsigned char) ((h2 >> 21) | (h3 << 5));
|
|
s[10] = (unsigned char) (h3 >> 3);
|
|
s[11] = (unsigned char) (h3 >> 11);
|
|
s[12] = (unsigned char) ((h3 >> 19) | (h4 << 6));
|
|
s[13] = (unsigned char) (h4 >> 2);
|
|
s[14] = (unsigned char) (h4 >> 10);
|
|
s[15] = (unsigned char) (h4 >> 18);
|
|
s[16] = (unsigned char) (h5 >> 0);
|
|
s[17] = (unsigned char) (h5 >> 8);
|
|
s[18] = (unsigned char) (h5 >> 16);
|
|
s[19] = (unsigned char) ((h5 >> 24) | (h6 << 1));
|
|
s[20] = (unsigned char) (h6 >> 7);
|
|
s[21] = (unsigned char) (h6 >> 15);
|
|
s[22] = (unsigned char) ((h6 >> 23) | (h7 << 3));
|
|
s[23] = (unsigned char) (h7 >> 5);
|
|
s[24] = (unsigned char) (h7 >> 13);
|
|
s[25] = (unsigned char) ((h7 >> 21) | (h8 << 4));
|
|
s[26] = (unsigned char) (h8 >> 4);
|
|
s[27] = (unsigned char) (h8 >> 12);
|
|
s[28] = (unsigned char) ((h8 >> 20) | (h9 << 6));
|
|
s[29] = (unsigned char) (h9 >> 2);
|
|
s[30] = (unsigned char) (h9 >> 10);
|
|
s[31] = (unsigned char) (h9 >> 18);
|
|
}
|