mirror of
https://github.com/henrydcase/pqc.git
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263 lines
8.5 KiB
C
263 lines
8.5 KiB
C
#include "gf2x_arith.h"
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#include <string.h> // memset(...)
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void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const DIGIT B[], int nr) {
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for (int i = 0; i < nr; i++) {
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Res[i] = A[i] ^ B[i];
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}
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}
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/* copies len digits from a to r if b == 1 */
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void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c) {
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size_t i;
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DIGIT mask = -(DIGIT)c;
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for (i = 0; i < len; i++) {
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r[i] ^= mask & (a[i] ^ r[i]);
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}
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}
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/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */
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void PQCLEAN_LEDAKEMLT52_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount) {
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if ( amount == 0 ) {
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return;
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}
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unsigned int j;
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DIGIT mask;
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mask = ((DIGIT)0x01 << amount) - 1;
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for (j = length - 1; j > 0 ; j--) {
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in[j] >>= amount;
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in[j] |= (in[j - 1] & mask) << (DIGIT_SIZE_b - amount);
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}
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in[j] >>= amount;
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}
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/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */
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void PQCLEAN_LEDAKEMLT52_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsigned int amount) {
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if ( amount == 0 ) {
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return;
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}
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int j;
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DIGIT mask;
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mask = ~(((DIGIT)0x01 << (DIGIT_SIZE_b - amount)) - 1);
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for (j = 0 ; j < length - 1 ; j++) {
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in[j] <<= amount;
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in[j] |= (in[j + 1] & mask) >> (DIGIT_SIZE_b - amount);
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}
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in[j] <<= amount;
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}
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static void gf2x_mul_comb(int nr, DIGIT Res[],
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int na, const DIGIT A[],
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int nb, const DIGIT B[]) {
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int i, j, k;
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DIGIT u, h;
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memset(Res, 0x00, nr * sizeof(DIGIT));
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for (k = DIGIT_SIZE_b - 1; k > 0; k--) {
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for (i = na - 1; i >= 0; i--) {
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if ( A[i] & (((DIGIT)0x1) << k) ) {
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for (j = nb - 1; j >= 0; j--) {
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Res[i + j + 1] ^= B[j];
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}
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}
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}
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u = Res[na + nb - 1];
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Res[na + nb - 1] = u << 0x1;
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for (j = 1; j < na + nb; ++j) {
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h = u >> (DIGIT_SIZE_b - 1);
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u = Res[na + nb - 1 - j];
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Res[na + nb - 1 - j] = h ^ (u << 0x1);
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}
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}
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for (i = na - 1; i >= 0; i--) {
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if ( A[i] & ((DIGIT)0x1) ) {
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for (j = nb - 1; j >= 0; j--) {
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Res[i + j + 1] ^= B[j];
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}
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}
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}
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}
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static void gf2x_cpy(DIGIT *R, const DIGIT *A, size_t len) {
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for (size_t i = 0; i < len; i++) {
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R[i] = A[i];
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}
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}
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/* Accumulate */
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#define gf2x_add(R, A, B, n) PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(R, A, B, n)
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#define gf2x_acc(R, B, n) PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(R, R, B, n)
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/* allows the operands to be of different size
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* first operand must be the bigger one.
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* aligns last array elements */
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static inline void gf2x_add_asymm(DIGIT *R,
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int na, const DIGIT *A,
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int nb, const DIGIT *B) {
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size_t delta = na - nb;
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gf2x_cpy(R, A, delta);
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PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(R + delta, A + delta, B, nb);;
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}
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/* aligns first array elements */
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static inline void gf2x_add_asymm2(DIGIT *R,
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int na, const DIGIT *A,
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int nb, const DIGIT *B) {
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size_t delta = na - nb;
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PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(R, A, B, nb);
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gf2x_cpy(R + nb, A + nb, delta);
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}
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/* Karatsuba with lowered space complexity
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* T(n) = 3 * ceil(n/2) + T(ceil(n / 2)) */
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static void gf2x_mul_kar(DIGIT *R,
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const DIGIT *A,
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const DIGIT *B,
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size_t n,
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DIGIT *stack) {
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if (n < MIN_KAR_DIGITS) {
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gf2x_mul_comb(2 * n, R, n, A, n, B);
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return;
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}
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size_t l = (n + 1) / 2; // limb size = ceil(n / 2)
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size_t d = n & 1;
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const DIGIT *a1 = A; // length n - d
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const DIGIT *a0 = A + l - d; // length n
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const DIGIT *b1 = B;
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const DIGIT *b0 = B + l - d;
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DIGIT *aa = stack;
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DIGIT *bb = aa + l;
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DIGIT *cc = bb + l;
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stack = cc + l; // 3l space requirement at each level
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DIGIT *c3 = R + l - 2 * d;
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DIGIT *c2 = c3 + l;
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DIGIT *c1 = c2 + l;
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gf2x_mul_kar(c2, a0, b0, l, stack); // L in low part of R
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gf2x_mul_kar(R, a1, b1, l - d, stack); // H in higher part of R
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gf2x_add_asymm(aa, l, a0, l - d, a1); // AH + AL
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gf2x_add_asymm(bb, l, b0, l - d, b1); // BH + BL
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gf2x_add(cc, c3, c2, l); // HL + LH in cc
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gf2x_mul_kar(c3, aa, bb, l, stack); // M = (AH + AL) x (BH + BL)
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gf2x_add_asymm(c3, l, c3, l - 2 * d, R); // add HH
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gf2x_acc(c2, c1, l); // add LL
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gf2x_acc(c3, cc, l); // add HL + LH
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gf2x_acc(c2, cc, l); // add HL + LH
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}
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static void gf2x_div_w_plus_one(DIGIT *A, size_t n) {
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size_t i;
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for (i = 0; i < n - 2; i++) {
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A[i + 1] ^= A[i]; // runs n - 2 times
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}
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}
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static void gf2x_shift_left_w(DIGIT *A, size_t n) {
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size_t i;
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for (i = 0; i < n - 1; i++) {
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A[i] = A[i + 1];
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}
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A[i] = 0;
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}
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/* Word-aligned Toom-Cook 3, source:
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* Brent, Richard P., et al. "Faster multiplication in GF (2)[x]."
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* International Algorithmic Number Theory Symposium.
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* Springer, Berlin, Heidelberg, 2008. */
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static void gf2x_mul_tc3w(DIGIT *R,
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const DIGIT *A,
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const DIGIT *B,
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size_t n,
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DIGIT *stack) {
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if (n < MIN_TOOM_DIGITS) {
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gf2x_mul_kar(R, A, B, n, stack);
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return;
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}
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size_t l = (n + 2) / 3; // size of a0, a1, b0, b1
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size_t r = n - 2 * l; // remaining sizes (a2, b2)
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size_t x = 2 * l + 4; // size of c1, c2, c3, c4
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size_t z = r + 2 > l + 1 ? r + 2 : l + 1; // size of c5
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const DIGIT *a0 = A;
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const DIGIT *a1 = A + l;
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const DIGIT *a2 = A + 2 * l;
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const DIGIT *b0 = B;
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const DIGIT *b1 = B + l;
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const DIGIT *b2 = B + 2 * l;
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DIGIT *c0 = R; // c0 and c4 in the result
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DIGIT *c4 = R + 4 * l;
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DIGIT *c1 = stack; // the rest in the stack
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DIGIT *c2 = c1 + x;
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DIGIT *c3 = c2 + x;
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DIGIT *c5 = c3 + x;
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stack = c5 + z; // Worst-case 7l + 14
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// Evaluation
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c0[0] = 0; // c0[z] = a1*W + a2*W^2
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c0[l + 1] = 0;
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gf2x_cpy(c0 + 1, a1, l);
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gf2x_acc(c0 + 2, a2, r);
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c4[0] = 0; // c4[z] = b1*W + b2*W^2
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c4[l + 1] = 0;
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gf2x_cpy(c4 + 1, b1, l);
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gf2x_acc(c4 + 2, b2, r);
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gf2x_cpy(c5, a0, l); // c5[l] = a0 + a1 + a2
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gf2x_acc(c5, a1, l);
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gf2x_acc(c5, a2, r);
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gf2x_cpy(c2, b0, l); // c2[l] = b0 + b1 + b2
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gf2x_acc(c2, b1, l);
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gf2x_acc(c2, b2, r);
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gf2x_mul_tc3w(c1, c2, c5, l, stack); // c1[2l] = c2 * c5
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gf2x_add_asymm2(c5, z, c0, l, c5); // c5[z] += c0, z >= l
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gf2x_add_asymm2(c2, z, c4, l, c2); // c2[z] += c4, idem
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gf2x_acc(c0, a0, l); // c0[l] += a0
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gf2x_acc(c4, b0, l); // c4[l] += b0
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gf2x_mul_tc3w(c3, c2, c5, z, stack); // c3[2z] = c2 * c5
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gf2x_mul_tc3w(c2, c0, c4, z, stack); // c2[2z] = c0 * c4
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gf2x_mul_tc3w(c0, a0, b0, l, stack); // c0[2l] = a0 * b0
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gf2x_mul_tc3w(c4, a2, b2, r, stack); // c4[2r] = a2 * b2
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// Interpolation
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gf2x_acc(c3, c2, 2 * z); // c3[2z] += c2
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gf2x_acc(c2, c0, 2 * l); // c2[2z] += c0
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gf2x_shift_left_w(c2, 2 * z); // c2[2z] = c2/y + c3
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gf2x_acc(c2, c3, 2 * z);
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gf2x_acc(c2, c4, 2 * r); // c2[2z] += c4 + c4**3
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gf2x_acc(c2 + 3, c4, 2 * r);
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gf2x_div_w_plus_one(c2, 2 * z); // c2[2z-1] = c2/(W+1)
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gf2x_acc(c1, c0, 2 * l); // c1[2l] += c0
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gf2x_acc(c3, c1, 2 * l); // c3[2z] += c1
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gf2x_shift_left_w(c3, 2 * z); // c3[2z-2] = c3/(W^2 + W)
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gf2x_div_w_plus_one(c3, 2 * z - 1);
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gf2x_add_asymm2(c1, 2 * z, c2, 2 * l, c1); // c1[2z-1] += c2 + c4
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gf2x_acc(c1, c4, 2 * r); // size c2 >= c1 >= c4
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gf2x_acc(c2, c3, 2 * z - 1); // c2[2z-1] += c3
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// Recombination
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gf2x_cpy(R + 2 * l, c2, 2 * l);
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gf2x_acc(R + l, c1, 2 * z - 1);
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gf2x_acc(R + 3 * l, c3, 2 * z - 1);
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}
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void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n) {
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DIGIT stack[STACK_WORDS];
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gf2x_mul_tc3w(R, A, B, n, stack);
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}
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