mirror of
https://github.com/henrydcase/pqc.git
synced 2024-11-27 01:41:40 +00:00
253 lines
8.2 KiB
C
253 lines
8.2 KiB
C
#include "gf2x_arith.h"
|
|
|
|
#include <string.h> // memset(...)
|
|
|
|
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const DIGIT B[], size_t n) {
|
|
for (size_t i = 0; i < n; i++) {
|
|
Res[i] = A[i] ^ B[i];
|
|
}
|
|
}
|
|
|
|
/* copies len digits from a to r if b == 1 */
|
|
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c) {
|
|
DIGIT mask = (DIGIT)(-c);
|
|
for (size_t i = 0; i < len; i++) {
|
|
r[i] ^= mask & (a[i] ^ r[i]);
|
|
}
|
|
}
|
|
|
|
/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */
|
|
void PQCLEAN_LEDAKEMLT12_LEAKTIME_right_bit_shift_n(size_t length, DIGIT in[], size_t amount) {
|
|
if ( amount == 0 ) {
|
|
return;
|
|
}
|
|
size_t j;
|
|
DIGIT mask;
|
|
mask = ((DIGIT)0x01 << amount) - 1;
|
|
for (j = length - 1; j > 0; j--) {
|
|
in[j] >>= amount;
|
|
in[j] |= (in[j - 1] & mask) << (DIGIT_SIZE_b - amount);
|
|
}
|
|
in[j] >>= amount;
|
|
}
|
|
|
|
/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */
|
|
void PQCLEAN_LEDAKEMLT12_LEAKTIME_left_bit_shift_n(size_t length, DIGIT in[], size_t amount) {
|
|
if ( amount == 0 ) {
|
|
return;
|
|
}
|
|
size_t j;
|
|
DIGIT mask;
|
|
mask = ~(((DIGIT)0x01 << (DIGIT_SIZE_b - amount)) - 1);
|
|
for (j = 0 ; j < length - 1; j++) {
|
|
in[j] <<= amount;
|
|
in[j] |= (in[j + 1] & mask) >> (DIGIT_SIZE_b - amount);
|
|
}
|
|
in[j] <<= amount;
|
|
}
|
|
|
|
|
|
static void gf2x_mul1(DIGIT *R, const DIGIT A, const DIGIT B) {
|
|
DIGIT tmp;
|
|
|
|
R[0] = 0;
|
|
R[1] = (A & 1) * B;
|
|
for (uint8_t i = 1; i < DIGIT_SIZE_b; i++) {
|
|
tmp = ((A >> i) & 1) * B;
|
|
R[1] ^= tmp << i;
|
|
R[0] ^= tmp >> (DIGIT_SIZE_b - i);
|
|
}
|
|
}
|
|
|
|
static void gf2x_mul_n(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n) {
|
|
DIGIT tmp[2];
|
|
|
|
memset(R, 0x00, 2 * n * sizeof(DIGIT));
|
|
for (size_t i = 0; i < n; i++) {
|
|
for (size_t j = 0; j < n; j++) {
|
|
gf2x_mul1(tmp, A[i], B[j]);
|
|
R[i + j] ^= tmp[0];
|
|
R[i + j + 1] ^= tmp[1];
|
|
}
|
|
}
|
|
}
|
|
|
|
static void gf2x_cpy(DIGIT *R, const DIGIT *A, size_t len) {
|
|
for (size_t i = 0; i < len; i++) {
|
|
R[i] = A[i];
|
|
}
|
|
}
|
|
|
|
/* Accumulate */
|
|
#define gf2x_add(R, A, B, n) PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(R, A, B, n)
|
|
#define gf2x_acc(R, B, n) PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(R, R, B, n)
|
|
|
|
/* allows the operands to be of different size
|
|
* first operand must be the bigger one.
|
|
* aligns last array elements */
|
|
static inline void gf2x_add_asymm(DIGIT *R,
|
|
size_t na, const DIGIT *A,
|
|
size_t nb, const DIGIT *B) {
|
|
size_t delta = na - nb;
|
|
gf2x_cpy(R, A, delta);
|
|
gf2x_add(R + delta, A + delta, B, nb);;
|
|
}
|
|
|
|
/* aligns first array elements */
|
|
static inline void gf2x_add_asymm2(DIGIT *R,
|
|
size_t na, const DIGIT *A,
|
|
size_t nb, const DIGIT *B) {
|
|
size_t delta = na - nb;
|
|
gf2x_add(R, A, B, nb);
|
|
gf2x_cpy(R + nb, A + nb, delta);
|
|
}
|
|
|
|
/* Karatsuba with lowered space complexity
|
|
* T(n) = 3 * ceil(n/2) + T(ceil(n / 2)) */
|
|
static void gf2x_mul_kar(DIGIT *R,
|
|
const DIGIT *A,
|
|
const DIGIT *B,
|
|
size_t n,
|
|
DIGIT *stack) {
|
|
|
|
if (n < MIN_KAR_DIGITS) {
|
|
gf2x_mul_n(R, A, B, n);
|
|
return;
|
|
}
|
|
|
|
size_t l = (n + 1) / 2; // limb size = ceil(n / 2)
|
|
size_t d = n & 1;
|
|
|
|
const DIGIT *a1 = A; // length n - d
|
|
const DIGIT *a0 = A + l - d; // length n
|
|
const DIGIT *b1 = B;
|
|
const DIGIT *b0 = B + l - d;
|
|
|
|
DIGIT *aa = stack;
|
|
DIGIT *bb = aa + l;
|
|
DIGIT *cc = bb + l;
|
|
stack = cc + l; // 3l space requirement at each level
|
|
|
|
DIGIT *c3 = R + l - 2 * d;
|
|
DIGIT *c2 = c3 + l;
|
|
DIGIT *c1 = c2 + l;
|
|
|
|
gf2x_mul_kar(c2, a0, b0, l, stack); // L in low part of R
|
|
gf2x_mul_kar(R, a1, b1, l - d, stack); // H in higher part of R
|
|
gf2x_add_asymm(aa, l, a0, l - d, a1); // AH + AL
|
|
gf2x_add_asymm(bb, l, b0, l - d, b1); // BH + BL
|
|
gf2x_add(cc, c3, c2, l); // HL + LH in cc
|
|
gf2x_mul_kar(c3, aa, bb, l, stack); // M = (AH + AL) x (BH + BL)
|
|
gf2x_add_asymm(c3, l, c3, l - 2 * d, R); // add HH
|
|
gf2x_acc(c2, c1, l); // add LL
|
|
gf2x_acc(c3, cc, l); // add HL + LH
|
|
gf2x_acc(c2, cc, l); // add HL + LH
|
|
}
|
|
|
|
static void gf2x_div_w_plus_one(DIGIT *A, size_t n) {
|
|
size_t i;
|
|
for (i = 0; i < n - 2; i++) {
|
|
A[i + 1] ^= A[i]; // runs n - 2 times
|
|
}
|
|
}
|
|
|
|
static void gf2x_shift_left_w(DIGIT *A, size_t n) {
|
|
size_t i;
|
|
for (i = 0; i < n - 1; i++) {
|
|
A[i] = A[i + 1];
|
|
}
|
|
A[i] = 0;
|
|
}
|
|
|
|
/* Word-aligned Toom-Cook 3, source:
|
|
* Brent, Richard P., et al. "Faster multiplication in GF (2)[x]."
|
|
* International Algorithmic Number Theory Symposium.
|
|
* Springer, Berlin, Heidelberg, 2008. */
|
|
static void gf2x_mul_tc3w(DIGIT *R,
|
|
const DIGIT *A,
|
|
const DIGIT *B,
|
|
size_t n,
|
|
DIGIT *stack) {
|
|
|
|
if (n < MIN_TOOM_DIGITS) {
|
|
gf2x_mul_kar(R, A, B, n, stack);
|
|
return;
|
|
}
|
|
|
|
size_t l = (n + 2) / 3; // size of a0, a1, b0, b1
|
|
size_t r = n - 2 * l; // remaining sizes (a2, b2)
|
|
size_t x = 2 * l + 4; // size of c1, c2, c3, c4
|
|
size_t z = r + 2 > l + 1 ? r + 2 : l + 1; // size of c5
|
|
|
|
const DIGIT *a0 = A;
|
|
const DIGIT *a1 = A + l;
|
|
const DIGIT *a2 = A + 2 * l;
|
|
const DIGIT *b0 = B;
|
|
const DIGIT *b1 = B + l;
|
|
const DIGIT *b2 = B + 2 * l;
|
|
|
|
DIGIT *c0 = R; // c0 and c4 in the result
|
|
DIGIT *c4 = R + 4 * l;
|
|
DIGIT *c1 = stack; // the rest in the stack
|
|
DIGIT *c2 = c1 + x;
|
|
DIGIT *c3 = c2 + x;
|
|
DIGIT *c5 = c3 + x;
|
|
stack = c5 + z; // Worst-case 7l + 14
|
|
|
|
// Evaluation
|
|
c0[0] = 0; // c0[z] = a1*W + a2*W^2
|
|
c0[l + 1] = 0;
|
|
gf2x_cpy(c0 + 1, a1, l);
|
|
gf2x_acc(c0 + 2, a2, r);
|
|
|
|
c4[0] = 0; // c4[z] = b1*W + b2*W^2
|
|
c4[l + 1] = 0;
|
|
gf2x_cpy(c4 + 1, b1, l);
|
|
gf2x_acc(c4 + 2, b2, r);
|
|
|
|
gf2x_cpy(c5, a0, l); // c5[l] = a0 + a1 + a2
|
|
gf2x_acc(c5, a1, l);
|
|
gf2x_acc(c5, a2, r);
|
|
|
|
gf2x_cpy(c2, b0, l); // c2[l] = b0 + b1 + b2
|
|
gf2x_acc(c2, b1, l);
|
|
gf2x_acc(c2, b2, r);
|
|
|
|
gf2x_mul_tc3w(c1, c2, c5, l, stack); // c1[2l] = c2 * c5
|
|
gf2x_add_asymm2(c5, z, c0, l, c5); // c5[z] += c0, z >= l
|
|
gf2x_add_asymm2(c2, z, c4, l, c2); // c2[z] += c4, idem
|
|
gf2x_acc(c0, a0, l); // c0[l] += a0
|
|
gf2x_acc(c4, b0, l); // c4[l] += b0
|
|
gf2x_mul_tc3w(c3, c2, c5, z, stack); // c3[2z] = c2 * c5
|
|
gf2x_mul_tc3w(c2, c0, c4, z, stack); // c2[2z] = c0 * c4
|
|
gf2x_mul_tc3w(c0, a0, b0, l, stack); // c0[2l] = a0 * b0
|
|
gf2x_mul_tc3w(c4, a2, b2, r, stack); // c4[2r] = a2 * b2
|
|
|
|
// Interpolation
|
|
gf2x_acc(c3, c2, 2 * z); // c3[2z] += c2
|
|
gf2x_acc(c2, c0, 2 * l); // c2[2z] += c0
|
|
gf2x_shift_left_w(c2, 2 * z); // c2[2z] = c2/y + c3
|
|
gf2x_acc(c2, c3, 2 * z);
|
|
gf2x_acc(c2, c4, 2 * r); // c2[2z] += c4 + c4**3
|
|
gf2x_acc(c2 + 3, c4, 2 * r);
|
|
gf2x_div_w_plus_one(c2, 2 * z); // c2[2z-1] = c2/(W+1)
|
|
gf2x_acc(c1, c0, 2 * l); // c1[2l] += c0
|
|
gf2x_acc(c3, c1, 2 * l); // c3[2z] += c1
|
|
gf2x_shift_left_w(c3, 2 * z); // c3[2z-2] = c3/(W^2 + W)
|
|
gf2x_div_w_plus_one(c3, 2 * z - 1);
|
|
gf2x_add_asymm2(c1, 2 * z, c2, 2 * l, c1); // c1[2z-1] += c2 + c4
|
|
gf2x_acc(c1, c4, 2 * r); // size c2 >= c1 >= c4
|
|
gf2x_acc(c2, c3, 2 * z - 1); // c2[2z-1] += c3
|
|
|
|
// Recombination
|
|
gf2x_cpy(R + 2 * l, c2, 2 * l);
|
|
gf2x_acc(R + l, c1, 2 * z - 1);
|
|
gf2x_acc(R + 3 * l, c3, 2 * z - 1);
|
|
}
|
|
|
|
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n) {
|
|
DIGIT stack[STACK_WORDS];
|
|
gf2x_mul_tc3w(R, A, B, n, stack);
|
|
}
|
|
|