@@ -8,6 +8,15 @@ void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const D | |||
} | |||
} | |||
/* 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) { | |||
size_t i; | |||
DIGIT mask = -(DIGIT)c; | |||
for (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(int length, DIGIT in[], unsigned int amount) { | |||
if ( amount == 0 ) { | |||
@@ -38,9 +47,10 @@ void PQCLEAN_LEDAKEMLT12_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsig | |||
in[j] <<= amount; | |||
} | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
static void gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
int i, j, k; | |||
DIGIT u, h; | |||
@@ -71,3 +81,182 @@ void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
} | |||
} | |||
} | |||
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, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
gf2x_cpy(R, A, delta); | |||
PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(R + delta, A + delta, B, nb);; | |||
} | |||
/* aligns first array elements */ | |||
static inline void gf2x_add_asymm2(DIGIT *R, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
PQCLEAN_LEDAKEMLT12_LEAKTIME_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_comb(2 * n, R, n, A, n, B); | |||
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); | |||
} | |||
@@ -48,11 +48,16 @@ typedef uint64_t DIGIT; | |||
#define DIGIT_SIZE_b (DIGIT_SIZE_B << 3) | |||
#define POSITION_T uint32_t | |||
#define GF2X_MUL PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul_comb | |||
#define MIN_KAR_DIGITS 10 | |||
#define MIN_TOOM_DIGITS 42 | |||
#define STACK_KAR_ONLY 2433 | |||
#define STACK_WORDS 2892 | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const DIGIT B[], int nr); | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c); | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void GF2X_MUL(int nr, DIGIT Res[], int na, const DIGIT A[], int nb, const DIGIT B[]); | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n); | |||
#endif |
@@ -259,9 +259,7 @@ int PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) | |||
void PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mod_mul(DIGIT Res[], const DIGIT A[], const DIGIT B[]) { | |||
DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT]; | |||
GF2X_MUL(2 * NUM_DIGITS_GF2X_ELEMENT, aux, | |||
NUM_DIGITS_GF2X_ELEMENT, A, | |||
NUM_DIGITS_GF2X_ELEMENT, B); | |||
PQCLEAN_LEDAKEMLT12_LEAKTIME_gf2x_mul(aux, A, B, NUM_DIGITS_GF2X_ELEMENT); | |||
gf2x_mod(Res, aux); | |||
} | |||
@@ -8,6 +8,15 @@ void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const D | |||
} | |||
} | |||
/* copies len digits from a to r if b == 1 */ | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c) { | |||
size_t i; | |||
DIGIT mask = -(DIGIT)c; | |||
for (i = 0; i < len; i++) { | |||
r[i] ^= mask & (a[i] ^ r[i]); | |||
} | |||
} | |||
/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */ | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount) { | |||
if ( amount == 0 ) { | |||
@@ -38,9 +47,10 @@ void PQCLEAN_LEDAKEMLT32_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsig | |||
in[j] <<= amount; | |||
} | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
static void gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
int i, j, k; | |||
DIGIT u, h; | |||
@@ -71,3 +81,182 @@ void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
} | |||
} | |||
} | |||
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_LEDAKEMLT32_LEAKTIME_gf2x_add(R, A, B, n) | |||
#define gf2x_acc(R, B, n) PQCLEAN_LEDAKEMLT32_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, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
gf2x_cpy(R, A, delta); | |||
PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_add(R + delta, A + delta, B, nb);; | |||
} | |||
/* aligns first array elements */ | |||
static inline void gf2x_add_asymm2(DIGIT *R, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
PQCLEAN_LEDAKEMLT32_LEAKTIME_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_comb(2 * n, R, n, A, n, B); | |||
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_LEDAKEMLT32_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); | |||
} | |||
@@ -48,11 +48,16 @@ typedef uint64_t DIGIT; | |||
#define DIGIT_SIZE_b (DIGIT_SIZE_B << 3) | |||
#define POSITION_T uint32_t | |||
#define GF2X_MUL PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mul_comb | |||
#define MIN_KAR_DIGITS 10 | |||
#define MIN_TOOM_DIGITS 42 | |||
#define STACK_KAR_ONLY 4497 | |||
#define STACK_WORDS 5336 | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const DIGIT B[], int nr); | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c); | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void GF2X_MUL(int nr, DIGIT Res[], int na, const DIGIT A[], int nb, const DIGIT B[]); | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mul(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n); | |||
#endif |
@@ -257,9 +257,7 @@ int PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) | |||
void PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mod_mul(DIGIT Res[], const DIGIT A[], const DIGIT B[]) { | |||
DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT]; | |||
GF2X_MUL(2 * NUM_DIGITS_GF2X_ELEMENT, aux, | |||
NUM_DIGITS_GF2X_ELEMENT, A, | |||
NUM_DIGITS_GF2X_ELEMENT, B); | |||
PQCLEAN_LEDAKEMLT32_LEAKTIME_gf2x_mul(aux, A, B, NUM_DIGITS_GF2X_ELEMENT); | |||
gf2x_mod(Res, aux); | |||
} | |||
@@ -8,6 +8,15 @@ void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const D | |||
} | |||
} | |||
/* copies len digits from a to r if b == 1 */ | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c) { | |||
size_t i; | |||
DIGIT mask = -(DIGIT)c; | |||
for (i = 0; i < len; i++) { | |||
r[i] ^= mask & (a[i] ^ r[i]); | |||
} | |||
} | |||
/* PRE: MAX ALLOWED ROTATION AMOUNT : DIGIT_SIZE_b */ | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount) { | |||
if ( amount == 0 ) { | |||
@@ -38,9 +47,10 @@ void PQCLEAN_LEDAKEMLT52_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsig | |||
in[j] <<= amount; | |||
} | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
static void gf2x_mul_comb(int nr, DIGIT Res[], | |||
int na, const DIGIT A[], | |||
int nb, const DIGIT B[]) { | |||
int i, j, k; | |||
DIGIT u, h; | |||
@@ -71,3 +81,182 @@ void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul_comb(int nr, DIGIT Res[], | |||
} | |||
} | |||
} | |||
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_LEDAKEMLT52_LEAKTIME_gf2x_add(R, A, B, n) | |||
#define gf2x_acc(R, B, n) PQCLEAN_LEDAKEMLT52_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, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
gf2x_cpy(R, A, delta); | |||
PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(R + delta, A + delta, B, nb);; | |||
} | |||
/* aligns first array elements */ | |||
static inline void gf2x_add_asymm2(DIGIT *R, | |||
int na, const DIGIT *A, | |||
int nb, const DIGIT *B) { | |||
size_t delta = na - nb; | |||
PQCLEAN_LEDAKEMLT52_LEAKTIME_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_comb(2 * n, R, n, A, n, B); | |||
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_LEDAKEMLT52_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); | |||
} | |||
@@ -48,11 +48,16 @@ typedef uint64_t DIGIT; | |||
#define DIGIT_SIZE_b (DIGIT_SIZE_B << 3) | |||
#define POSITION_T uint32_t | |||
#define GF2X_MUL PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul_comb | |||
#define MIN_KAR_DIGITS 10 | |||
#define MIN_TOOM_DIGITS 42 | |||
#define STACK_KAR_ONLY 7137 | |||
#define STACK_WORDS 8401 | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_add(DIGIT Res[], const DIGIT A[], const DIGIT B[], int nr); | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_cmov(DIGIT *r, const DIGIT *a, size_t len, int c); | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_right_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_left_bit_shift_n(int length, DIGIT in[], unsigned int amount); | |||
void GF2X_MUL(int nr, DIGIT Res[], int na, const DIGIT A[], int nb, const DIGIT B[]); | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul(DIGIT *R, const DIGIT *A, const DIGIT *B, size_t n); | |||
#endif |
@@ -257,9 +257,7 @@ int PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) | |||
void PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mod_mul(DIGIT Res[], const DIGIT A[], const DIGIT B[]) { | |||
DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT]; | |||
GF2X_MUL(2 * NUM_DIGITS_GF2X_ELEMENT, aux, | |||
NUM_DIGITS_GF2X_ELEMENT, A, | |||
NUM_DIGITS_GF2X_ELEMENT, B); | |||
PQCLEAN_LEDAKEMLT52_LEAKTIME_gf2x_mul(aux, A, B, NUM_DIGITS_GF2X_ELEMENT); | |||
gf2x_mod(Res, aux); | |||
} | |||
@@ -7,7 +7,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||
- kem.c | |||
@@ -23,7 +22,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||
- kem.c | |||
@@ -7,7 +7,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||
- kem.c | |||
@@ -23,7 +22,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||
- kem.c | |||
@@ -7,7 +7,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||
- kem.c | |||
@@ -22,7 +21,6 @@ consistency_checks: | |||
- dfr_test.c | |||
- dfr_test.h | |||
- gf2x_arith.c | |||
- gf2x_arith.h | |||
- gf2x_arith_mod_xPplusOne.c | |||
- H_Q_matrices_generation.c | |||
- H_Q_matrices_generation.h | |||