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pqcrypto/crypto_kem/ledakemlt12/clean/gf2x_arith_mod_xPplusOne.c

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#include "gf2x_arith_mod_xPplusOne.h"
#include "rng.h"
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#include <string.h> // memcpy(...), memset(...)
#include <assert.h>
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static void gf2x_mod(DIGIT out[],
const int nin, const DIGIT in[]) {
long int i, j, posTrailingBit, maskOffset;
DIGIT mask, aux[nin];
memcpy(aux, in, nin * DIGIT_SIZE_B);
memset(out, 0x00, NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
if (nin < NUM_DIGITS_GF2X_MODULUS) {
for (i = 0; i < nin; i++) {
out[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = in[nin - 1 - i];
}
return;
}
for (i = 0; i < nin - NUM_DIGITS_GF2X_MODULUS; i += 1) {
for (j = DIGIT_SIZE_b - 1; j >= 0; j--) {
mask = ((DIGIT)0x1) << j;
if (aux[i] & mask) {
aux[i] ^= mask;
posTrailingBit = (DIGIT_SIZE_b - 1 - j) + i * DIGIT_SIZE_b + P;
maskOffset = (DIGIT_SIZE_b - 1 - (posTrailingBit % DIGIT_SIZE_b));
mask = (DIGIT) 0x1 << maskOffset;
aux[posTrailingBit / DIGIT_SIZE_b] ^= mask;
}
}
}
for (j = DIGIT_SIZE_b - 1; j >= MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS; j--) {
mask = ((DIGIT)0x1) << j;
if (aux[i] & mask) {
aux[i] ^= mask;
posTrailingBit = (DIGIT_SIZE_b - 1 - j) + i * DIGIT_SIZE_b + P;
maskOffset = (DIGIT_SIZE_b - 1 - (posTrailingBit % DIGIT_SIZE_b));
mask = (DIGIT) 0x1 << maskOffset;
aux[posTrailingBit / DIGIT_SIZE_b] ^= mask;
}
}
int to_copy = (nin > NUM_DIGITS_GF2X_ELEMENT) ? NUM_DIGITS_GF2X_ELEMENT : nin;
for (i = 0; i < to_copy; i++) {
out[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = aux[nin - 1 - i];
}
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}
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static void left_bit_shift(const int length, DIGIT in[]) {
int j;
for (j = 0; j < length - 1; j++) {
in[j] <<= 1; /* logical shift does not need clearing */
in[j] |= in[j + 1] >> (DIGIT_SIZE_b - 1);
}
in[j] <<= 1;
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}
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static void right_bit_shift(const int length, DIGIT in[]) {
int j;
for (j = length - 1; j > 0 ; j--) {
in[j] >>= 1;
in[j] |= (in[j - 1] & (DIGIT)0x01) << (DIGIT_SIZE_b - 1);
}
in[j] >>= 1;
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}
/* shifts by whole digits */
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static inline void left_DIGIT_shift_n(const int length, DIGIT in[], int amount) {
int j;
for (j = 0; (j + amount) < length; j++) {
in[j] = in[j + amount];
}
for (; j < length; j++) {
in[j] = (DIGIT)0;
}
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}
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/* may shift by an arbitrary amount*/
static void left_bit_shift_wide_n(const int length, DIGIT in[], int amount) {
left_DIGIT_shift_n(length, in, amount / DIGIT_SIZE_b);
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PQCLEAN_LEDAKEMLT12_CLEAN_left_bit_shift_n(length, in, amount % DIGIT_SIZE_b);
}
#if (defined(DIGIT_IS_UINT8) || defined(DIGIT_IS_UINT16))
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static uint8_t byte_reverse_with_less32bitDIGIT(uint8_t b) {
uint8_t r = b;
int s = (sizeof(b) << 3) - 1;
for (b >>= 1; b; b >>= 1) {
r <<= 1;
r |= b & 1;
s--;
}
r <<= s;
return r;
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}
#endif
#if defined(DIGIT_IS_UINT32)
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static uint8_t byte_reverse_with_32bitDIGIT(uint8_t b) {
b = ( (b * 0x0802LU & 0x22110LU) | (b * 0x8020LU & 0x88440LU)
) * 0x10101LU >> 16;
return b;
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}
#endif
#if defined(DIGIT_IS_UINT64)
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static uint8_t byte_reverse_with_64bitDIGIT(uint8_t b) {
b = (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;
return b;
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}
#endif
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static DIGIT reverse_digit(const DIGIT b) {
int i;
union toReverse_t {
uint8_t inByte[DIGIT_SIZE_B];
DIGIT digitValue;
} toReverse;
toReverse.digitValue = b;
#if defined(DIGIT_IS_UINT64)
for (i = 0; i < DIGIT_SIZE_B; i++) {
toReverse.inByte[i] = byte_reverse_with_64bitDIGIT(toReverse.inByte[i]);
}
return __builtin_bswap64(toReverse.digitValue);
#elif defined(DIGIT_IS_UINT32)
for (i = 0; i < DIGIT_SIZE_B; i++) {
toReverse.inByte[i] = byte_reverse_with_32bitDIGIT(toReverse.inByte[i]);
}
return __builtin_bswap32(toReverse.digitValue);
#elif defined(DIGIT_IS_UINT16)
for (i = 0; i < DIGIT_SIZE_B; i++) {
toReverse.inByte[i] = byte_reverse_with_less32bitDIGIT(toReverse.inByte[i]);
}
reversed = __builtin_bswap16(toReverse.digitValue);
#elif defined(DIGIT_IS_UINT8)
return byte_reverse_with_less32bitDIGIT(toReverse.inByte[0]);
#else
#error "Missing implementation for reverse_digit(...) \
with this CPU word bitsize !!! "
#endif
return toReverse.digitValue;
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_transpose_in_place(DIGIT A[]) {
/* it keeps the lsb in the same position and
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* inverts the sequence of the remaining bits */
DIGIT mask = (DIGIT)0x1;
DIGIT rev1, rev2, a00;
int i, slack_bits_amount = NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_b - P;
if (NUM_DIGITS_GF2X_ELEMENT == 1) {
a00 = A[0] & mask;
right_bit_shift(1, A);
rev1 = reverse_digit(A[0]);
#if (NUM_DIGITS_GF2X_MOD_P_ELEMENT*DIGIT_SIZE_b - P)
rev1 >>= (DIGIT_SIZE_b - (P % DIGIT_SIZE_b));
#endif
A[0] = (rev1 & (~mask)) | a00;
return;
}
a00 = A[NUM_DIGITS_GF2X_ELEMENT - 1] & mask;
right_bit_shift(NUM_DIGITS_GF2X_ELEMENT, A);
for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= (NUM_DIGITS_GF2X_ELEMENT + 1) / 2; i--) {
rev1 = reverse_digit(A[i]);
rev2 = reverse_digit(A[NUM_DIGITS_GF2X_ELEMENT - 1 - i]);
A[i] = rev2;
A[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = rev1;
}
if (NUM_DIGITS_GF2X_ELEMENT % 2 == 1) {
A[NUM_DIGITS_GF2X_ELEMENT / 2] = reverse_digit(A[NUM_DIGITS_GF2X_ELEMENT / 2]);
}
if (slack_bits_amount) {
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PQCLEAN_LEDAKEMLT12_CLEAN_right_bit_shift_n(NUM_DIGITS_GF2X_ELEMENT, A, slack_bits_amount);
}
A[NUM_DIGITS_GF2X_ELEMENT - 1] = (A[NUM_DIGITS_GF2X_ELEMENT - 1] & (~mask)) | a00;
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}
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static void rotate_bit_left(DIGIT in[]) { /* equivalent to x * in(x) mod x^P+1 */
DIGIT mask, rotated_bit;
if (NUM_DIGITS_GF2X_MODULUS == NUM_DIGITS_GF2X_ELEMENT) {
int msb_offset_in_digit = MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS - 1;
mask = ((DIGIT)0x1) << msb_offset_in_digit;
rotated_bit = !!(in[0] & mask);
in[0] &= ~mask; /* clear shifted bit */
left_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
} else {
/* NUM_DIGITS_GF2X_MODULUS == 1 + NUM_DIGITS_GF2X_ELEMENT and
* MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS == 0
*/
mask = ((DIGIT)0x1) << (DIGIT_SIZE_b - 1);
rotated_bit = !!(in[0] & mask);
in[0] &= ~mask; /* clear shifted bit */
left_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
}
in[NUM_DIGITS_GF2X_ELEMENT - 1] |= rotated_bit;
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}
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static void rotate_bit_right(DIGIT in[]) { /* x^{-1} * in(x) mod x^P+1 */
DIGIT rotated_bit = in[NUM_DIGITS_GF2X_ELEMENT - 1] & ((DIGIT)0x1);
right_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
if (NUM_DIGITS_GF2X_MODULUS == NUM_DIGITS_GF2X_ELEMENT) {
int msb_offset_in_digit = MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS - 1;
rotated_bit = rotated_bit << msb_offset_in_digit;
} else {
/* NUM_DIGITS_GF2X_MODULUS == 1 + NUM_DIGITS_GF2X_ELEMENT and
* MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS == 0
*/
rotated_bit = rotated_bit << (DIGIT_SIZE_b - 1);
}
in[0] |= rotated_bit;
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}
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static void gf2x_swap(const int length,
DIGIT f[],
DIGIT s[]) {
DIGIT t;
for (int i = length - 1; i >= 0; i--) {
t = f[i];
f[i] = s[i];
s[i] = t;
}
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}
/*
* Optimized extended GCD algorithm to compute the multiplicative inverse of
* a non-zero element in GF(2)[x] mod x^P+1, in polyn. representation.
*
* H. Brunner, A. Curiger, and M. Hofstetter. 1993.
* On Computing Multiplicative Inverses in GF(2^m).
* IEEE Trans. Comput. 42, 8 (August 1993), 1010-1015.
* DOI=http://dx.doi.org/10.1109/12.238496
*
*
* Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange,
* Kim Nguyen, and Frederik Vercauteren. 2012.
* Handbook of Elliptic and Hyperelliptic Curve Cryptography,
* Second Edition (2nd ed.). Chapman & Hall/CRC.
* (Chapter 11 -- Algorithm 11.44 -- pag 223)
*
*/
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int PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) { /* in^{-1} mod x^P-1 */
int i;
long int delta = 0;
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DIGIT u[NUM_DIGITS_GF2X_ELEMENT] = {0};
DIGIT v[NUM_DIGITS_GF2X_ELEMENT] = {0};
DIGIT s[NUM_DIGITS_GF2X_MODULUS] = {0};
DIGIT f[NUM_DIGITS_GF2X_MODULUS] = {0}; // alignas(32)?
DIGIT mask;
u[NUM_DIGITS_GF2X_ELEMENT - 1] = 0x1;
v[NUM_DIGITS_GF2X_ELEMENT - 1] = 0x0;
s[NUM_DIGITS_GF2X_MODULUS - 1] = 0x1;
if (MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS == 0) {
mask = 0x1;
} else {
mask = (((DIGIT)0x1) << MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS);
}
s[0] |= mask;
for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0 && in[i] == 0; i--);
if (i < 0) {
return 0;
}
if (NUM_DIGITS_GF2X_MODULUS == 1 + NUM_DIGITS_GF2X_ELEMENT)
for (i = NUM_DIGITS_GF2X_MODULUS - 1; i >= 1 ; i--) {
f[i] = in[i - 1];
} else /* they are equal */
for (i = NUM_DIGITS_GF2X_MODULUS - 1; i >= 0 ; i--) {
f[i] = in[i];
}
for (i = 1; i <= 2 * P; i++) {
if ( (f[0] & mask) == 0 ) {
left_bit_shift(NUM_DIGITS_GF2X_MODULUS, f);
rotate_bit_left(u);
delta += 1;
} else {
if ( (s[0] & mask) != 0) {
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gf2x_add(s, s, f, NUM_DIGITS_GF2X_MODULUS);
gf2x_mod_add(v, v, u);
}
left_bit_shift(NUM_DIGITS_GF2X_MODULUS, s);
if ( delta == 0 ) {
gf2x_swap(NUM_DIGITS_GF2X_MODULUS, f, s);
gf2x_swap(NUM_DIGITS_GF2X_ELEMENT, u, v);
rotate_bit_left(u);
delta = 1;
} else {
rotate_bit_right(u);
delta = delta - 1;
}
}
}
for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0 ; i--) {
out[i] = u[i];
}
return (delta == 0);
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_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);
gf2x_mod(Res, 2 * NUM_DIGITS_GF2X_ELEMENT, aux);
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}
/*PRE: the representation of the sparse coefficients is sorted in increasing
order of the coefficients themselves */
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_mul_dense_to_sparse(
DIGIT Res[],
const DIGIT dense[],
POSITION_T sparse[], unsigned int nPos) {
DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT] = {0x00};
DIGIT resDouble[2 * NUM_DIGITS_GF2X_ELEMENT] = {0x00};
memcpy(aux + NUM_DIGITS_GF2X_ELEMENT, dense, NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
memcpy(resDouble + NUM_DIGITS_GF2X_ELEMENT, dense,
NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
if (sparse[0] != INVALID_POS_VALUE) {
left_bit_shift_wide_n(2 * NUM_DIGITS_GF2X_ELEMENT, resDouble, sparse[0]);
left_bit_shift_wide_n(2 * NUM_DIGITS_GF2X_ELEMENT, aux, sparse[0]);
for (unsigned int i = 1; i < nPos; i++) {
if (sparse[i] != INVALID_POS_VALUE) {
left_bit_shift_wide_n(2 * NUM_DIGITS_GF2X_ELEMENT, aux, (sparse[i] - sparse[i - 1]) );
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gf2x_add(resDouble, aux, resDouble, 2 * NUM_DIGITS_GF2X_ELEMENT);
}
}
}
gf2x_mod(Res, 2 * NUM_DIGITS_GF2X_ELEMENT, resDouble);
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_transpose_in_place_sparse(int sizeA, POSITION_T A[]) {
POSITION_T t;
int i = 0, j;
if (A[i] == 0) {
i = 1;
}
j = i;
for (; i < sizeA && A[i] != INVALID_POS_VALUE; i++) {
A[i] = P - A[i];
}
for (i -= 1; j < i; j++, i--) {
t = A[j];
A[j] = A[i];
A[i] = t;
}
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_mul_sparse(size_t sizeR, POSITION_T Res[],
size_t sizeA, const POSITION_T A[],
size_t sizeB, const POSITION_T B[]) {
/* compute all the coefficients, filling invalid positions with P*/
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size_t lastFilledPos = 0;
for (size_t i = 0 ; i < sizeA ; i++) {
for (size_t j = 0 ; j < sizeB ; j++) {
uint32_t prod = ((uint32_t) A[i]) + ((uint32_t) B[j]);
prod = ( (prod >= P) ? prod - P : prod);
if ((A[i] != INVALID_POS_VALUE) &&
(B[j] != INVALID_POS_VALUE)) {
Res[lastFilledPos] = prod;
} else {
Res[lastFilledPos] = INVALID_POS_VALUE;
}
lastFilledPos++;
}
}
while (lastFilledPos < sizeR) {
Res[lastFilledPos] = INVALID_POS_VALUE;
lastFilledPos++;
}
quicksort(Res, sizeR);
/* eliminate duplicates */
POSITION_T lastReadPos = Res[0];
int duplicateCount;
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size_t write_idx = 0;
size_t read_idx = 0;
while (read_idx < sizeR && Res[read_idx] != INVALID_POS_VALUE) {
lastReadPos = Res[read_idx];
read_idx++;
duplicateCount = 1;
while ( (Res[read_idx] == lastReadPos) && (Res[read_idx] != INVALID_POS_VALUE)) {
read_idx++;
duplicateCount++;
}
if (duplicateCount % 2) {
Res[write_idx] = lastReadPos;
write_idx++;
}
}
/* fill remaining cells with INVALID_POS_VALUE */
for (; write_idx < sizeR; write_idx++) {
Res[write_idx] = INVALID_POS_VALUE;
}
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}
/* the implementation is safe even in case A or B alias with the result */
/* PRE: A and B should be sorted and have INVALID_POS_VALUE at the end */
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_add_sparse(
int sizeR, POSITION_T Res[],
int sizeA, POSITION_T A[],
int sizeB, POSITION_T B[]) {
POSITION_T tmpRes[sizeR];
int idxA = 0, idxB = 0, idxR = 0;
while ( idxA < sizeA &&
idxB < sizeB &&
A[idxA] != INVALID_POS_VALUE &&
B[idxB] != INVALID_POS_VALUE ) {
if (A[idxA] == B[idxB]) {
idxA++;
idxB++;
} else {
if (A[idxA] < B[idxB]) {
tmpRes[idxR] = A[idxA];
idxA++;
} else {
tmpRes[idxR] = B[idxB];
idxB++;
}
idxR++;
}
}
while (idxA < sizeA && A[idxA] != INVALID_POS_VALUE) {
tmpRes[idxR] = A[idxA];
idxA++;
idxR++;
}
while (idxB < sizeB && B[idxB] != INVALID_POS_VALUE) {
tmpRes[idxR] = B[idxB];
idxB++;
idxR++;
}
while (idxR < sizeR) {
tmpRes[idxR] = INVALID_POS_VALUE;
idxR++;
}
memcpy(Res, tmpRes, sizeof(POSITION_T)*sizeR);
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}
/* Return a uniform random value in the range 0..n-1 inclusive,
* applying a rejection sampling strategy and exploiting as a random source
* the NIST seedexpander seeded with the proper key.
* Assumes that the maximum value for the range n is 2^32-1
*/
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static uint32_t rand_range(const unsigned int n, const int logn, AES_XOF_struct *seed_expander_ctx) {
unsigned long required_rnd_bytes = (logn + 7) / 8;
unsigned char rnd_char_buffer[4];
uint32_t rnd_value;
uint32_t mask = ( (uint32_t)1 << logn) - 1;
do {
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PQCLEAN_LEDAKEMLT12_CLEAN_seedexpander(seed_expander_ctx, rnd_char_buffer, required_rnd_bytes);
/* obtain an endianness independent representation of the generated random
bytes into an unsigned integer */
rnd_value = ((uint32_t)rnd_char_buffer[3] << 24) +
((uint32_t)rnd_char_buffer[2] << 16) +
((uint32_t)rnd_char_buffer[1] << 8) +
((uint32_t)rnd_char_buffer[0] << 0) ;
rnd_value = mask & rnd_value;
} while (rnd_value >= n);
return rnd_value;
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}
/* Obtains fresh randomness and seed-expands it until all the required positions
* for the '1's in the circulant block are obtained */
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void PQCLEAN_LEDAKEMLT12_CLEAN_rand_circulant_sparse_block(POSITION_T *pos_ones,
const int countOnes,
AES_XOF_struct *seed_expander_ctx) {
int duplicated, placedOnes = 0;
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uint32_t p;
while (placedOnes < countOnes) {
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p = rand_range(NUM_BITS_GF2X_ELEMENT,
BITS_TO_REPRESENT(P),
seed_expander_ctx);
duplicated = 0;
for (int j = 0; j < placedOnes; j++) if (pos_ones[j] == p) {
duplicated = 1;
}
if (duplicated == 0) {
pos_ones[placedOnes] = p;
placedOnes++;
}
}
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_rand_circulant_blocks_sequence(DIGIT sequence[N0 * NUM_DIGITS_GF2X_ELEMENT],
const int countOnes,
AES_XOF_struct *seed_expander_ctx) {
int rndPos[countOnes], duplicated, counter = 0;
memset(sequence, 0x00, N0 * NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
while (counter < countOnes) {
int p = rand_range(N0 * NUM_BITS_GF2X_ELEMENT, BITS_TO_REPRESENT(P),
seed_expander_ctx);
duplicated = 0;
for (int j = 0; j < counter; j++) if (rndPos[j] == p) {
duplicated = 1;
}
if (duplicated == 0) {
rndPos[counter] = p;
counter++;
}
}
for (int j = 0; j < counter; j++) {
int polyIndex = rndPos[j] / P;
int exponent = rndPos[j] % P;
gf2x_set_coeff( sequence + NUM_DIGITS_GF2X_ELEMENT * polyIndex, exponent,
( (DIGIT) 1));
}
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}