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pqcrypto/crypto_kem/ledakemlt32/clean/gf2x_arith_mod_xPplusOne.c

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#include "gf2x_arith_mod_xPplusOne.h"
#include "rng.h"
#include <assert.h>
#include <string.h> // memcpy(...), memset(...)
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_copy(DIGIT dest[], const DIGIT in[]) {
for (int i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0; i--) {
dest[i] = in[i];
}
}
/* returns the coefficient of the x^exponent term as the LSB of a digit */
DIGIT PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_get_coeff(const DIGIT poly[], unsigned int exponent) {
unsigned int straightIdx = (NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_b - 1) - exponent;
unsigned int digitIdx = straightIdx / DIGIT_SIZE_b;
unsigned int inDigitIdx = straightIdx % DIGIT_SIZE_b;
return (poly[digitIdx] >> (DIGIT_SIZE_b - 1 - inDigitIdx)) & ((DIGIT) 1) ;
}
/* sets the coefficient of the x^exponent term as the LSB of a digit */
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_set_coeff(DIGIT poly[], unsigned int exponent, DIGIT value) {
unsigned int straightIdx = (NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_b - 1) - exponent;
unsigned int digitIdx = straightIdx / DIGIT_SIZE_b;
unsigned int inDigitIdx = straightIdx % DIGIT_SIZE_b;
/* clear given coefficient */
DIGIT mask = ~( ((DIGIT) 1) << (DIGIT_SIZE_b - 1 - inDigitIdx));
poly[digitIdx] = poly[digitIdx] & mask;
poly[digitIdx] = poly[digitIdx] | (( value & ((DIGIT) 1)) << (DIGIT_SIZE_b - 1 - inDigitIdx));
}
/* toggles (flips) the coefficient of the x^exponent term as the LSB of a digit */
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_toggle_coeff(DIGIT poly[], unsigned int exponent) {
unsigned int straightIdx = (NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_b - 1) - exponent;
unsigned int digitIdx = straightIdx / DIGIT_SIZE_b;
unsigned int inDigitIdx = straightIdx % DIGIT_SIZE_b;
/* clear given coefficient */
DIGIT mask = ( ((DIGIT) 1) << (DIGIT_SIZE_b - 1 - inDigitIdx));
poly[digitIdx] = poly[digitIdx] ^ mask;
}
/* population count for an unsigned 64-bit integer
Source: Hacker's delight, p.66 */
static int popcount_uint64t(uint64_t x) {
x -= (x >> 1) & 0x5555555555555555;
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
x = (x + (x >> 4)) & 0x0f0f0f0f0f0f0f0f;
return (int)((x * 0x0101010101010101) >> 56);
}
/* population count for a single polynomial */
int PQCLEAN_LEDAKEMLT32_CLEAN_population_count(DIGIT *poly) {
int ret = 0;
for (int i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0; i--) {
ret += popcount_uint64t(poly[i]);
}
return ret;
}
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_mod_add(DIGIT Res[], const DIGIT A[], const DIGIT B[]) {
PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_add(Res, A, B, NUM_DIGITS_GF2X_ELEMENT);
}
static int partition(POSITION_T arr[], int lo, int hi) {
POSITION_T x = arr[hi];
POSITION_T tmp;
int i = (lo - 1);
for (int j = lo; j <= hi - 1; j++) {
if (arr[j] <= x) {
i++;
tmp = arr[i];
arr[i] = arr[j];
arr[j] = tmp;
}
}
tmp = arr[i + 1];
arr[i + 1] = arr[hi];
arr[hi] = tmp;
return i + 1;
}
void PQCLEAN_LEDAKEMLT32_CLEAN_quicksort_sparse(POSITION_T Res[]) {
int stack[DV * M];
int hi, lo, pivot, tos = -1;
stack[++tos] = 0;
stack[++tos] = (DV * M) - 1;
while (tos >= 0 ) {
hi = stack[tos--];
lo = stack[tos--];
pivot = partition(Res, lo, hi);
if ( (pivot - 1) > lo) {
stack[++tos] = lo;
stack[++tos] = pivot - 1;
}
if ( (pivot + 1) < hi) {
stack[++tos] = pivot + 1;
stack[++tos] = hi;
}
}
}
static void gf2x_mod(DIGIT out[], const DIGIT in[]) {
int i, j, posTrailingBit, maskOffset;
DIGIT mask, aux[2 * NUM_DIGITS_GF2X_ELEMENT];
memcpy(aux, in, 2 * NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
memset(out, 0x00, NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
for (i = 0; i < (2 * NUM_DIGITS_GF2X_ELEMENT) - 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;
}
}
for (i = 0; i < NUM_DIGITS_GF2X_ELEMENT; i++) {
out[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = aux[2 * NUM_DIGITS_GF2X_ELEMENT - 1 - i];
}
}
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;
}
static void right_bit_shift(unsigned int length, DIGIT in[]) {
unsigned 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;
}
/* shifts by whole digits */
static void left_DIGIT_shift_n(unsigned int length, DIGIT in[], unsigned int amount) {
unsigned int j;
for (j = 0; (j + amount) < length; j++) {
in[j] = in[j + amount];
}
for (; j < length; j++) {
in[j] = (DIGIT)0;
}
}
/* may shift by an arbitrary amount*/
static void left_bit_shift_wide_n(const int length, DIGIT in[], unsigned int amount) {
left_DIGIT_shift_n(length, in, amount / DIGIT_SIZE_b);
PQCLEAN_LEDAKEMLT32_CLEAN_left_bit_shift_n(length, in, amount % DIGIT_SIZE_b);
}
/* Hackers delight, reverses a uint64_t */
static DIGIT reverse_digit(DIGIT x) {
uint64_t t;
x = (x << 31) | (x >> 33);
t = (x ^ (x >> 20)) & 0x00000FFF800007FFLL;
x = (t | (t << 20)) ^ x;
t = (x ^ (x >> 8)) & 0x00F8000F80700807LL;
x = (t | (t << 8)) ^ x;
t = (x ^ (x >> 4)) & 0x0808708080807008LL;
x = (t | (t << 4)) ^ x;
t = (x ^ (x >> 2)) & 0x1111111111111111LL;
x = (t | (t << 2)) ^ x;
return x;
}
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_transpose_in_place(DIGIT A[]) {
/* it keeps the lsb in the same position and
* 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;
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;
}
// A[NUM_DIGITS_GF2X_ELEMENT / 2] = reverse_digit(A[NUM_DIGITS_GF2X_ELEMENT / 2]); // no middle digit
if (slack_bits_amount) {
PQCLEAN_LEDAKEMLT32_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;
}
static void rotate_bit_left(DIGIT in[]) { /* equivalent to x * in(x) mod x^P+1 */
DIGIT mask, rotated_bit;
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;
left_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
in[NUM_DIGITS_GF2X_ELEMENT - 1] |= rotated_bit;
}
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);
int msb_offset_in_digit = MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS - 1;
rotated_bit = rotated_bit << msb_offset_in_digit;
in[0] |= rotated_bit;
}
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;
}
}
/*
* 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)
*
*/
int PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) { /* in^{-1} mod x^P-1 */
int i;
int delta = 0;
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;
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;
}
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) {
PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_add(s, s, f, NUM_DIGITS_GF2X_MODULUS);
PQCLEAN_LEDAKEMLT32_CLEAN_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);
}
void PQCLEAN_LEDAKEMLT32_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, aux);
}
/*PRE: the representation of the sparse coefficients is sorted in increasing
order of the coefficients themselves */
void PQCLEAN_LEDAKEMLT32_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]) );
PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_add(resDouble, aux, resDouble, 2 * NUM_DIGITS_GF2X_ELEMENT);
}
}
}
gf2x_mod(Res, resDouble);
}
void PQCLEAN_LEDAKEMLT32_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;
}
}
void PQCLEAN_LEDAKEMLT32_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*/
size_t lastFilledPos = 0;
for (size_t i = 0 ; i < sizeA ; i++) {
for (size_t j = 0 ; j < sizeB ; j++) {
uint32_t prod = A[i] + 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++;
}
PQCLEAN_LEDAKEMLT32_CLEAN_quicksort_sparse(Res);
/* eliminate duplicates */
POSITION_T lastReadPos = Res[0];
int duplicateCount;
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;
}
}
/* 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 */
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_mod_add_sparse(
int sizeR, POSITION_T Res[],
int sizeA, const POSITION_T A[],
int sizeB, const POSITION_T B[]) {
POSITION_T tmpRes[DV * M]; // TODO: now function only works for adding (disjunct) DV and M positions
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);
}
/* 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
*/
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 {
PQCLEAN_LEDAKEMLT32_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;
}
/* Obtains fresh randomness and seed-expands it until all the required positions
* for the '1's in the circulant block are obtained */
void PQCLEAN_LEDAKEMLT32_CLEAN_rand_circulant_sparse_block(POSITION_T *pos_ones,
int countOnes,
AES_XOF_struct *seed_expander_ctx) {
int duplicated, placedOnes = 0;
uint32_t p;
while (placedOnes < countOnes) {
p = rand_range(NUM_BITS_GF2X_ELEMENT,
P_BITS,
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++;
}
}
}
/* Returns random weight-t circulant block */
void PQCLEAN_LEDAKEMLT32_CLEAN_rand_circulant_blocks_sequence(
DIGIT sequence[N0 * NUM_DIGITS_GF2X_ELEMENT],
AES_XOF_struct *seed_expander_ctx) {
int rndPos[NUM_ERRORS_T], duplicated, counter = 0;
int p, polyIndex, exponent;
memset(sequence, 0x00, N0 * NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
while (counter < NUM_ERRORS_T) {
p = rand_range(N0 * NUM_BITS_GF2X_ELEMENT, P_BITS,
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++) {
polyIndex = rndPos[j] / P;
exponent = rndPos[j] % P;
PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_set_coeff( sequence + NUM_DIGITS_GF2X_ELEMENT * polyIndex, exponent,
( (DIGIT) 1));
}
}
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_tobytes(uint8_t *bytes, const DIGIT *poly) {
size_t i, j;
for (i = 0; i < NUM_DIGITS_GF2X_ELEMENT; i++) {
for (j = 0; j < DIGIT_SIZE_B; j++) {
bytes[i * DIGIT_SIZE_B + j] = (uint8_t) (poly[i] >> 8 * j);
}
}
}
void PQCLEAN_LEDAKEMLT32_CLEAN_gf2x_frombytes(DIGIT *poly, const uint8_t *poly_bytes) {
size_t i, j;
for (i = 0; i < NUM_DIGITS_GF2X_ELEMENT; i++) {
poly[i] = (DIGIT) 0;
for (j = 0; j < DIGIT_SIZE_B; j++) {
poly[i] |= (DIGIT) poly_bytes[i * DIGIT_SIZE_B + j] << 8 * j;
}
}
}
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