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480 lines
15 KiB
C
480 lines
15 KiB
C
#include "gf2x_arith_mod_xPplusOne.h"
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#include "rng.h"
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#include <assert.h>
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#include <string.h> // memcpy(...), memset(...)
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static void gf2x_mod(DIGIT out[], const DIGIT in[]) {
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int i, j, posTrailingBit, maskOffset;
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DIGIT mask, aux[2 * NUM_DIGITS_GF2X_ELEMENT];
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memcpy(aux, in, 2 * NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
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memset(out, 0x00, NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
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for (i = 0; i < (2 * NUM_DIGITS_GF2X_ELEMENT) - NUM_DIGITS_GF2X_MODULUS; i += 1) {
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for (j = DIGIT_SIZE_b - 1; j >= 0; j--) {
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mask = ((DIGIT)0x1) << j;
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if (aux[i] & mask) {
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aux[i] ^= mask;
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posTrailingBit = (DIGIT_SIZE_b - 1 - j) + i * DIGIT_SIZE_b + P;
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maskOffset = (DIGIT_SIZE_b - 1 - (posTrailingBit % DIGIT_SIZE_b));
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mask = (DIGIT) 0x1 << maskOffset;
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aux[posTrailingBit / DIGIT_SIZE_b] ^= mask;
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}
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}
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}
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for (j = DIGIT_SIZE_b - 1; j >= MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS; j--) {
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mask = ((DIGIT)0x1) << j;
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if (aux[i] & mask) {
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aux[i] ^= mask;
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posTrailingBit = (DIGIT_SIZE_b - 1 - j) + i * DIGIT_SIZE_b + P;
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maskOffset = (DIGIT_SIZE_b - 1 - (posTrailingBit % DIGIT_SIZE_b));
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mask = (DIGIT) 0x1 << maskOffset;
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aux[posTrailingBit / DIGIT_SIZE_b] ^= mask;
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}
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}
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for (i = 0; i < NUM_DIGITS_GF2X_ELEMENT; i++) {
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out[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = aux[2 * NUM_DIGITS_GF2X_ELEMENT - 1 - i];
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}
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}
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static void left_bit_shift(const int length, DIGIT in[]) {
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int j;
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for (j = 0; j < length - 1; j++) {
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in[j] <<= 1; /* logical shift does not need clearing */
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in[j] |= in[j + 1] >> (DIGIT_SIZE_b - 1);
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}
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in[j] <<= 1;
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}
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static void right_bit_shift(unsigned int length, DIGIT in[]) {
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unsigned int j;
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for (j = length - 1; j > 0 ; j--) {
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in[j] >>= 1;
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in[j] |= (in[j - 1] & (DIGIT)0x01) << (DIGIT_SIZE_b - 1);
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}
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in[j] >>= 1;
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}
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/* shifts by whole digits */
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static inline void left_DIGIT_shift_n(unsigned int length, DIGIT in[], unsigned int amount) {
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unsigned int j;
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for (j = 0; (j + amount) < length; j++) {
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in[j] = in[j + amount];
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}
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for (; j < length; j++) {
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in[j] = (DIGIT)0;
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}
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}
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/* may shift by an arbitrary amount*/
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static void left_bit_shift_wide_n(const int length, DIGIT in[], unsigned int amount) {
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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);
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}
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/* Hackers delight, reverses a uint64_t */
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static DIGIT reverse_digit(DIGIT x) {
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uint64_t t;
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x = (x << 31) | (x >> 33);
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t = (x ^ (x >> 20)) & 0x00000FFF800007FFLL;
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x = (t | (t << 20)) ^ x;
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t = (x ^ (x >> 8)) & 0x00F8000F80700807LL;
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x = (t | (t << 8)) ^ x;
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t = (x ^ (x >> 4)) & 0x0808708080807008LL;
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x = (t | (t << 4)) ^ x;
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t = (x ^ (x >> 2)) & 0x1111111111111111LL;
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x = (t | (t << 2)) ^ x;
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return x;
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_transpose_in_place(DIGIT A[]) {
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/* it keeps the lsb in the same position and
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* inverts the sequence of the remaining bits */
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DIGIT mask = (DIGIT)0x1;
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DIGIT rev1, rev2, a00;
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int i, slack_bits_amount = NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_b - P;
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a00 = A[NUM_DIGITS_GF2X_ELEMENT - 1] & mask;
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right_bit_shift(NUM_DIGITS_GF2X_ELEMENT, A);
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for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= (NUM_DIGITS_GF2X_ELEMENT + 1) / 2; i--) {
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rev1 = reverse_digit(A[i]);
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rev2 = reverse_digit(A[NUM_DIGITS_GF2X_ELEMENT - 1 - i]);
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A[i] = rev2;
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A[NUM_DIGITS_GF2X_ELEMENT - 1 - i] = rev1;
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}
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A[NUM_DIGITS_GF2X_ELEMENT / 2] = reverse_digit(A[NUM_DIGITS_GF2X_ELEMENT / 2]); // reverse middle digit
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if (slack_bits_amount) {
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PQCLEAN_LEDAKEMLT12_CLEAN_right_bit_shift_n(NUM_DIGITS_GF2X_ELEMENT, A, slack_bits_amount);
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}
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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 */
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DIGIT mask, rotated_bit;
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int msb_offset_in_digit = MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS - 1;
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mask = ((DIGIT)0x1) << msb_offset_in_digit;
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rotated_bit = !!(in[0] & mask);
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in[0] &= ~mask;
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left_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
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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 */
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DIGIT rotated_bit = in[NUM_DIGITS_GF2X_ELEMENT - 1] & ((DIGIT)0x1);
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right_bit_shift(NUM_DIGITS_GF2X_ELEMENT, in);
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int msb_offset_in_digit = MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS - 1;
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rotated_bit = rotated_bit << msb_offset_in_digit;
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in[0] |= rotated_bit;
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}
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static void gf2x_swap(const int length,
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DIGIT f[],
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DIGIT s[]) {
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DIGIT t;
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for (int i = length - 1; i >= 0; i--) {
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t = f[i];
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f[i] = s[i];
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s[i] = t;
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}
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}
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/*
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* Optimized extended GCD algorithm to compute the multiplicative inverse of
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* a non-zero element in GF(2)[x] mod x^P+1, in polyn. representation.
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*
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* H. Brunner, A. Curiger, and M. Hofstetter. 1993.
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* On Computing Multiplicative Inverses in GF(2^m).
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* IEEE Trans. Comput. 42, 8 (August 1993), 1010-1015.
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* DOI=http://dx.doi.org/10.1109/12.238496
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*
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*
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* Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange,
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* Kim Nguyen, and Frederik Vercauteren. 2012.
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* Handbook of Elliptic and Hyperelliptic Curve Cryptography,
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* Second Edition (2nd ed.). Chapman & Hall/CRC.
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* (Chapter 11 -- Algorithm 11.44 -- pag 223)
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*
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*/
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int PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_inverse(DIGIT out[], const DIGIT in[]) { /* in^{-1} mod x^P-1 */
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int i;
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long int delta = 0;
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DIGIT u[NUM_DIGITS_GF2X_ELEMENT] = {0};
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DIGIT v[NUM_DIGITS_GF2X_ELEMENT] = {0};
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DIGIT s[NUM_DIGITS_GF2X_MODULUS] = {0};
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DIGIT f[NUM_DIGITS_GF2X_MODULUS] = {0}; // alignas(32)?
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DIGIT mask;
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u[NUM_DIGITS_GF2X_ELEMENT - 1] = 0x1;
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v[NUM_DIGITS_GF2X_ELEMENT - 1] = 0x0;
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s[NUM_DIGITS_GF2X_MODULUS - 1] = 0x1;
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mask = (((DIGIT)0x1) << MSb_POSITION_IN_MSB_DIGIT_OF_MODULUS);
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s[0] |= mask;
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for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0 && in[i] == 0; i--) { };
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if (i < 0) {
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return 0;
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}
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for (i = NUM_DIGITS_GF2X_MODULUS - 1; i >= 0 ; i--) {
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f[i] = in[i];
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}
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for (i = 1; i <= 2 * P; i++) {
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if ( (f[0] & mask) == 0 ) {
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left_bit_shift(NUM_DIGITS_GF2X_MODULUS, f);
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rotate_bit_left(u);
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delta += 1;
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} else {
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if ( (s[0] & mask) != 0) {
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gf2x_add(s, s, f, NUM_DIGITS_GF2X_MODULUS);
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gf2x_mod_add(v, v, u);
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}
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left_bit_shift(NUM_DIGITS_GF2X_MODULUS, s);
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if ( delta == 0 ) {
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gf2x_swap(NUM_DIGITS_GF2X_MODULUS, f, s);
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gf2x_swap(NUM_DIGITS_GF2X_ELEMENT, u, v);
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rotate_bit_left(u);
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delta = 1;
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} else {
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rotate_bit_right(u);
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delta = delta - 1;
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}
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}
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}
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for (i = NUM_DIGITS_GF2X_ELEMENT - 1; i >= 0 ; i--) {
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out[i] = u[i];
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}
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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[]) {
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DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT];
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GF2X_MUL(2 * NUM_DIGITS_GF2X_ELEMENT, aux,
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NUM_DIGITS_GF2X_ELEMENT, A,
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NUM_DIGITS_GF2X_ELEMENT, B);
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gf2x_mod(Res, aux);
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}
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/*PRE: the representation of the sparse coefficients is sorted in increasing
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order of the coefficients themselves */
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_mul_dense_to_sparse(
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DIGIT Res[],
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const DIGIT dense[],
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POSITION_T sparse[], unsigned int nPos) {
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DIGIT aux[2 * NUM_DIGITS_GF2X_ELEMENT] = {0x00};
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DIGIT resDouble[2 * NUM_DIGITS_GF2X_ELEMENT] = {0x00};
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memcpy(aux + NUM_DIGITS_GF2X_ELEMENT, dense, NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
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memcpy(resDouble + NUM_DIGITS_GF2X_ELEMENT, dense,
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NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
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if (sparse[0] != INVALID_POS_VALUE) {
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left_bit_shift_wide_n(2 * NUM_DIGITS_GF2X_ELEMENT, resDouble, sparse[0]);
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left_bit_shift_wide_n(2 * NUM_DIGITS_GF2X_ELEMENT, aux, sparse[0]);
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for (unsigned int i = 1; i < nPos; i++) {
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if (sparse[i] != INVALID_POS_VALUE) {
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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);
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}
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}
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}
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gf2x_mod(Res, resDouble);
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_transpose_in_place_sparse(int sizeA, POSITION_T A[]) {
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POSITION_T t;
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int i = 0, j;
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if (A[i] == 0) {
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i = 1;
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}
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j = i;
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for (; i < sizeA && A[i] != INVALID_POS_VALUE; i++) {
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A[i] = P - A[i];
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}
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for (i -= 1; j < i; j++, i--) {
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t = A[j];
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A[j] = A[i];
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A[i] = t;
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}
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_mod_mul_sparse(size_t sizeR, POSITION_T Res[],
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size_t sizeA, const POSITION_T A[],
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size_t sizeB, const POSITION_T B[]) {
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/* compute all the coefficients, filling invalid positions with P*/
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size_t lastFilledPos = 0;
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for (size_t i = 0 ; i < sizeA ; i++) {
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for (size_t j = 0 ; j < sizeB ; j++) {
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uint32_t prod = A[i] + B[j];
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prod = ( (prod >= P) ? prod - P : prod);
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if ((A[i] != INVALID_POS_VALUE) &&
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(B[j] != INVALID_POS_VALUE)) {
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Res[lastFilledPos] = prod;
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} else {
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Res[lastFilledPos] = INVALID_POS_VALUE;
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}
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lastFilledPos++;
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}
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}
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while (lastFilledPos < sizeR) {
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Res[lastFilledPos] = INVALID_POS_VALUE;
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lastFilledPos++;
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}
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quicksort_sparse(Res);
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/* eliminate duplicates */
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POSITION_T lastReadPos = Res[0];
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int duplicateCount;
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size_t write_idx = 0;
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size_t read_idx = 0;
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while (read_idx < sizeR && Res[read_idx] != INVALID_POS_VALUE) {
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lastReadPos = Res[read_idx];
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read_idx++;
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duplicateCount = 1;
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while ( (Res[read_idx] == lastReadPos) && (Res[read_idx] != INVALID_POS_VALUE)) {
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read_idx++;
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duplicateCount++;
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}
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if (duplicateCount % 2) {
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Res[write_idx] = lastReadPos;
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write_idx++;
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}
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}
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/* fill remaining cells with INVALID_POS_VALUE */
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for (; write_idx < sizeR; write_idx++) {
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Res[write_idx] = INVALID_POS_VALUE;
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}
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}
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/* the implementation is safe even in case A or B alias with the result */
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/* 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(
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int sizeR, POSITION_T Res[],
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int sizeA, const POSITION_T A[],
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int sizeB, const POSITION_T B[]) {
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POSITION_T tmpRes[DV * M]; // TODO: now function only works for adding (disjunct) DV and M positions
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int idxA = 0, idxB = 0, idxR = 0;
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while ( idxA < sizeA &&
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idxB < sizeB &&
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A[idxA] != INVALID_POS_VALUE &&
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B[idxB] != INVALID_POS_VALUE ) {
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if (A[idxA] == B[idxB]) {
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idxA++;
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idxB++;
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} else {
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if (A[idxA] < B[idxB]) {
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tmpRes[idxR] = A[idxA];
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idxA++;
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} else {
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tmpRes[idxR] = B[idxB];
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idxB++;
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}
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idxR++;
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}
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}
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while (idxA < sizeA && A[idxA] != INVALID_POS_VALUE) {
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tmpRes[idxR] = A[idxA];
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idxA++;
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idxR++;
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}
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while (idxB < sizeB && B[idxB] != INVALID_POS_VALUE) {
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tmpRes[idxR] = B[idxB];
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idxB++;
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idxR++;
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}
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while (idxR < sizeR) {
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tmpRes[idxR] = INVALID_POS_VALUE;
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idxR++;
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}
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memcpy(Res, tmpRes, sizeof(POSITION_T)*sizeR);
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}
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/* Return a uniform random value in the range 0..n-1 inclusive,
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* applying a rejection sampling strategy and exploiting as a random source
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* the NIST seedexpander seeded with the proper key.
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* Assumes that the maximum value for the range n is 2^32-1
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*/
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static uint32_t rand_range(const unsigned int n, const int logn, AES_XOF_struct *seed_expander_ctx) {
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unsigned long required_rnd_bytes = (logn + 7) / 8;
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unsigned char rnd_char_buffer[4];
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uint32_t rnd_value;
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uint32_t mask = ( (uint32_t)1 << logn) - 1;
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do {
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PQCLEAN_LEDAKEMLT12_CLEAN_seedexpander(seed_expander_ctx, rnd_char_buffer, required_rnd_bytes);
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/* obtain an endianness independent representation of the generated random
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bytes into an unsigned integer */
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rnd_value = ((uint32_t)rnd_char_buffer[3] << 24) +
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((uint32_t)rnd_char_buffer[2] << 16) +
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((uint32_t)rnd_char_buffer[1] << 8) +
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((uint32_t)rnd_char_buffer[0] << 0) ;
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rnd_value = mask & rnd_value;
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} while (rnd_value >= n);
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return rnd_value;
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}
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/* Obtains fresh randomness and seed-expands it until all the required positions
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* 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,
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int countOnes,
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AES_XOF_struct *seed_expander_ctx) {
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int duplicated, placedOnes = 0;
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uint32_t p;
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while (placedOnes < countOnes) {
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p = rand_range(NUM_BITS_GF2X_ELEMENT,
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P_BITS,
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seed_expander_ctx);
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duplicated = 0;
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for (int j = 0; j < placedOnes; j++) {
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if (pos_ones[j] == p) {
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duplicated = 1;
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}
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}
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if (duplicated == 0) {
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pos_ones[placedOnes] = p;
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placedOnes++;
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}
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}
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}
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/* Returns random weight-t circulant block */
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void PQCLEAN_LEDAKEMLT12_CLEAN_rand_circulant_blocks_sequence(DIGIT sequence[N0 * NUM_DIGITS_GF2X_ELEMENT],
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AES_XOF_struct *seed_expander_ctx) {
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int rndPos[NUM_ERRORS_T], duplicated, counter = 0;
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int p, polyIndex, exponent;
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memset(sequence, 0x00, N0 * NUM_DIGITS_GF2X_ELEMENT * DIGIT_SIZE_B);
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while (counter < NUM_ERRORS_T) {
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p = rand_range(N0 * NUM_BITS_GF2X_ELEMENT, P_BITS,
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seed_expander_ctx);
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duplicated = 0;
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for (int j = 0; j < counter; j++) {
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if (rndPos[j] == p) {
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duplicated = 1;
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}
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}
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if (duplicated == 0) {
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rndPos[counter] = p;
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counter++;
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}
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}
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for (int j = 0; j < counter; j++) {
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polyIndex = rndPos[j] / P;
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exponent = rndPos[j] % P;
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gf2x_set_coeff( sequence + NUM_DIGITS_GF2X_ELEMENT * polyIndex, exponent,
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( (DIGIT) 1));
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}
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}
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void PQCLEAN_LEDAKEMLT12_CLEAN_gf2x_tobytes(uint8_t *bytes, const DIGIT *poly) {
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size_t i, j;
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for (i = 0; i < NUM_DIGITS_GF2X_ELEMENT; i++) {
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for (j = 0; j < DIGIT_SIZE_B; j++) {
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bytes[i * DIGIT_SIZE_B + j] = (uint8_t) (poly[i] >> 8 * j);
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}
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}
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}
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