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88 lines
2.3 KiB
C
88 lines
2.3 KiB
C
/* Melas forward error correction, reference code (as implemented in the paper) */
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#include "melas_fec.h"
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/* Return s/2^n mod R */
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static fec_gf_t step(size_t n, fec_gf_t R, fec_gf_t s) {
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for (; n; n--) {
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s = (s ^ ((s & 1) * R)) >> 1;
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}
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return s;
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}
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/* Compute syndrome(data), where data has length len */
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#define syndrome18(data,len) s18update(0,data,len)
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static fec_gf_t s18update(fec_gf_t r, const uint8_t *data, size_t len) {
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for (size_t i = 0; i < len; i++) {
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r = step(8, 0x46231, r ^ data[i]);
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}
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return r;
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}
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/* Append 3 bytes of FEC(data) to data, so that the FEC becomes 0 */
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void PQCLEAN_PAPABEAR_CLEAN_melas_fec_set(
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uint8_t out[MELAS_FEC_BYTES],
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const uint8_t *data,
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size_t len
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) {
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fec_gf_t fec = syndrome18(data, len);
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for (size_t i = 0; i < MELAS_FEC_BYTES; i++, fec >>= 8) {
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out[i] = (uint8_t)fec;
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}
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}
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/* Return a*b mod Q */
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static fec_gf_t mul(fec_gf_t a, fec_gf_t b) {
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fec_gf_t r = 0;
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for (size_t i = 0; i < 9; i++) {
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r ^= ((b >> (8 - i)) & 1) * a;
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a = step(1, Q, a);
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}
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return r;
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}
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/* Reverse an 18-bit number x */
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static fec_gf_t reverse18(fec_gf_t x) {
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fec_gf_t ret = 0;
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for (size_t i = 0; i < 18; i++) {
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ret ^= ((x >> i) & 1) << (17 - i);
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}
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return ret;
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}
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/* Correct data to have the given FEC */
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void PQCLEAN_PAPABEAR_CLEAN_melas_fec_correct (
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uint8_t *data,
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size_t len,
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const uint8_t fec[MELAS_FEC_BYTES]
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) {
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fec_gf_t a = s18update(syndrome18(data, len), fec, MELAS_FEC_BYTES);
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fec_gf_t c, r, htr;
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size_t i;
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const uint8_t table[9] = {36, 10, 43, 215, 52, 11, 116, 244, 0};
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fec_gf_t e0, e1;
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/* Form a quadratic equation from the syndrome */
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c = mul(step(9, Q, a), step(9, Q, reverse18(a)));
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for (i = 0, r = 0x100; i < 510; i++) {
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r = mul(r, c);
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}
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r = step(17, Q, r);
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a = step(511 - (len + MELAS_FEC_BYTES) * 8, Q, a);
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/* Solve using the half trace */
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for (i = 0, htr = 0; i < 9; i++) {
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htr ^= ((r >> i) & 1) * table[i];
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}
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e0 = mul(a, htr);
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e1 = e0 ^ a;
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/* Correct the errors using the locators */
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for (i = 0; i < len; i++) {
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data[i] ^= (uint8_t)(e0 & (((e0 & (e0 - 1)) - 1) >> 9));
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data[i] ^= (uint8_t)(e1 & (((e1 & (e1 - 1)) - 1) >> 9));
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e0 = step(8, Q, e0);
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e1 = step(8, Q, e1);
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}
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}
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