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238 lines
8.2 KiB
C
238 lines
8.2 KiB
C
#include "parameters.h"
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#include "reed_muller.h"
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#include <stdint.h>
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#include <string.h>
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/**
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* @file reed_muller.c
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* Constant time implementation of Reed-Muller code RM(1,7)
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*/
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// number of repeated code words
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#define MULTIPLICITY CEIL_DIVIDE(PARAM_N2, 128)
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// copy bit 0 into all bits of a 32 bit value
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#define BIT0MASK(x) (-((x) & 1))
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static void encode(uint8_t *word, uint8_t message);
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static void hadamard(uint16_t src[128], uint16_t dst[128]);
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static void expand_and_sum(uint16_t dest[128], const uint8_t src[16 * MULTIPLICITY]);
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static uint8_t find_peaks(const uint16_t transform[128]);
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/**
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* @brief Encode a single byte into a single codeword using RM(1,7)
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*
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* Encoding matrix of this code:
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* bit pattern (note that bits are numbered big endian)
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* 0 aaaaaaaa aaaaaaaa aaaaaaaa aaaaaaaa
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* 1 cccccccc cccccccc cccccccc cccccccc
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* 2 f0f0f0f0 f0f0f0f0 f0f0f0f0 f0f0f0f0
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* 3 ff00ff00 ff00ff00 ff00ff00 ff00ff00
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* 4 ffff0000 ffff0000 ffff0000 ffff0000
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* 5 ffffffff 00000000 ffffffff 00000000
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* 6 ffffffff ffffffff 00000000 00000000
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* 7 ffffffff ffffffff ffffffff ffffffff
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*
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* @param[out] word An RM(1,7) codeword
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* @param[in] message A message
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*/
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static void encode(uint8_t *word, uint8_t message) {
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uint32_t e;
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// bit 7 flips all the bits, do that first to save work
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e = BIT0MASK(message >> 7);
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// bits 0, 1, 2, 3, 4 are the same for all four longs
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// (Warning: in the bit matrix above, low bits are at the left!)
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e ^= BIT0MASK(message >> 0) & 0xaaaaaaaa;
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e ^= BIT0MASK(message >> 1) & 0xcccccccc;
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e ^= BIT0MASK(message >> 2) & 0xf0f0f0f0;
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e ^= BIT0MASK(message >> 3) & 0xff00ff00;
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e ^= BIT0MASK(message >> 4) & 0xffff0000;
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// we can store this in the first quarter
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word[0 + 0] = (e >> 0x00) & 0xff;
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word[0 + 1] = (e >> 0x08) & 0xff;
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word[0 + 2] = (e >> 0x10) & 0xff;
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word[0 + 3] = (e >> 0x18) & 0xff;
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// bit 5 flips entries 1 and 3; bit 6 flips 2 and 3
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e ^= BIT0MASK(message >> 5);
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word[4 + 0] = (e >> 0x00) & 0xff;
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word[4 + 1] = (e >> 0x08) & 0xff;
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word[4 + 2] = (e >> 0x10) & 0xff;
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word[4 + 3] = (e >> 0x18) & 0xff;
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e ^= BIT0MASK(message >> 6);
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word[12 + 0] = (e >> 0x00) & 0xff;
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word[12 + 1] = (e >> 0x08) & 0xff;
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word[12 + 2] = (e >> 0x10) & 0xff;
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word[12 + 3] = (e >> 0x18) & 0xff;
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e ^= BIT0MASK(message >> 5);
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word[8 + 0] = (e >> 0x00) & 0xff;
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word[8 + 1] = (e >> 0x08) & 0xff;
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word[8 + 2] = (e >> 0x10) & 0xff;
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word[8 + 3] = (e >> 0x18) & 0xff;
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}
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/**
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* @brief Hadamard transform
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*
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* Perform hadamard transform of src and store result in dst
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* src is overwritten: it is also used as intermediate buffer
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* Method is best explained if we use H(3) instead of H(7):
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*
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* The routine multiplies by the matrix H(3):
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* [1 1 1 1 1 1 1 1]
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* [1 -1 1 -1 1 -1 1 -1]
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* [1 1 -1 -1 1 1 -1 -1]
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* [a b c d e f g h] * [1 -1 -1 1 1 -1 -1 1] = result of routine
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* [1 1 1 1 -1 -1 -1 -1]
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* [1 -1 1 -1 -1 1 -1 1]
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* [1 1 -1 -1 -1 -1 1 1]
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* [1 -1 -1 1 -1 1 1 -1]
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* You can do this in three passes, where each pass does this:
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* set lower half of buffer to pairwise sums,
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* and upper half to differences
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* index 0 1 2 3 4 5 6 7
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* input: a, b, c, d, e, f, g, h
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* pass 1: a+b, c+d, e+f, g+h, a-b, c-d, e-f, g-h
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* pass 2: a+b+c+d, e+f+g+h, a-b+c-d, e-f+g-h, a+b-c-d, e+f-g-h, a-b-c+d, e-f-g+h
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* pass 3: a+b+c+d+e+f+g+h a+b-c-d+e+f-g-h a+b+c+d-e-f-g-h a+b-c-d-e+-f+g+h
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* a-b+c-d+e-f+g-h a-b-c+d+e-f-g+h a-b+c-d-e+f-g+h a-b-c+d-e+f+g-h
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* This order of computation is chosen because it vectorises well.
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* Likewise, this routine multiplies by H(7) in seven passes.
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*
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* @param[out] src Structure that contain the expanded codeword
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* @param[out] dst Structure that contain the expanded codeword
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*/
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static void hadamard(uint16_t src[128], uint16_t dst[128]) {
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// the passes move data:
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// src -> dst -> src -> dst -> src -> dst -> src -> dst
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// using p1 and p2 alternately
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uint16_t *p1 = src;
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uint16_t *p2 = dst;
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uint16_t *p3;
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for (uint32_t pass = 0; pass < 7; pass++) {
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for (uint32_t i = 0; i < 64; i++) {
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p2[i] = p1[2 * i] + p1[2 * i + 1];
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p2[i + 64] = p1[2 * i] - p1[2 * i + 1];
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}
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// swap p1, p2 for next round
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p3 = p1;
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p1 = p2;
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p2 = p3;
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}
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}
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/**
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* @brief Add multiple codewords into expanded codeword
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*
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* Accesses memory in order
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* Note: this does not write the codewords as -1 or +1 as the green machine does
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* instead, just 0 and 1 is used.
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* The resulting hadamard transform has:
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* all values are halved
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* the first entry is 64 too high
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*
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* @param[out] dest Structure that contain the expanded codeword
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* @param[in] src Structure that contain the codeword
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*/
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static void expand_and_sum(uint16_t dest[128], const uint8_t src[16 * MULTIPLICITY]) {
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size_t part, bit, copy;
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// start with the first copy
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for (part = 0; part < 16; part++) {
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for (bit = 0; bit < 8; bit++) {
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dest[part * 8 + bit] = (uint16_t) ((src[part] >> bit) & 1);
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}
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}
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// sum the rest of the copies
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for (copy = 1; copy < MULTIPLICITY; copy++) {
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for (part = 0; part < 16; part++) {
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for (bit = 0; bit < 8; bit++) {
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dest[part * 8 + bit] += (uint16_t) ((src[16 * copy + part] >> bit) & 1);
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}
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}
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}
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}
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/**
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* @brief Finding the location of the highest value
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*
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* This is the final step of the green machine: find the location of the highest value,
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* and add 128 if the peak is positive
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* if there are two identical peaks, the peak with smallest value
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* in the lowest 7 bits it taken
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* @param[in] transform Structure that contain the expanded codeword
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*/
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static uint8_t find_peaks(const uint16_t transform[128]) {
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uint16_t peak_abs = 0;
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uint16_t peak = 0;
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uint16_t pos = 0;
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uint16_t t, abs, mask;
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for (uint16_t i = 0; i < 128; i++) {
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t = transform[i];
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abs = t ^ ((-(t >> 15)) & (t ^ -t)); // t = abs(t)
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mask = -(((uint16_t)(peak_abs - abs)) >> 15);
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peak ^= mask & (peak ^ t);
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pos ^= mask & (pos ^ i);
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peak_abs ^= mask & (peak_abs ^ abs);
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}
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pos |= 128 & ((peak >> 15) - 1);
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return (uint8_t) pos;
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}
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/**
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* @brief Encodes the received word
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*
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* The message consists of N1 bytes each byte is encoded into PARAM_N2 bits,
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* or MULTIPLICITY repeats of 128 bits
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*
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* @param[out] cdw Array of size VEC_N1N2_SIZE_64 receiving the encoded message
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* @param[in] msg Array of size VEC_N1_SIZE_64 storing the message
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*/
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void PQCLEAN_HQCRMRS192_CLEAN_reed_muller_encode(uint8_t *cdw, const uint8_t *msg) {
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for (size_t i = 0; i < VEC_N1_SIZE_BYTES; i++) {
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// encode first word
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encode(&cdw[16 * i * MULTIPLICITY], msg[i]);
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// copy to other identical codewords
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for (size_t copy = 1; copy < MULTIPLICITY; copy++) {
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memcpy(&cdw[16 * i * MULTIPLICITY + 16 * copy], &cdw[16 * i * MULTIPLICITY], 16);
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}
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}
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}
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/**
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* @brief Decodes the received word
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*
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* Decoding uses fast hadamard transform, for a more complete picture on Reed-Muller decoding, see MacWilliams, Florence Jessie, and Neil James Alexander Sloane.
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* The theory of error-correcting codes codes @cite macwilliams1977theory
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*
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* @param[out] msg Array of size VEC_N1_SIZE_64 receiving the decoded message
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* @param[in] cdw Array of size VEC_N1N2_SIZE_64 storing the received word
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*/
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void PQCLEAN_HQCRMRS192_CLEAN_reed_muller_decode(uint8_t *msg, const uint8_t *cdw) {
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uint16_t expanded[128];
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uint16_t transform[128];
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for (size_t i = 0; i < VEC_N1_SIZE_BYTES; i++) {
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// collect the codewords
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expand_and_sum(expanded, &cdw[16 * i * MULTIPLICITY]);
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// apply hadamard transform
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hadamard(expanded, transform);
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// fix the first entry to get the half Hadamard transform
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transform[0] -= 64 * MULTIPLICITY;
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// finish the decoding
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msg[i] = find_peaks(transform);
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}
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}
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