303 lines
9.8 KiB
C
303 lines
9.8 KiB
C
#include <assert.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <string.h>
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void xxtea128(uint32_t const key[4], uint32_t block[4]) {
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// Encryption half of the XXTEA algorithm, with block size limited
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// to 128 bits or 4 words. This avoids all the weaknesses that
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// Wikipedia knows of, since both depend on only running 6 rounds
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// per block, and we will run 6 + 52//4 = 6 + 13 = 19
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uint32_t roundconstant = 0;
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for (unsigned round = 0; round < 19; round++) {
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// This took a while to puzzle out since the original
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// specification is a mess, and the mess is only added to
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// by needing to support custom blockwidths.
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//
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// The algorithm is as follows:
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//
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// 1. Set the round constant (sum) to round * 0x9e3779b9
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// (implemented by addition)
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//
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// 2. Create a reduced version of the round constant (e)
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// which is the bits 3…2 of the round constant. The
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// reduced version is needed for changing the pattern of
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// key accesses, since key is only 4 words long
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//
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// 3. Go through each word in the block and derive its new
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// value based on its current value (v[p]), the next (y)
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// and the previous word (z), wrapping around the ends
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// of the block as needed.
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//
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// The function for deriving the new value of a word is a
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// xor of sums of xors, followed by an in-place addition.
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// The first sum adds together combinations of the next and
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// previous word, and the second sum adds together
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// previous/next combined with a value dependant on the
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// round constant. The key is also mixed into the word in
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// the first xor of second sum. After this the result is
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// added back into the original word.
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//
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// I have changed the operand order in the second xor of
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// first add and in the second add. This is to keep the
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// part dependant of previous word on the left and the part
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// dependant on the next word on the right.
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roundconstant += 0x9e3779b9;
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uint32_t reduced = (roundconstant >> 2) & 3;
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block[0] += ((block[3]>>5 ^ block[1]<<2) + (block[3]<<4 ^ block[1]>>3)) ^ ((key[reduced ^ 0] ^ block[3]) + (roundconstant ^ block[1]));
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block[1] += ((block[0]>>5 ^ block[2]<<2) + (block[0]<<4 ^ block[2]>>3)) ^ ((key[reduced ^ 1] ^ block[0]) + (roundconstant ^ block[2]));
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block[2] += ((block[1]>>5 ^ block[3]<<2) + (block[1]<<4 ^ block[3]>>3)) ^ ((key[reduced ^ 2] ^ block[1]) + (roundconstant ^ block[3]));
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block[3] += ((block[2]>>5 ^ block[0]<<2) + (block[2]<<4 ^ block[0]>>3)) ^ ((key[reduced ^ 3] ^ block[2]) + (roundconstant ^ block[0]));
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}
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}
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uint32_t bytes2word(unsigned char const bytes[4]) {
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return bytes[0] | bytes[1]<<8 | bytes[2]<<16 | bytes[3]<<24;
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}
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void word2bytes(unsigned char *bytes, uint32_t word) {
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bytes[0] = word;
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bytes[1] = word>>8;
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bytes[2] = word>>16;
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bytes[3] = word>>24;
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}
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struct hashstate {
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// A_n and B_n of the MDC-2 algorithm
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uint32_t a[4];
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uint32_t b[4];
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// Buffer to hold data until next full block
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unsigned char buffer[16];
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size_t length;
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// Counter that keeps tracks of how much data we've hashed
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uint64_t totalbits;
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};
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void initialize_hash(struct hashstate *state) {
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// Hash function is MDC-2 with xxtea128, which is nice since it
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// gives us a 256 bit hash. The constants are based on binary
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// expansion of the square root of two, A1 being the first 128 bits
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// and B1 the next 128.
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//
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// If we treat A1 and B1 as 128bit little endian integers, they
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// have the values:
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//
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// A1 = 6a09e667 f3bcc908 b2fb1366 ea957d3e
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// A2 = 3adec175 12775099 da2f590b 0667322a
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state->a[0] = 0xea957d3eUL;
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state->a[1] = 0xb2fb1366UL;
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state->a[2] = 0xf3bcc908UL;
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state->a[3] = 0x6a09e667UL;
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state->b[0] = 0x0667322aUL;
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state->b[1] = 0xda2f590bUL;
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state->b[2] = 0x12775099UL;
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state->b[3] = 0x3adec175UL;
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memset(state->buffer, 0, sizeof(state->buffer));
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state->length = 0;
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state->totalbits = 0;
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}
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void compress_hash(struct hashstate *state) {
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assert(state->length == 16);
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// M_i
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uint32_t message[4];
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message[0] = bytes2word(&state->buffer[0]);
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message[1] = bytes2word(&state->buffer[4]);
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message[2] = bytes2word(&state->buffer[8]);
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message[3] = bytes2word(&state->buffer[12]);
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// V_i = M_i ^ E(M_i, A_i)
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// Note: In this description A_i is the *key*, not the plaintext
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uint32_t v[4];
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memcpy(v, message, sizeof(v));
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xxtea128(state->a, v);
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v[0] ^= message[0];
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v[1] ^= message[1];
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v[2] ^= message[2];
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v[3] ^= message[3];
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// W_i = M_i ^ E(M_i, B_i);
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uint32_t w[4];
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memcpy(w, message, sizeof(w));
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xxtea128(state->b, w);
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w[0] ^= message[0];
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w[1] ^= message[1];
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w[2] ^= message[2];
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w[3] ^= message[3];
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// A_{i+1} = Vwi^L || W_i^R
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state->a[0] = v[0];
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state->a[1] = v[1];
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state->a[2] = w[2];
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state->a[3] = w[3];
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// B_{i+1} = W_i^L || V_i^R
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state->b[0] = w[0];
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state->b[1] = w[1];
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state->b[2] = v[2];
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state->b[3] = v[3];
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// Mark that we have consumed the buffer
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state->length = 0;
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}
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void feed_hash(struct hashstate *state, unsigned char input[], size_t length) {
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// Invariant: The buffer will be filled somewhere between 0 and 15
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// when we enter this loop. This is because once it reaches 16, the
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// hash compression function is executed.
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for (size_t i = 0; i < length; i++) {
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// Must not overflow the internat counter. In practice we will not
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// hit this.
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assert(state->totalbits <= UINT64_MAX - 8);
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state->buffer[state->length++] = input[i];
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state->totalbits += 8;
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if (state->length == 16) {
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compress_hash(state);
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}
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}
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}
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void finalize_hash(struct hashstate *state, unsigned char hash[32]) {
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// Feed the padding. It consists of one-bit, followed by zero-bits,
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// followed by the number of bits in the message as big-endian
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// uint64. This is the same padding as in SHA-2.
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// We can assume that this works due to the invariant that buffer
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// fill when entering this function is between 0 and 15
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state->buffer[state->length++] = 0x80;
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while(state->length != 8) {
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if (state->length == 16) {
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compress_hash(state);
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}
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state->buffer[state->length++] = 0;
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}
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// Add the number of bits, and do one last compression
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state->buffer[8] = state->totalbits >> 56;
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state->buffer[9] = state->totalbits >> 48;
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state->buffer[10] = state->totalbits >> 40;
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state->buffer[11] = state->totalbits >> 32;
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state->buffer[12] = state->totalbits >> 24;
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state->buffer[13] = state->totalbits >> 16;
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state->buffer[14] = state->totalbits >> 8;
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state->buffer[15] = state->totalbits;
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state->length += 8;
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compress_hash(state);
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// Extract the hash state
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for (size_t i = 0; i < 4; i++) {
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word2bytes(&hash[i*4], state->a[i]);
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}
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for (size_t i = 0; i < 4; i++) {
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word2bytes(&hash[i*4 + 16], state->b[i]);
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}
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// Clear all of the hash state, in case there was sth important
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// there
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explicit_bzero(state, sizeof(struct hashstate));
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}
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void hmac(unsigned char output[32], unsigned char key[], size_t keylen, unsigned char message[], size_t messagelen) {
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// The blocksize of the underlying has function is 128 bits (16B)
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// but HMAC is specified assuming that the hash function output (in
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// our case 256 bits or 32B) fits in one block. As far as I can
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// tell extending the key to be two blocks long is not a problem.
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unsigned char padded_key[32];
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if (keylen > 16) {
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// We hash it even if it is shorter than our extended key
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// length to avoid giving attacker any funny surfaces to
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// play with at the interface of two blocks
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struct hashstate state;
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initialize_hash(&state);
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feed_hash(&state, key, keylen);
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finalize_hash(&state, padded_key);
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} else {
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// Copy the key and zero-pad if necessary
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memset(padded_key, 0, 32);
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memcpy(padded_key, key, keylen);
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}
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// Outer and inner key derivation
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unsigned char outer_key[32], inner_key[32];
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for (size_t i = 0; i < 32; i++) {
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outer_key[i] = padded_key[i] ^ 0x5c;
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inner_key[i] = padded_key[i] ^ 0x36;
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}
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// Inner hash
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unsigned char inner_hash[32];
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struct hashstate state;
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initialize_hash(&state);
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feed_hash(&state, inner_key, 32);
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feed_hash(&state, message, messagelen);
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finalize_hash(&state, inner_hash);
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// Outer hash
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initialize_hash(&state);
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feed_hash(&state, outer_key, 32);
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feed_hash(&state, inner_hash, 32);
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finalize_hash(&state, output);
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}
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// KDF_ROUNDS must be at least 2
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#define KDF_ROUNDS 100000
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unsigned char kdf_buf[KDF_ROUNDS * 32];
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void kdf(unsigned char key[16], unsigned char salt[32], unsigned char passphrase[], size_t passphraselen) {
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// This is based on the design of PBKDF2 but aims to be memory hard
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// This is achieved by storing all the hashes in a buffer and the
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// in the end hashing them together in reverse order, instead of
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// just xoring together.
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//
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// The memory-hardness of this scheme rests of the assumption that
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// it is not feasible to compute the final hash backwards, that is,
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// starting with the first hash and working towards the final hash.
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// While I cannot prove this to be the case, the fact that our hash
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// is made out of a one-way compression function makes me
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// relatively confident in it.
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// Place the hash of the salt at the top of the buffer. We do not
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// include the counter i from PBKDF2 since we will ever only
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// produce one block of output
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size_t index = KDF_ROUNDS*32 - 32;
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hmac(&kdf_buf[index], passphrase, passphraselen, salt, 32);
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index -= 32;
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// Walk back along the buffer, at each step hashing the previous
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// hashes
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while (index > 0) {
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hmac(&kdf_buf[index], passphrase, passphraselen, &kdf_buf[index+32], 32);
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index -= 32;
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}
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hmac(kdf_buf, passphrase, passphraselen, &kdf_buf[32], 32);
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// Perform the final hash
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unsigned char final_hash[32];
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hmac(final_hash, passphrase, passphraselen, kdf_buf, KDF_ROUNDS * 32);
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// Use first 128 bits of final hash as the key
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memcpy(key, final_hash, 16);
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}
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int main(void) {
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unsigned char key[16] = {0};
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unsigned char salt[32] = "seasaltrocksalt seasaltrocksalt";
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unsigned char passphrase[] = "a quick brown fox jumps over the lazy dog";
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kdf(key, salt, passphrase, sizeof(passphrase) - 1);
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for (size_t i = 0; i < 16; i++) {
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printf("%02hhx ", key[i]);
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}
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printf("\n");
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return 0;
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}
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