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shamir_wrapper.c
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#include <stdint.h>
#include <assert.h>
#include <stdlib.h>
/***********************************************/
/**GALOIS**/
static uint8_t galois_exp[] = {
1,3,5,15,17,51,85,255,26,46,114,150,161,248,19,53,
95,225,56,72,216,115,149,164,247,2,6,10,30,34,102,170,
229,52,92,228,55,89,235,38,106,190,217,112,144,171,230,49,
83,245,4,12,20,60,68,204,79,209,104,184,211,110,178,205,
76,212,103,169,224,59,77,215,98,166,241,8,24,40,120,136,
131,158,185,208,107,189,220,127,129,152,179,206,73,219,118,154,
181,196,87,249,16,48,80,240,11,29,39,105,187,214,97,163,
254,25,43,125,135,146,173,236,47,113,147,174,233,32,96,160,
251,22,58,78,210,109,183,194,93,231,50,86,250,21,63,65,
195,94,226,61,71,201,64,192,91,237,44,116,156,191,218,117,
159,186,213,100,172,239,42,126,130,157,188,223,122,142,137,128,
155,182,193,88,232,35,101,175,234,37,111,177,200,67,197,84,
252,31,33,99,165,244,7,9,27,45,119,153,176,203,70,202,
69,207,74,222,121,139,134,145,168,227,62,66,198,81,243,14,
18,54,90,238,41,123,141,140,143,138,133,148,167,242,13,23,
57,75,221,124,132,151,162,253,28,36,108,180,199,82,246,1
};
static uint8_t galois_log[] = {
0,0,25,1,50,2,26,198,75,199,27,104,51,238,223,3,100,
4,224,14,52,141,129,239,76,113,8,200,248,105,28,193,125,
194,29,181,249,185,39,106,77,228,166,114,154,201,9,120,101,
47,138,5,33,15,225,36,18,240,130,69,53,147,218,142,150,
143,219,189,54,208,206,148,19,92,210,241,64,70,131,56,102,
221,253,48,191,6,139,98,179,37,226,152,34,136,145,16,126,
110,72,195,163,182,30,66,58,107,40,84,250,133,61,186,43,
121,10,21,155,159,94,202,78,212,172,229,243,115,167,87,175,
88,168,80,244,234,214,116,79,174,233,213,231,230,173,232,44,
215,117,122,235,22,11,245,89,203,95,176,156,169,81,160,127,
12,246,111,23,196,73,236,216,67,31,45,164,118,123,183,204,
187,62,90,251,96,177,134,59,82,161,108,170,85,41,157,151,
178,135,144,97,190,220,252,188,149,207,205,55,63,91,209,83,
57,132,60,65,162,109,71,20,42,158,93,86,242,211,171,68,
17,146,217,35,32,46,137,180,124,184,38,119,153,227,165,103,
74,237,222,197,49,254,24,13,99,140,128,192,247,112,7
};
static uint8_t galois_add(uint8_t a, uint8_t b) {
return a ^ b;
}
static uint8_t galois_diff(uint8_t a, uint8_t b) {
return a ^ b;
}
static uint8_t galois_mul(uint8_t a, uint8_t b) {
if(a==0 || b==0)
return 0;
uint8_t ans_log = ((uint16_t)galois_log[a] + (uint16_t)galois_log[b])%255;
return galois_exp[ans_log];
}
static uint8_t galois_div(uint8_t a, uint8_t b) {
assert(b!=0);
uint8_t ans_log = ((uint16_t)galois_log[a] + (uint16_t)(255 - galois_log[b]))%255;
return galois_exp[ans_log];
}
static uint8_t galois_pow(uint8_t a, uint16_t p) {
uint8_t ans_log = ((uint32_t)galois_log[a] * (uint32_t)p)%255;
return galois_exp[ans_log];
}
/***********************************************/
static int GetOneRandomNumber() {
return rand();
}
static void FillRandomVectorInARange(uint16_t arr_size, uint8_t arr[arr_size], uint8_t l, uint8_t h) {
for (uint16_t i = 0; i < arr_size; i++) {
arr[i] = (GetOneRandomNumber()%(h-l+1)) + l;
}
}
static uint8_t eval(uint16_t n, uint8_t coeffs[n], uint8_t x) {
// calculates coeff[0]*x^n + ... + coeff[n-2]*x^2 + coeff[n-1]*x^1
uint8_t ret = 0;
for (uint16_t i = 0; i < n; i++) {
ret = galois_add(ret, galois_mul(galois_pow(x, n-i), coeffs[i]));
}
return ret;
}
/***
*
method: convert_to_shares
memory to be allocated by client
size of shares_OUT must be shares_OUT[total_number_of_shares][secret_len]
shares_OUT's ith index will have shares corresponding to x = (i+1)
secret is considered to be corresponding to x = 0
*
***/
void convert_to_shares(
uint8_t secret_len, uint8_t secret[secret_len],
uint8_t total_number_of_shares,
uint8_t threshold_number_of_shares,
uint8_t shares_OUT[total_number_of_shares][secret_len]
) {
for (uint8_t j = 0; j < secret_len; j++) {
uint8_t coeffs[threshold_number_of_shares-1];
FillRandomVectorInARange(threshold_number_of_shares-1, coeffs, 1, 255);
for(uint8_t i = 0; i < total_number_of_shares; i++) {
shares_OUT[i][j] = galois_add(secret[j], eval(threshold_number_of_shares-1, coeffs, i+1));//galois_add(galois_mul(m, i+1), secret[j]);
}
}
}
/***
*
method: recover_secret_from_shares
memory to be allocated by client
size of secret_OUT must be equal to number_of_bytes
secret is considered to be corresponding to x = 0
*
***/
void recover_secret_from_shares(
uint8_t number_of_bytes, // visualise this as horizontal length
uint8_t num_shares, //threshold. shares is a 2D array. visualise this as vertical height
uint8_t shares[num_shares][number_of_bytes],
uint8_t x_coords[num_shares],
uint8_t secret_OUT[number_of_bytes]
) {
for (uint8_t j = 0; j < number_of_bytes; j++) {
uint8_t acc = 0; //accumulate
for (uint8_t n = 0; n < num_shares; n++) { //this 'n' is what's j in wikipedia as of 3/feb/2020
uint8_t prod = 1;
for (uint8_t m = 0; m < num_shares; m++) {
if (m == n)
continue;
uint8_t factor = galois_div(x_coords[m],
galois_diff(x_coords[m], x_coords[n]));
prod = galois_mul(prod, factor);
}
acc = galois_add(acc, galois_mul(shares[n][j], prod));
}
secret_OUT[j] = acc;
}
}
//TODO:
// void verify_shares(shares, secret); //to verify by all nCr combinations
/* LEGACY:
static void convert_to_shares_threshold_2(
uint8_t secret_len, uint8_t secret[secret_len],
uint8_t total_number_of_shares,
uint8_t shares_OUT[total_number_of_shares][secret_len]
) {
for (uint8_t j = 0; j < secret_len; j++) {
uint8_t m = 1 + (GetOneRandomNumber()%255);
for(uint8_t i = 0; i < total_number_of_shares; i++) {
shares_OUT[i][j] = galois_add(galois_mul(m, i+1), secret[j]);
}
}
}
static void recover_secret_from_shares_threshold_2(
uint8_t number_of_bytes, // visualise this as horizontal length
uint8_t shares[2][number_of_bytes],
uint8_t x[2],
uint8_t secret_OUT[number_of_bytes]
) {
for (uint8_t j = 0; j < number_of_bytes; j++) {
uint8_t m = galois_div(
galois_diff(shares[0][j], shares[1][j]),
galois_diff(x[0], x[1])
);
secret_OUT[j] = galois_diff(shares[0][j], galois_mul(m, x[0]));
}
}
*/