Published
Edited
Jun 20, 2020
md`# RenVM exploration - Shamir's Secret Sharing test`
{
var sh = split(33, 5, 3);
sh[1][1] += 2;
sh[3][1] += 2;
sh[4][1] += 2;
// sh[1][1] *= 2;
// sh[3][1] *= 2;
// sh[4][1] *= 2;
var newshares = [sh[1], sh[3], sh[4]];
return join(newshares);
}
prime = 9846517
/* Split number into the shares */
function split(number, available, needed) {
var coef = [number, 166, 94],
x,
exp,
c,
accum,
shares = [];
/* Normally, we use the line:*/
for (c = 1, coef[0] = number; c < needed; c++)
coef[c] = Math.floor(Math.random() * (prime - 1));
//* where (prime - 1) is the maximum allowable value.
//* However, to follow this example, we hardcode the values:
//* coef = [number, 166, 94];
//* For production, replace the hardcoded value with the random loop
/* For each share that is requested to be available, run through the formula plugging the corresponding coefficient
* The result is f(x), where x is the byte we are sharing (in the example, 1234)
*/
for (x = 1; x <= available; x++) {
/* coef = [1234, 166, 94] which is 1234x^0 + 166x^1 + 94x^2 */
for (exp = 1, accum = coef[0]; exp < needed; exp++)
accum =
(accum + ((coef[exp] * (Math.pow(x, exp) % prime)) % prime)) % prime;
/* Store values as (1, 132), (2, 66), (3, 188), (4, 241), (5, 225) (6, 140) */
shares[x - 1] = [x, accum];
}
return shares;
}
/* Join the shares into a number */
function join(shares) {
var accum, count, formula, startposition, nextposition, value, numerator, denominator;
for(formula = accum = 0; formula < shares.length; formula++) {
/* Multiply the numerator across the top and denominators across the bottom to do Lagrange's interpolation
* Result is x0(2), x1(4), x2(5) -> -4*-5 and (2-4=-2)(2-5=-3), etc for l0, l1, l2...
*/
for(count = 0, numerator = denominator = 1; count < shares.length; count++) {
if(formula == count) continue; // If not the same value
startposition = shares[formula][0];
nextposition = shares[count][0];
numerator = (numerator * -nextposition) % prime;
denominator = (denominator * (startposition - nextposition)) % prime;
}
value = shares[formula][1];
accum = (prime + accum + (value * numerator * modInverse(denominator))) % prime;
}
return accum;
}
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