I try to use shamir secret sharing. I implement the code that I find in wikipedia. But when I run it, for enormous numbers the result of reconstruction is different from the real secret value.
https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing
The reconstruction function is:
function join(shares) {
var accum, count, formula, startposition, nextposition, value, numerator, denominator;
for(formula = accum = 0; formula < shares.length; formula++) {
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;
}
var sh = split(9846513, 5, 3)
var newshares = [sh[1], sh[3], sh[4]];
document.write(join(newshares));
</script>
When I try to run this code, instead of 9846513
the result is 761
.
Can someone help me to fix this logical error?