shamir-sharing.js

const β = require('bignumber.js');

function Ω(a, m) {
  const b = new β(a).mod(m);
  for (let x = new β(1); x.lt(m); x = x.plus(1)) {
    if (b.times(x).mod(m).eq(1)) {
      return x;
    }
  }
  return new β(1);
}

function ζ(num) {
    if (num < 2) {  return false;  }
    for (let i = 2; i <= Math.sqrt(num); i++) {
      if (num % i === 0) {   return false;   }
    }
    return true;
  }

function Φ(bits) {
  const min = new β(2).pow(bits - 1);
  const max = new β(2).pow(bits).minus(1);
  while (true) {
    const num = new β(max).minus(min).times(Math.random()).plus(min);
    if (ζ(num)) {
      return num;
    }
  }
}

function Σ(µ, Θ, λ) {
  const prime = Φ(256);
  const ε = [new β(µ)];
  for (let i = 1; i < λ; i++) {
    ε.push(new β(Math.floor(Math.random() * prime.toNumber())));
  }

  const ξ = [];
  for (let i = 1; i <= Θ; i++) {
    let share = new β(0);
    for (let j = 0; j < ε.length; j++) {
      const term = ε[j].times(new β(i).pow(j));
      share = share.plus(term).mod(prime);
    }
    ξ.push({   x: i,  y: share  });
  }

  return ξ;
}

function Ξ(ξ) {
  let δ = new β(0);
  const prime = new β(ξ[0].y).c;
  for (let i = 0; i < ξ.length; i++) {
    const x_i = new β(ξ[i].x);
    const y_i = new β(ξ[i].y);
    let term = new β(1);
    for (let j = 0; j < ξ.length; j++) {
      if (j !== i) {
        const x_j = new β(ξ[j].x);
        term = term.times(x_j).dividedBy(x_j.minus(x_i));
      }
    }
    const inv = Ω(term, prime);
    δ = δ.plus(y_i.times(term).times(inv)).mod(prime);
  }
  return δ.toString();
}

// Example usage:
const µ = 4321; // secret
const Θ = 4;  
const λ = 3;

const ξ = Σ(µ, Θ, λ);
console.log('Generated shares:', ξ);

const æ = [ξ[0], ξ[3], ξ[6], ξ[9]];
const Љ = Ξ(æ);
console.log('Combined µ:', Љ);