Add Example for Shamir's Secret Sharing

examples/_data.ts

@@ -696,7 +696,7 @@ export const sidebar = [
     ],
   },
   {
-    title: "Crypotography",
+    title: "Cryptography",
     items: [
       {
         label: "Generating & validating UUIDs",

examples/scripts/sss.ts

@@ -0,0 +1,100 @@
+/**
+ * @title Shamir's Secret Sharing Implementation
+ * @difficulty intermediate
+ * @tags cli
+ * @run <url>
+ * @group Cryptography
+ *
+ * This example demonstrates Shamir's Secret Sharing, where a secret, split into shares, allows its
+ * reconstruction only when a sufficient number of shares are combined.
+ */
+
+// Random Number Generation within a range
+async function getSecureRandom(min: number, max: number): Promise<number> {
+  const range = max - min;
+  const buffer = new Uint8Array(4);
+  crypto.getRandomValues(buffer);
+  const randomValue = new DataView(buffer.buffer).getUint32(0);
+  return min + (randomValue % range);
+}
+
+// Finding the value of the polynomial at x
+function evaluatePolynomial(coefficients: number[], x: number): number {
+  return coefficients.reduce(
+    (result, coeff, power) => result + coeff * Math.pow(x, power),
+    0,
+  );
+}
+
+// Generates shares based on the secret and threshold
+async function generateShares(
+  secret: number,
+  totalShares: number,
+  threshold: number,
+) {
+  // Generate random coefficients for the polynomial
+  const coefficients = [secret];
+  for (let i = 1; i < threshold; i++) {
+    coefficients.push(await getSecureRandom(1, 1000));
+  }
+
+  const usedXValues = new Set<number>();
+  const shares = [];
+
+  // Generate unique random x values for shares
+  while (shares.length < totalShares) {
+    const x = await getSecureRandom(1, 1000);
+    if (!usedXValues.has(x)) {
+      usedXValues.add(x);
+      shares.push({
+        x,
+        y: evaluatePolynomial(coefficients, x),
+      });
+    }
+  }
+
+  return { shares, coefficients };
+}
+
+// Secret Reconstuction from a subset of shares using Lagrange interpolation
+function reconstructSecret(shares: Array<{ x: number; y: number }>): number {
+  const secret = shares.reduce((sum, share, i) => {
+    let product = share.y;
+    for (let j = 0; j < shares.length; j++) {
+      if (i !== j) {
+        product *= shares[j].x / (shares[j].x - share.x);
+      }
+    }
+    return sum + product;
+  }, 0);
+
+  return Math.round(secret);
+}
+
+const secret = 12345;
+const totalShares = 5;
+const threshold = 3;
+
+// Generate shares
+const { shares, coefficients } = await generateShares(
+  secret,
+  totalShares,
+  threshold,
+);
+console.log("Generated Shares:", shares);
+
+// Select random subset of shares to reconstruct the secret
+const selectedIndices = new Set<number>();
+while (selectedIndices.size < threshold) {
+  selectedIndices.add(await getSecureRandom(0, totalShares));
+}
+
+const selectedShares = Array.from(selectedIndices).map((index) =>
+  shares[index]
+);
+console.log("Selected Shares for Reconstruction:", selectedShares);
+
+// Reconstruct the secret
+const reconstructedSecret = reconstructSecret(selectedShares);
+console.log("Original Secret:", secret);
+console.log("Reconstructed Secret:", reconstructedSecret);