<!DOCTYPE html>
<html>
<head>
<meta charset="UTF-8">
<title>ECC Decode Tool (k⁻¹ · C)</title>
<style>
body {
font-family: Arial, sans-serif;
background: #f0f0f0;
padding: 20px;
}
.box {
background: white;
padding: 15px;
border-radius: 8px;
margin-bottom: 20px;
box-shadow: 0 0 5px rgba(0,0,0,0.1);
}
input {
width: 100%;
padding: 8px;
margin-top: 5px;
margin-bottom: 10px;
border-radius: 5px;
border: 1px solid #aaa;
}
button {
padding: 10px 20px;
background: #0078ff;
color: white;
border: none;
border-radius: 5px;
cursor: pointer;
}
button:hover { background: #005fcc; }
pre {
background: #222;
color: #0f0;
padding: 10px;
border-radius: 5px;
overflow-x: auto;
}
</style>
</head>
<body>
<h2>ECC Decode Tool — Compute P = k⁻¹ · C</h2>
<div class="box">
<label>C.x:</label>
<input id="cx" type="text">
<label>C.y
<label>Scalar k:</label>
<input id="k" type="number">
<button onclick="decodeECC()">Decode</button>
</div>
<div class="box">
<h3>Decoded Output</h3>
<pre id="output"></pre>
</div>
<script>
// secp256k1 parameters
const p = BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F");
const n = BigInt("0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
// Point class
class Point {
constructor(x, y) { this.x = x; this.y = y; }
}
// Modular exponentiation
function modPow(base, exp, mod) {
let r = 1n;
base %= mod;
while (exp > 0) {
if (exp & 1n) r = (r * base) % mod;
base = (base * base) % mod;
exp >>= 1n;
}
return r;
}
// Modular inverse
function modInv(a, m) {
return modPow(a, m - 2n, m);
}
// Point addition
function pointAdd(P, Q) {
if (P === null) return null) return P;
if (P.x === Q.x && P.y !== Q.y) return null;
let m;
if (P.x === Q.x && P.y === Q.y) {
m = (3n * P.x * P.x) * modInv(2n * P.y, p) % p;
} else {
m = (Q.y - P.y) * modInv(Q.x - P.x, p) % p;
}
const rx = (m*m - P.x - Q.x) % p;
const ry = (m*(P.x - rx) - P.y) % p;
return new Point((rx+p)%p, (ry+p)%p);
}
// Scalar multiplication
function scalarMult(k, P) {
let R = null;
let A = P;
while (k > 0n) {
if (k & 1n) R = pointAdd(R, A);
A = pointAdd(A, A);
k >>= 1n;
}
return R;
}
// Convert integer → text
function intToText(x) {
let hex = x.toString(16);
if (hex.length % 2) hex = "0" + hex;
let bytes = new Uint8Array(hex.match(/.{1,2}/g).map(b => parseInt(b,16)));
return new TextDecoder().decode(bytes);
}
// Main decode function
function decodeECC() {
const cx = BigInt(document.getElementById("cx").value);
const cy = BigInt(document.getElementById("cy").value);
const k = BigInt(document.getElementById("k").value);
const C = new Point(cx, cy);
const k_inv = modInv(k, n);
const P = scalarMult(k_inv, C);
let recovered = "";
try { recovered = intToText(P.x); }
catch { recovered = "(invalid UTF‑8 data)"; }
document.getElementById("output").textContent =
"k⁻¹ mod n:\n" + k_inv + "\n\n" +
"Decoded point P:\n" + JSON.stringify(P, null, 2) + "\n\n" +
"Recovered message:\n" + recovered;
}
</script>
</body>
</html>
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