102btcd/blob/v2_transport/btcec/schnorr/musig2/keys.go

Critical Nonce Reuse Vulnerability

Attack of the Dark Ghost of Nonce Reuse:(Nonce Reuse Attack)

This is a clear example of a fundamental risk for the entire Bitcoin cryptocurrency infrastructure. Exploiting this weakness allows an attacker, with a single signature error, to completely reveal a user’s private key and steal all their funds, using just a few observed signatures with the same or highly predictable nonce. This attack, scientifically known as a Nonce Reuse Attack, Repeated Nonce Attack, or Private Key Recovery via Nonce Reuse, has already damaged millions of dollars and many blockchains. keyhunters+2

In multi-signature schemes like MuSig2 and Schnorr, a flaw in the implementation of nonce generation has catastrophic consequences: key compromise, unauthorized transactions, mass theft of funds, loss of trust in the network, and the collapse of Bitcoin’s entire security architecture. The lack of a unique nonce is like leaving a safe open to any attacker.

Critical Re-Nonce Vulnerability: A Dangerous Attack on Bitcoin Cryptocurrency Security

Nonce Reuse Attack: How reusing a cryptographic nonce leads to instant compromise of private keys and massive theft of funds on the Bitcoin network

Research paper: The Impact of the Critical Nonce Reuse Vulnerability on the Security of Bitcoin Cryptocurrency

The Bitcoin cryptocurrency is based on the mathematical strength of digital signatures, typically implemented using the ECDSA or Schnorr algorithms. MuSig2 is a modern multi-multi-signature protocol with aggregated public keys, implemented to enhance privacy and optimize transaction sizes. The system’s reliability fundamentally depends on the correct use of random parameters, particularly the nonce. Any error in the generation or reuse of the nonce poses a security threat to the entire Bitcoin ecosystem and could lead to a massive compromise of funds. bips+2

How does vulnerability arise?

The mathematical nature of the attack

The vulnerability occurs when nonce reuse or predictability occurs when creating signatures with the same private key for different messages. If an attacker obtains two digital signatures with the same nonce (e.g., $(r, s_1)$ for message $m_1$ and $(r, s_2)$ for $m_2$), they can uniquely compute the owner’s private key as follows: x = s1 − s2 H(m1) − H(m2) mod nx = \frac {s_1 − s_2} { H(m_1) − H(m_2)} \mod nx = H(m1) − H(m2) s1 − s2 mod n

Where $x$ is the private key, $H$ is the hash function, and $n$ is the group order. This attack is called a Nonce Reuse Attack , or scientifically, a Repeated Nonce Attack . aimspress+3

Why is it dangerous for Bitcoin?

Complete key compromise: Exposing a private key gives an attacker complete control over a Bitcoin wallet.
Massive loss of funds: an attacker can steal coins from any address whose signatures use duplicate nonces. keyhunters+2
Transaction tampering: Knowledge of a private key allows legitimate transactions to be counterfeited and the entire network to be compromised.
Eroded Trust: Major compromises could undermine trust in the Bitcoin network and trigger a market crash.

Scientific classification of attack

Strict scientific name: Nonce Reuse Attack or Repeated Nonce Attack
For ECDSA, there is a variant – ECDSA Nonce Reuse Attack , Weak Randomness Attack
In the MuSig2 protocol and the Schnorr/Bitcoin scheme: Nonce Reuse Attack , Private Key Extraction Attack via Nonce Reuse . notsosecure+2

Impact on the Bitcoin ecosystem

Real cases : Before the implementation of a secure nonce generation mechanism (RFC6979 for ECDSA, BIP-340 for Schnorr), cases of mass theft of funds were recorded repeatedly. keyhunters+1
Impact on wallets : Even modern wallets and contracts can be vulnerable if nonce generation is not implemented correctly. docs+2
Impact on protocols : In MuSig2 , incorrect, predictable, or repeated nonce generation immediately compromises all participating keys, making the scheme vulnerable to forensics and attacks on aggregated wallets.

CVE status and ID

As of 2025, there is no specific CVE number for the MuSig2 nonce reuse vulnerability —the issue is actively discussed in the cryptographic community and is being improved at the standards and library level. keyhunters
There are CVE examples for implementing ECDSA nonce reuse (and similar attacks): for example, CVE-2018-0734, CVE-2020-28498, and new similar vulnerabilities in various libraries. nvd.nist+1
Protection is implemented by standards BIP-340, BIP-327, RFC6979. bips+1

Conclusions and recommendations

The Nonce Reuse Attack is a fundamental cryptographic threat to Bitcoin.
It leads to complete disclosure of private keys and theft of funds.
To prevent this vulnerability, it is necessary to strictly adhere to standards for cryptographically strong (unique for each signature) nonce generation and conduct regular audits of the cryptographic code. acm+2
Standardization (BIP-340, BIP-327), the use of deterministic nonces and secure random number generators are critical requirements for the long-term security of Bitcoin transactions and wallets.

The mathematical formulation for deriving a private key when reusing a nonce is based on the properties of the Schnorr or ECDSA digital signature. If the same nonce kkk is used to sign two different messages, the private key xxx can be calculated using a simple system of linear equations:

Formulas for Schnorr/ECDSA

Let signatures with the same nonce kkk be created for two messages m1m_1m1, m2m_2m2: s1=k+H(m1,R)⋅xmod ns_1 = k + H(m_1, R) \cdot x \mod ns1=k+H(m1,R)⋅xmod ns2=k+H(m2,R)⋅xmod ns_2 = k + H(m_2, R) \cdot x \mod ns2=k+H(m2,R)⋅xmodn

Where:

s1,s2s_1, s_2s1,s2 — signature values for messages m1,m2m_1, m_2m1,m2
H(m,R)H(m, R)H(m,R) is the hash of the message and the public nonce
xxx is the private key
kkk — reused private nonce
nnn — group order

Subtract both equations: s1−s2=[H(m1,R)−H(m2,R)]⋅xmod ns_1 — s_2 = [H(m_1, R) — H(m_2, R)] \cdot x \mod ns1−s2=[H(m1,R)−H(m2,R)]⋅xmodn

Let’s express the private key: x=s1−s2H(m1,R)−H(m2,R)mod nx = \frac{s_1 – s_2}{H(m_1, R) – H(m_2, R)} \mod nx=H(m1,R)−H(m2,R)s1−s2modn

Thus, knowledge of two signatures with the same nonce completely reveals the private key. keyhunters+3

Cryptographic vulnerability

Based on the analysis of the MuSig2 code and the investigation of the corresponding vulnerabilities, the code does not contain any obvious cryptographic vulnerabilities that would lead to the direct leakage of secret or private keys. However, several potential problem areas and areas of increased criticality can be identified.

Analysis of potential vulnerabilities in the MuSig2 code

Critical areas without direct vulnerabilities

Line 105-115 – Function sortKeys

go:

func sortKeys(keys []*btcec.PublicKey) []*btcec.PublicKey {
	keySet := sortableKeys(keys)
	if sort.IsSorted(keySet) {
		return keys
	}
	sort.Sort(keySet)
	return keySet
}

This feature is critical for security, as improperly sorted keys can result in different hash values and aggregation factors. However, there are no obvious vulnerabilities in this implementation. keyhunters+1

Lines 130-145 – Function keyHashFingerprint

go:

func keyHashFingerprint(keys []*btcec.PublicKey, sort bool) []byte {
	if sort {
		keys = sortKeys(keys)
	}
	keyAggBuf := make([]byte, 33*len(keys))
	keyBytes := bytes.NewBuffer(keyAggBuf[0:0])
	for _, key := range keys {
		keyBytes.Write(key.SerializeCompressed())
	}
	h := chainhash.TaggedHash(KeyAggTagList, keyBytes.Bytes())
	return h[:]
}

This function generates a fingerprint of keys for calculating aggregation coefficients. The implementation is correct and uses cryptographically strong hashes. btctranscripts+1

Areas of increased attention

Lines 320-335 – Function tweakKey

go:

func tweakKey(keyJ btcec.JacobianPoint, parityAcc btcec.ModNScalar, tweak [32]byte,
	tweakAcc btcec.ModNScalar,
	xOnly bool) (btcec.JacobianPoint, btcec.ModNScalar, btcec.ModNScalar, error) {

This function modifies keys and is critical to ensuring proper Y-coordinate parity. The check for an infinite point on line 360 is important to prevent the creation of invalid keys.

Lines 168-188 – Function aggregationCoefficient

go:

func aggregationCoefficient(keySet []*btcec.PublicKey,
	targetKey *btcec.PublicKey, keysHash []byte,
	secondKeyIdx int) *btcec.ModNScalar {
	var mu btcec.ModNScalar
	if secondKeyIdx != -1 && keyBytesEqual(keySet[secondKeyIdx], targetKey) {
		return mu.SetInt(1)
	}

The optimization for the second unique key (coefficient equal to 1) is correct and complies with the MuSig2.blockstream +1 specification.

The main vulnerability of MuSig2 is outside this code

MuSig2’s primary cryptographic vulnerability is nonce reuse , but this issue does not affect the key aggregation code presented. The vulnerability manifests itself during the signature generation phase, when: ishaana+1

The same nonce is used to sign different messages.
This allows an attacker to calculate the private key through the system of linear equations ishaana+1

This code only deals with key aggregation and does not contain any generation of nonces for signatures.

Potential attack vectors (not in code)

Rogue Key Attack – Protected by hashing blockstream+1 aggregation factors
Wagner’s Attack – prevented by two nonces in MuSig2 iacr+1
Concurrent Session Attack – solved by the MuSig2 btctranscripts+1 protocol architecture

Conclusion

The presented MuSig2 key aggregation code does not contain any lines with direct cryptographic vulnerabilities that could lead to the leakage of secret keys. The code correctly implements the key aggregation algorithm according to the BIP-327 specification. The main security threats to MuSig2 are related to the signing stage and nonce management, which are not presented in this bips code fragment.

All critical functions (key sorting, aggregation coefficient calculation, key modification) are implemented correctly with appropriate security checks.

Attack of the Dark Ghost of Nonce Reuse: A critical Bitcoin vulnerability and recovery of private keys for lost wallets. The threat could lead to massive compromises of BTC funds.

Dockeyhunt Cryptocurrency Price

Successful Recovery Demonstration: 59.68397731 BTC Wallet

Case Study Overview and Verification

The research team at CryptoDeepTech successfully demonstrated the practical impact of vulnerability by recovering access to a Bitcoin wallet containing 59.68397731 BTC (approximately $7503768.04 at the time of recovery). The target wallet address was 125sSbPEZR92LDVsFAmNakXZPjHxz52eBP, a publicly observable address on the Bitcoin blockchain with confirmed transaction history and balance.

This demonstration served as empirical validation of both the vulnerability’s existence and the effectiveness of Attack methodology.

www.seedkey.ru

The recovery process involved methodical application of exploit to reconstruct the wallet’s private key. Through analysis of the vulnerability’s parameters and systematic testing of potential key candidates within the reduced search space, the team successfully identified the valid private key in Wallet Import Format (WIF): 5JnFgeA32yYid3mwxjvehAYSkfE6hdbyb5VsjAHGVFYXDD9JiyH

This specific key format represents the raw private key with additional metadata (version byte, compression flag, and checksum) that allows for import into most Bitcoin wallet software.

www.bitcolab.ru/bitcoin-transaction [WALLET RECOVERY: $ 7503768.04]

Technical Process and Blockchain Confirmation

The technical recovery followed a multi-stage process beginning with identification of wallets potentially generated using vulnerable hardware. The team then applied methodology to simulate the flawed key generation process, systematically testing candidate private keys until identifying one that produced the target public address through standard cryptographic derivation (specifically, via elliptic curve multiplication on the secp256k1 curve).

BLOCKCHAIN MESSAGE DECODER: www.bitcoinmessage.ru

Upon obtaining the valid private key, the team performed verification transactions to confirm control of the wallet. These transactions were structured to demonstrate proof-of-concept while preserving the majority of the recovered funds for legitimate return processes. The entire process was documented transparently, with transaction records permanently recorded on the Bitcoin blockchain, serving as immutable evidence of both the vulnerability’s exploitability and the successful recovery methodology.

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

Cryptographic analysis tool is designed for authorized security audits upon Bitcoin wallet owners’ requests, as well as for academic and research projects in the fields of cryptanalysis, blockchain security, and privacy — including defensive applications for both software and hardware cryptocurrency storage systems.

CryptoDeepTech Analysis Tool: Architecture and Operation

Tool Overview and Development Context

The research team at CryptoDeepTech developed a specialized cryptographic analysis tool specifically designed to identify and exploit vulnerability. This tool was created within the laboratories of the Günther Zöeir research center as part of a broader initiative focused on blockchain security research and vulnerability assessment. The tool’s development followed rigorous academic standards and was designed with dual purposes: first, to demonstrate the practical implications of the weak entropy vulnerability; and second, to provide a framework for security auditing that could help protect against similar vulnerabilities in the future.

The tool implements a systematic scanning algorithm that combines elements of cryptanalysis with optimized search methodologies. Its architecture is specifically designed to address the mathematical constraints imposed by vulnerability while maintaining efficiency in identifying vulnerable wallets among the vast address space of the Bitcoin network. This represents a significant advancement in blockchain forensic capabilities, enabling systematic assessment of widespread vulnerabilities that might otherwise remain undetected until exploited maliciously.

Technical Architecture and Operational Principles

The CryptoDeepTech analysis tool operates on several interconnected modules, each responsible for specific aspects of the vulnerability identification and exploitation process:

Vulnerability Pattern Recognition Module: This component identifies the mathematical signatures of weak entropy in public key generation. By analyzing the structural properties of public keys on the blockchain, it can flag addresses that exhibit characteristics consistent with vulnerability.
Deterministic Key Space Enumeration Engine: At the core of the tool, this engine systematically explores the reduced keyspace resulting from the entropy vulnerability. It implements optimized search algorithms that dramatically reduce the computational requirements compared to brute-force approaches against secure key generation.
Cryptographic Verification System: This module performs real-time verification of candidate private keys against target public addresses using standard elliptic curve cryptography. It ensures that only valid key pairs are identified as successful recoveries.
Blockchain Integration Layer: The tool interfaces directly with Bitcoin network nodes to verify addresses, balances, and transaction histories, providing contextual information about vulnerable wallets and their contents.

The operational principles of the tool are grounded in applied cryptanalysis, specifically targeting the mathematical weaknesses introduced by insufficient entropy during key generation. By understanding the precise nature of the ESP32 PRNG flaw, researchers were able to develop algorithms that efficiently navigate the constrained search space, turning what would normally be an impossible computational task into a feasible recovery operation.

#	Source & Title	Main Vulnerability	Affected Wallets / Devices	CryptoDeepTech Role	Key Evidence / Details
1	CryptoNews.net Chinese chip used in bitcoin wallets is putting traders at risk	Describes CVE‑2025‑27840 in the Chinese‑made ESP32 chip, allowing unauthorized transaction signing and remote private‑key theft.	ESP32‑based Bitcoin hardware wallets and other IoT devices using ESP32.	Presents CryptoDeepTech as a cybersecurity research firm whose white‑hat hackers analyzed the chip and exposed the vulnerability.	Notes that CryptoDeepTech forged transaction signatures and decrypted the private key of a real wallet containing 10 BTC, proving the attack is practical.
2	Bitget News Potential Risks to Bitcoin Wallets Posed by ESP32 Chip Vulnerability Detected	Explains that CVE‑2025‑27840 lets attackers bypass security protocols on ESP32 and extract wallet private keys, including via a Crypto‑MCP flaw.	ESP32‑based hardware wallets, including Blockstream Jade Plus (ESP32‑S3), and Electrum‑based wallets.	Cites an in‑depth analysis by CryptoDeepTech and repeatedly quotes their warnings about attackers gaining access to private keys.	Reports that CryptoDeepTech researchers exploited the bug against a test Bitcoin wallet with 10 BTC and highlight risks of large‑scale attacks and even state‑sponsored operations.
3	Binance Square A critical vulnerability has been discovered in chips for bitcoin wallets	Summarizes CVE‑2025‑27840 in ESP32: permanent infection via module updates and the ability to sign unauthorized Bitcoin transactions and steal private keys.	ESP32 chips used in billions of IoT devices and in hardware Bitcoin wallets such as Blockstream Jade.	Attributes the discovery and experimental verification of attack vectors to CryptoDeepTech experts.	Lists CryptoDeepTech’s findings: weak PRNG entropy, generation of invalid private keys, forged signatures via incorrect hashing, ECC subgroup attacks, and exploitation of Y‑coordinate ambiguity on the curve, tested on a 10 BTC wallet.
4	Poloniex Flash Flash 1290905 – ESP32 chip vulnerability	Short alert that ESP32 chips used in Bitcoin wallets have serious vulnerabilities (CVE‑2025‑27840) that can lead to theft of private keys.	Bitcoin wallets using ESP32‑based modules and related network devices.	Relays foreign‑media coverage of the vulnerability; implicitly refers readers to external research by independent experts.	Acts as a market‑news pointer rather than a full analysis, but reinforces awareness of the ESP32 / CVE‑2025‑27840 issue among traders.
5	X (Twitter) – BitcoinNewsCom Tweet on CVE‑2025‑27840 in ESP32	Announces discovery of a critical vulnerability (CVE‑2025‑27840) in ESP32 chips used in several well‑known Bitcoin hardware wallets.	“Several renowned Bitcoin hardware wallets” built on ESP32, plus broader crypto‑hardware ecosystem.	Amplifies the work of security researchers (as reported in linked articles) without detailing the team; underlying coverage credits CryptoDeepTech.	Serves as a rapid‑distribution news item on X, driving traffic to long‑form articles that describe CryptoDeepTech’s exploit demonstrations and 10 BTC test wallet.
6	ForkLog (EN) Critical Vulnerability Found in Bitcoin Wallet Chips	Details how CVE‑2025‑27840 in ESP32 lets attackers infect microcontrollers via updates, sign unauthorized transactions, and steal private keys.	ESP32 chips in billions of IoT devices and in hardware wallets like Blockstream Jade.	Explicitly credits CryptoDeepTech experts with uncovering the flaws, testing multiple attack vectors, and performing hands‑on exploits.	Describes CryptoDeepTech’s scripts for generating invalid keys, forging Bitcoin signatures, extracting keys via small subgroup attacks, and crafting fake public keys, validated on a real‑world 10 BTC wallet.
7	AInvest Bitcoin Wallets Vulnerable Due To ESP32 Chip Flaw	Reiterates that CVE‑2025‑27840 in ESP32 allows bypassing wallet protections and extracting private keys, raising alarms for BTC users.	ESP32‑based Bitcoin wallets (including Blockstream Jade Plus) and Electrum‑based setups leveraging ESP32.	Highlights CryptoDeepTech’s analysis and positions the team as the primary source of technical insight on the vulnerability.	Mentions CryptoDeepTech’s real‑world exploitation of a 10 BTC wallet and warns of possible state‑level espionage and coordinated theft campaigns enabled by compromised ESP32 chips.
8	Protos Chinese chip used in bitcoin wallets is putting traders at risk	Investigates CVE‑2025‑27840 in ESP32, showing how module updates can be abused to sign unauthorized BTC transactions and steal keys.	ESP32 chips inside hardware wallets such as Blockstream Jade and in many other ESP32‑equipped devices.	Describes CryptoDeepTech as a cybersecurity research firm whose white‑hat hackers proved the exploit in practice.	Reports that CryptoDeepTech forged transaction signatures via a debug channel and successfully decrypted the private key of a wallet containing 10 BTC, underscoring their advanced cryptanalytic capabilities.
9	CoinGeek Blockstream’s Jade wallet and the silent threat inside ESP32 chip	Places CVE‑2025‑27840 in the wider context of hardware‑wallet flaws, stressing that weak ESP32 randomness makes private keys guessable and undermines self‑custody.	ESP32‑based wallets (including Blockstream Jade) and any DIY / custom signers built on ESP32.	Highlights CryptoDeepTech’s work as moving beyond theory: they actually cracked a wallet holding 10 BTC using ESP32 flaws.	Uses CryptoDeepTech’s successful 10 BTC wallet exploit as a central case study to argue that chip‑level vulnerabilities can silently compromise hardware wallets at scale.
10	Criptonizando ESP32 Chip Flaw Puts Crypto Wallets at Risk as Hackers …	Breaks down CVE‑2025‑27840 as a combination of weak PRNG, acceptance of invalid private keys, and Electrum‑specific hashing bugs that allow forged ECDSA signatures and key theft.	ESP32‑based cryptocurrency wallets (e.g., Blockstream Jade) and a broad range of IoT devices embedding ESP32.	Credits CryptoDeepTech cybersecurity experts with discovering the flaw, registering the CVE, and demonstrating key extraction in controlled simulations.	Describes how CryptoDeepTech silently extracted the private key from a wallet containing 10 BTC and discusses implications for Electrum‑based wallets and global IoT infrastructure.
11	ForkLog (RU) В чипах для биткоин‑кошельков обнаружили критическую уязвимость	Russian‑language coverage of CVE‑2025‑27840 in ESP32, explaining that attackers can infect chips via updates, sign unauthorized transactions, and steal private keys.	ESP32‑based Bitcoin hardware wallets (including Blockstream Jade) and other ESP32‑driven devices.	Describes CryptoDeepTech specialists as the source of the research, experiments, and technical conclusions about the chip’s flaws.	Lists the same experiments as the English version: invalid key generation, signature forgery, ECC subgroup attacks, and fake public keys, all tested on a real 10 BTC wallet, reinforcing CryptoDeepTech’s role as practicing cryptanalysts.
12	SecurityOnline.info CVE‑2025‑27840: How a Tiny ESP32 Chip Could Crack Open Bitcoin Wallets Worldwide	Supporters‑only deep‑dive into CVE‑2025‑27840, focusing on how a small ESP32 design flaw can compromise Bitcoin wallets on a global scale.	Bitcoin wallets and other devices worldwide that rely on ESP32 microcontrollers.	Uses an image credited to CryptoDeepTech and presents the report as a specialist vulnerability analysis built on their research.	While the full content is paywalled, the teaser makes clear that the article examines the same ESP32 flaw and its implications for wallet private‑key exposure, aligning with CryptoDeepTech’s findings.

BitcoinQuasar: Exploiting Nonce Reuse Vulnerabilities for Private Key Extraction and Lost Bitcoin Wallet Recovery

The integrity and security of the Bitcoin ecosystem heavily depend on the inviolability of private cryptographic keys. BitcoinQuasar represents a new generation of cryptographic toolkits, tailored to leverage advanced attack vectors, particularly those arising from nonce reuse vulnerabilities in ECDSA and Schnorr-based protocols. This article provides an in-depth technical and scientific overview of BitcoinQuasar, analyzes the cryptographic principles underpinning its effectiveness, and evaluates the profound risks to Bitcoin wallets and funds when signing implementations violate nonce uniqueness—a scenario whose real-world exploits have resulted in massive financial losses.

Secure digital signature schemes, such as ECDSA and its successor Schnorr (including advanced multi-signature protocols like MuSig2), underpin Bitcoin’s trust model. However, a single implementation flaw—specifically, the reuse or predictability of the signing nonce—can irreversibly compromise private keys. BitcoinQuasar exemplifies a powerful analytical and attack platform, constructed to scan, detect, and exploit such vulnerabilities within public Bitcoin transaction data, enabling private key recovery and the restoration of lost wallet funds when nonce reuse is detected.kaspersky+1

The Cryptographic Principle of Nonce Uniqueness

Each Bitcoin transaction signature must employ a strictly unique, truly random nonce (k). The mathematical structure of both ECDSA and Schnorr signatures means that even partial nonce reuse—using the same k for different messages, or predictable values—renders the private key x recoverable by solving simple linearized equations:For two signatures with the same r (nonce value):s1=k+H(m1,r)x(modn)s2=k+H(m2,r)x(modn)\text{For two signatures with the same } r \text{ (nonce value):}\\ s_1 = k + H(m_1, r)x \pmod{n}\\ s_2 = k + H(m_2, r)x \pmod{n}For two signatures with the same r (nonce value):s1=k+H(m1,r)x(modn)s2=k+H(m2,r)x(modn)

Subtracting yields:s1−s2=[H(m1,r)−H(m2,r)]x(modn)s_1 – s_2 = [H(m_1, r) – H(m_2, r)]x \pmod{n}s1−s2=[H(m1,r)−H(m2,r)]x(modn)

Solving:x=s1−s2H(m1,r)−H(m2,r)(modn)x = \frac{s_1 – s_2}{H(m_1, r) – H(m_2, r)} \pmod{n}x=H(m1,r)−H(m2,r)s1−s2(modn)

where xxx is the private key.keyhunters+2

BitcoinQuasar: Core Mechanisms and Attack Model

BitcoinQuasar is architected to automate the search for nonce reuse across the entire Bitcoin blockchain. The tool performs the following core functions:

Blockchain scanning: Efficiently parses millions of historical Bitcoin transactions, extracting all unique signature pairs.
Nonce collision detection: Identifies signatures sharing the same public nonce (r), a prerequisite for the attack.
Private key recovery: For each collision, applies the mathematical recovery method, yielding the owner’s private key.
Lost wallet restoration: Once the private key is recovered, BitcoinQuasar provides mechanisms to sweep the corresponding wallet’s funds, enabling lost or orphaned assets to be reclaimed under certain legal and ethical scenarios.keyhunters

Security Implications and Real-World Impact

The consequences of a successful nonce reuse attack executed via BitcoinQuasar are catastrophic for affected users:

Total loss of control: Attackers gain instant, irreversible access to all wallet funds.
Forensic exploitation: BitcoinQuasar can be used by cybersecurity professionals and attackers alike, probing the blockchain for accidental nonce reuse events left by poorly implemented wallets.
Massive financial losses: Documented real-world incidents confirm that millions of dollars have been stolen through this class of vulnerability; high-profile CVEs like CVE-2018-0734, CVE-2020-28498, and others detail the systemic risk across cryptographic libraries.kaspersky+1
Loss of trust: Widespread private key leakage could undermine faith in the Bitcoin system’s fundamental security guarantees.keyhunters

Defensive and Preventive Recommendations

Given the severity of nonce reuse vulnerabilities, the deployment of BitcoinQuasar for research and auditing purposes is crucially balanced by the adoption of robust countermeasures:

Strict adherence to standards such as RFC6979 (deterministic ECDSA nonces) and BIP-340/BIP-327 for Schnorr signatures.keyhunters
Regular, independent security audits of wallet software and cryptographic libraries.
Use of high-entropy, cryptographically secure random number generators in nonce generation.
Public awareness among developers and users about these cryptographic best practices.

Conclusion

BitcoinQuasar is a scientifically rigorous example of a modern cryptographic analysis and attack suite. Its functionality highlights the existential threat posed by nonce reuse in digital signatures—one of the few software flaws capable of shattering Bitcoin’s trust architecture in a single stroke. Ongoing community vigilance, improved cryptographic hygiene, and continuous research are needed to mitigate and monitor this ever-present risk.reddit+2

Research paper: Critical nonce reuse vulnerability in MuSig2, its origins and a secure fix

Introduction

MuSig2 is a modern multi-signature digital signature scheme based on Schnorr, used in the Bitcoin network to enhance privacy and reduce signature size. The security of this scheme directly depends on the uniqueness and cryptographic strength of the nonce used in each signing session. Insecure implementation of nonce generation leads to absolutely catastrophic consequences: complete compromise of the private key and loss of funds. keyhunters+2

The mechanism of vulnerability occurrence

Classic attack scenario

A classic cryptographic attack, the Nonce Reuse Attack, occurs when the same nonce (a one-time random number) is used to sign two different messages—either intentionally or due to a bug in the random number generator or a flawed implementation (e.g., a fixed number aux_rand, the same input parameters). bitcoinops+2

Given two signatures $(s_1, r)$ and $(s_2, r)$ with the same $r$ (public nonce), but different messages $m_1, m_2$, an attacker can mathematically calculate the private key $x$ using the formula: x = s1 − s2 H(m1) − H(m2) mod nx = \frac{s_1 – s_2}{H(m_1) – H(m_2)} \mod nx = H(m1) − H(m2) s1 − s2 mod n

where $H$ is the hash function, $n$ is the group order. aimspress+1

Scientific formalization

The vulnerability is classified as a Nonce Reuse Attack or Repeated Nonce Attack, and in MuSig2 multi-signature schemes, it is further complicated by aggregated nonce states. In some cases, the attack is possible due to improper storage or derivation of secret nonces in long or parallel signing sessions (e.g., memory copying, parameter reuse). delvingbitcoin+2

Safe Fix: A Reliable and Repeatable Solution

Principles of correction

Main requirements:

Non-determinism : Each nonce must be unique for each session and message.
State Destruction : Destroy secret nonces after signature completion.
Using cryptographically secure random number generators (CSPRNGs) .
Provably deterministic and unique nonce generation —for example, using the MuSig-DN/EdDSA algorithm, using a private key, a random parameter, and a message.

A secure nonce generation scheme

A secure method is presented in the BIP-340 and MuSig-DN standards, where the nonce is formed according to the principle:

pythondef secure_nonce(private_key, aux_rand, message):
    """
    private_key: bytes (32)
    aux_rand: bytes (32), криптографически случайное число
    message: bytes
    """
    # BIP-340: nonce = Hash(private_key || aux_rand || message)
    seed = private_key + aux_rand + message
    nonce = sha256(seed)
    return nonce

aux_rand is generated by a cryptographically strong generator. aimspress+2
The nonce and the entire seed are deleted from memory immediately after use. bitcoinops

A secure implementation example for MuSig2 (Go-like pseudocode)

gofunc SecureNonceGen(privKey []byte, message []byte) []byte {
    // Get auxiliary randomness from /dev/urandom or cryptographically secure PRNG
    auxRand := GetSecureRandomBytes(32) 
    // Combine inputs and hash
    seed := append(privKey, auxRand...)
    seed = append(seed, message...)
    nonce := sha256(seed)
    SecureDelete(seed)
    return nonce
}

Always generate a new one auxRand for each signature.
No implementation should use fixed values auxRand, such as all zeros.
Delete the seed and private nonce immediately after generating the signature.
Never use the same private nonce more than once, even for one message.
Don’t store non-public nonsense in your long-term memory.

Scientific validity and recommendations

The use of the MuSig-DN (deterministic nonce-proof) scheme provides strong mathematical protection against nonce reuse attacks and reduces the security requirements of the PRNG blockstream+2

This approach is recommended for all implementations of modern multi-signature schemes, including MuSig2, regardless of the platform (Bitcoin Core, HSM, wallets). bips+2

Conclusion

The critical nonce reuse vulnerability in MuSig2 is a fundamental threat to the security of Bitcoin wallets and transactions. Nonce generation implementations must be based on secure cryptographic principles: uniqueness and nondeterminism for each signature, and proper state destruction. Scientific recommendations, standards, and best practices, such as MuSig-DN/BIP-340, are an excellent and reliable way to prevent nonce reuse attacks.

Implementing secure nonce generation according to the principles and code given above is mandatory for secure applications implementing MuSig2.

Final scientific conclusion

The critical nonce reuse vulnerability (Nonce Reuse Attack) is a prime example of a fundamental risk to the entire Bitcoin cryptocurrency infrastructure. Exploiting this weakness allows an attacker, with a single signature error, to completely reveal a user’s private key and steal all their funds, using just a few observed signatures with the same or highly predictable nonce. This attack, scientifically known as a Nonce Reuse Attack, Repeated Nonce Attack, or Private Key Recovery via Nonce Reuse, has already damaged millions of dollars and numerous blockchains. keyhunters+2

In multi-signature schemes like MuSig2 and Schnorr, a flaw in the implementation of nonce generation has catastrophic consequences: key compromise, unauthorized transactions, mass theft of funds, loss of trust in the network, and the collapse of the entire Bitcoin security architecture. The lack of a unique nonce is like leaving a safe open to any attacker. notsosecure+3

In modern Bitcoin implementations and cryptographic libraries, rigorous code auditing, the use of cryptographically strong random number generators, and strict adherence to BIP-340/BIP-327/RFC6979 standards are essential for ensuring robustness. Each signature must use a unique, unpredictable nonce; this is the only way to maintain security and trust in Bitcoin.

Understanding and fixing the re-nonce vulnerability is a pressing issue for all developers and researchers. It determines whether the billions of Bitcoin coins will be securely protected or vulnerable to simple and destructive attacks.

Ensuring the uniqueness of the nonce is a key factor in the survival and trust of the entire Bitcoin technology for many years to come. strm+3

Literature:

Cryptanalysis