100btcd/blob/v2_transport/btcec/schnorr/musig2/nonces.go

A critical cryptographic vulnerability related to nonce reuse in digital signatures in Bitcoin is a fundamental issue that threatens the security of the entire blockchain system. The attack, scientifically known as a Nonce Reuse Attack , creates a backdoor for an attacker: by obtaining two signatures with the same nonce for a single private key, an attacker can easily recover the owner’s private key and steal their funds. This threat is not theoretical—in the real history of Bitcoin, similar exploits have allowed hackers to steal hundreds of bitcoins.

“Critical Nonce Reuse Vulnerability: A Fatal Attack on Bitcoin Cryptocurrency Security”

Stolen Echo Attack: Deadly Resonance of the Nonce highlights the nature of the vulnerability, highlights its criticality, and demonstrates the real danger to the entire Bitcoin cryptocurrency ecosystem. notsosecure+2

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

Introduction

Bitcoin uses digital signatures to confirm transactions and protect user funds. Modern implementations, including the Schnorr scheme and the MuSig2 protocol, require the nonce—the random number generated for each signature—to be unique and unpredictable. Violating this property leads to one of the most dangerous cryptographic threats: a nonce reuse attack, which has dire consequences for the security of the entire Bitcoin ecosystem. keyhunters+2

Description of the vulnerability

Mechanism of occurrence

A critical vulnerability occurs when the same nonce (kkk) is used in multiple signatures for different messages with the same private key. This can be due to implementation errors, a weak random number generator, or improper management of auxiliary randomness (aux_rand). As shown in academic research, nonce reuse or predictability allows an attacker to extract the private key from two signatures using the following transformations: ishaana+4 x=s1−s2H(m1)−H(m2)mod nx = \frac{s_1 — s_2}{H(m_1) — H(m_2)} \mod nx=H(m1)−H(m2)s1−s2modn

where s1,s2s_1, s_2s1,s2 are the signature values, H(m1),H(m2)H(m_1), H(m_2)H(m1),H(m2) are the hashes of different messages, xxx is the private key.

Scientific name of the attack

In scientific literature and industry, this attack is called Nonce Reuse Attack, sometimes Repeated Nonce Attack , Virtual Rewinding Attack , or Side-channel attack on nonce reuse in digital signatures . arxiv+4

Impact on Bitcoin Security

Loss of private keys: A successful attack allows the attacker to recover the private key and gain access to the user’s funds. christian-rossow+2
Transaction tampering: An attacker can sign any transaction on behalf of a user, leading to theft of Bitcoins.
Multi-signature compromise: For MuSig2, a mistake by one participant can lead to the loss of funds for all signatories.
Undermining trust in the network: If such attacks become widespread, it will threaten the stability and reputation of the entire Bitcoin cryptocurrency. acm+2
Real-life cases: Scientific blockchain monitoring shows that attacks of this kind have resulted in millions of dollars in damage. christian-rossow+1

CVE number and recognition status

At the time of publication (September 2025), the nonce reuse vulnerability in Schnorr/MuSig2 implementations in Bitcoin has not officially received an individual CVE number , but there are a number of related cases: access.redhat+2

CVE-2025-9288 (RedHat, 2025, “indirect cryptographic breakages described, such as nonce reuse leading to private key extraction”). access.redhat
CVE-2015-6924 (“Nonce Reuse Attack, in which repeated or predictable use of a random number”). feedly
In scientific papers and industrial documentation, the vulnerability and attack are clearly classified as a Nonce Reuse Attack, with a detailed analysis of the consequences. aimspress+2

Recommendations and safe practices

Implementation of deterministic nonce generation according to RFC6979/BIP340 standard;
Using cryptographically secure sources of randomness;
Tracking and preventing nonce reuse at the wallet software level;
Passing regular security audits and updating vulnerable libraries;
Conducting testing of all multi-signature implementations. keyhunters+2

Conclusion

A nonce reuse attack ( sometimes listed in CVE as CVE-2025-9288) is a fundamental cryptographic threat that can lead to the complete compromise of a Bitcoin user’s private keys and funds. It can only be prevented through strict adherence to nonce generation standards and industry best practices. As multi-signature technologies and new cryptographic solutions evolve, these issues should be a focus for researchers and developers to ensure the security and resilience of the world’s largest cryptocurrency. feedly+5

Cryptographic vulnerability

Cryptographic vulnerability in btcsuite/musig2 code: Analysis of private key leakage threats

After a detailed analysis of the provided btcsuite musig2 code and reviewing the documentation on cryptographic attacks on MuSig2, I identified several critical lines containing potential secret key leakage vulnerabilities.

Main vulnerability: Lack of protection against Nonce Reuse Attack

The main cryptographic vulnerability in the code is related to the lack of reliable protection against nonce reuse (Nonce Reuse Attack), which is a critical threat to the security of private keys in cryptographic schemes based on Schnorr signatures. keyhunters+3

Problematic lines of code

Line ~45-46: Global variable zeroSecNonce

go:

var zeroSecNonce [SecNonceSize]byte

Problem : This global variable is used to check for null nonces, but the code lacks an active check to prevent nonce reuse between different signing sessions. delvingbitcoin+1

Stolen Echo Attack: Deadly Resonance of the Nonce, a critical nonce reuse vulnerability and recovery of private keys for lost Bitcoin wallets. Similar errors and bugs allowed hackers to steal hundreds of bitcoins. — https://github.com/keyhunters/btcd/blob/v2_transport/btcec/schnorr/musig2/nonces.go

Lines ~290-291: Randomness generation without quality validation

go:

if _, err := opts.randReader.Read(randBytes[:]); err != nil {
    return nil, err
}

Problem : The code doesn’t check the entropy quality of the generated random numbers. Weak entropy can lead to predictable nonces and subsequent compromise of private keys. bitcoinops+1

Lines ~297-299: XOR operation with the secret key

go:

if len(opts.secretKey) == 32 {
    taggedHash := chainhash.TaggedHash(NonceAuxTag, randBytes[:])
    for i := 0; i < chainhash.HashSize; i++ {
        randBytes[i] = opts.secretKey[i] ^ taggedHash[i]
    }
}

Problem : XORing a secret key with a hash of random data can create temporary variables in memory containing the secret key. If not properly cleared, this can lead to an information leak. blockstream+1

Lines ~315-316: Using PutBytesUnchecked without validation

go:

k1Mod.PutBytesUnchecked(nonces.SecNonce[:])
k2Mod.PutBytesUnchecked(nonces.SecNonce[btcec.PrivKeyBytesLen:])

Problem : Using this method PutBytesUnchecked without first checking the uniqueness of the nonce can result in identical values being written in different bitcoinops+1 sessions.

Nonce Reuse Attack Mechanism

When the same nonce is reused in two different signatures with the same secret key, an attacker can recover the private key using the following mathematical relationship: wikipedia+2

For two signatures with the same nonce:

s₁ = k⁻¹(H(m₁) + r·x)
s₂ = k⁻¹(H(m₂) + r·x)

An attacker can calculate: x = (s₁ - s₂)⁻¹ · (H(m₁) - H(m₂)) mod n

Recommendations for eliminating vulnerabilities

Implementation of deterministic nonce generation according to RFC6979 to prevent aimspress+1 reuse
Adding nonce uniqueness checks before using them in signing
Improving the validation of entropy of generated random numbers
Safely clear memory after operations with sensitive data
Implementation of state protection between signing rounds as described in BIP-327 delvingbitcoin+1

These vulnerabilities pose a critical threat to the security of Bitcoin transactions using MuSig2, as compromising private keys leads to complete loss of control over the funds involved. aimspress+2

Dockeyhunt Cryptocurrency Price

Successful Recovery Demonstration: 41.37955486 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 41.37955486 BTC (approximately $5202444.53 at the time of recovery). The target wallet address was 1MvCkGWZm9QFb9r7VpE6H7WRAKcNyCFGUj, 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.btcseed.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): 5JBWbCHDW14ZaocpUo9nAMhtx342xeJm3BjgY5Knpjb8LmMX252

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: $ 61025]

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.

中文版密碼分析與比特幣錢包恢復

한국어 버전의 암호 분석 및 비트코인 지갑 복구

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.

KeyTrueCrack and the Exploitation of Nonce Reuse Vulnerabilities in Bitcoin Signatures

This paper explores the interaction between KeyTrueCrack, a cryptographic analysis framework, and one of the most devastating Bitcoin vulnerabilities: nonce reuse in Schnorr and MuSig2-based signature schemes. Through theoretical analysis and practical considerations, the study demonstrates how KeyTrueCrack leverages critical implementation flaws—specifically in nonce generation and entropy randomness checks—to recover private keys. By reconstructing lost Bitcoin wallets, this attack vector illustrates the catastrophic risks posed to financial security in blockchain ecosystems.

In Bitcoin and related cryptocurrencies, digital signatures provide both authenticity and ownership over digital funds. Schnorr signatures and their multi-signature variant MuSig2 have been integrated into Bitcoin as a scalable, privacy-preserving replacement for legacy ECDSA. Security, however, fundamentally depends on the generation of a unique, unpredictable nonce for every transaction.

KeyTrueCrack is a specialized cryptographic vulnerability analysis instrument designed to detect and exploit repeated nonce values. Unlike general-purpose cracking tools, KeyTrueCrack focuses on the deterministic algebraic weaknesses of signature schemes when nonce reuse occurs. By analyzing transaction signatures across blockchain data, it enables feasible mathematical recovery of secret keys in real scenarios.

Mechanism of Vulnerability

A nonce reuse vulnerability emerges when the same randomness kkk is employed more than once in the signature process. For two signatures with the same nonce but different messages, the following mathematical principle applies:s1=k−1(H(m1)+r⋅x)s2=k−1(H(m2)+r⋅x)s_1 = k^{-1}(H(m_1) + r \cdot x) \quad\quad s_2 = k^{-1}(H(m_2) + r \cdot x)s1=k−1(H(m1)+r⋅x)s2=k−1(H(m2)+r⋅x)

where

s1,s2s_1, s_2s1,s2 are signature values,
H(m1),H(m2)H(m_1), H(m_2)H(m1),H(m2) are cryptographic hashes of distinct messages,
xxx is the private key,
rrr is the elliptic curve point derived from the nonce,
kkk is the nonce.

By eliminating kkk, the attacker directly computes the victim’s private key:x=s1−s2H(m1)−H(m2)(modn)x = \frac{s_1 – s_2}{H(m_1) – H(m_2)} \pmod{n}x=H(m1)−H(m2)s1−s2(modn)

The entire integrity of a Bitcoin wallet thus collapses from a single coding oversight or entropy failure.

KeyTrueCrack: Functional Role

KeyTrueCrack operates as a forensic cryptoanalysis framework with the following core capabilities:

Automatic Nonce Reuse Detection: By scanning blockchain signatures, KeyTrueCrack identifies repeated or predictable nonce values in public datasets.
Private Key Extraction: Using algebraic derivations, it reconstructs private keys as soon as two vulnerable signatures are detected.
Wallet Recovery Operations: Once the key is derived, the tool allows reconstruction of lost or inaccessible Bitcoin wallets, effectively recovering funds.
Exploit Simulation for Developers: It provides a testing toolkit to simulate real-world attacks against wallet or node implementations, enabling developers to assess resilience.

Impact on Bitcoin Security

The combination of nonce reuse and automated exploitation through tools such as KeyTrueCrack introduces multiple systemic risks:

Private Key Compromise: Even a single repeated nonce leaks the entire private key for that address, enabling attackers unrestricted access to funds.
Multi-Signature Failure: In MuSig2, if one participant mismanages randomness, the compromise can cascade to all co-signers of the transaction.
Mass-scale Fund Theft: Automated detection of nonce reuse across blockchain data enables large-scale systematic attacks.
Loss of Trust in Infrastructure: The very foundation of Bitcoin relies on cryptographic soundness; demonstrated nonce failures undermine market confidence.

Notably, blockchain analysis has proven that nonce-related exploits have historically resulted in millions of dollars worth of losses.

Recommendations for Mitigation

To neutralize the attack surface exploited by KeyTrueCrack, the following security measures must be rigorously enforced:

Deterministic Nonce Generation: Enforce standards such as RFC6979 and BIP340 for signature nonce generation.
High-quality Entropy: Integrate operating system–level cryptographically secure randomness, avoiding low-entropy or zero-seeded inputs.
Nonce Uniqueness Validation: Implement rejection protocols if a duplicate nonce is detected in active signing sessions.
Constant Security Audits: Audit libraries and Bitcoin clients, paying special attention to MuSig2 and Schnorr implementations.
Secure Memory Clearing: Avoid leakage of nonce and key material through unsafe memory operations.

Case Study: MuSig2 and KeyTrueCrack

In multi-signature scenarios, KeyTrueCrack demonstrates particularly severe implications. If even one co-signer generates a weak nonce and repeats it, the entire aggregated private signing key becomes derivable. This failure compromises all participating wallets simultaneously, enabling attackers to drain multi-party funds.

Conclusion

KeyTrueCrack underscores the reality that cryptographic vulnerabilities are not merely theoretical curiosities—they have direct, devastating consequences in financial and blockchain systems. By systematically exploiting nonce reuse flaws in Schnorr and MuSig2 digital signature protocols, private keys can be reconstructed with precision.

What makes this vulnerability particularly dangerous is its silent nature: once nonce reuse occurs, the collapse of private key secrecy is mathematically inevitable. For the global Bitcoin ecosystem, preventing nonce reuse is not optional—it is fundamental. Proper adherence to deterministic nonce generation, secure entropy practices, and continued auditing is the only scientifically proven defense against catastrophic key exposure.

Future investigations should continue to analyze real blockchain data for nonce irregularities and develop preventive verification systems. Without these measures, tools like KeyTrueCrack present a constant existential threat to the world’s largest cryptocurrency.

Research paper: Cryptographic nonce reuse vulnerability in MuSig2/BIP340 and secure protection practices

Introduction

Modern cryptocurrency systems, including Bitcoin, use multi-signature protocols based on the Schnorr protocol (BIP340, MuSig2) to enhance privacy, scalability, and mitigate the risk of multi-signature attacks. A key element of digital signature security is the uniqueness and unpredictability of the nonce—the random number generated for each signature operation. Violating this property leads to a critical cryptographic vulnerability known as a nonce reuse attack. keyhunters+4

Causes of vulnerability

Nonce generation mechanism

In the standard Schnorr/MuSig2 implementation, the nonce is calculated based on the private key and additional random data (aux_rand): k = Hash(d, aux_rand, message) k = \mathrm{Hash}(d, \text{aux\_rand}, \text{message}) k = Hash(d, aux_rand, message)

where ddd is the private key, aux_rand is a random byte block (or session parameters), and message is the message being signed. aimspress+1

Implementation Bugs – Predictability and Nonce Reuse

In many implementations, aux_rand is missing or fixed to zero, or the old seed is used. keyhunters+1
If the same nonce is used for different messages with the same private key, an attacker, having two signatures, can easily calculate the private key using the following formula:

x=s1−s2H(m1)−H(m2)mod nx = \frac{s_1 – s_2}{H(m_1) – H(m_2)} \mod nx=H(m1)−H(m2)s1−s2modn

where s1, s2s_1, s_2s1, s2 are signature values, H(m1), H(m2)H(m_1), H(m_2)H(m1), H(m2) are message hashes, nnn is the group order. delvingbitcoin+2

In multi-signature (MuSig2), the vulnerability is even more devastating: the compromise of one participant leads to the risk of losing control over the funds of all signatories. iacr+2

Attack scenario

Having received two signatures for different messages, but with the same nonce, the attacker calculates the private key.
This leads to a complete compromise of the multisig address, the possibility of theft of funds and counterfeit transactions. blockstream+2

Safe Fix: Deterministic Nonce Generation

Recommendations

For each message, the nonce must be unique and unpredictable.
Before using a nonce, you must check that it does not match nonces from previous sessions—element-by-element comparison. bitcoinops+2
Nonce generation according to BIP340 or RFC6979 is deterministic using a private key, message, and random seed. aimspress+1

A safe implementation example in Go

go:

import (
    "crypto/sha256"
    "crypto/rand"
)

func GenerateDeterministicNonce(privKey, message []byte) ([]byte, error) {
    auxRand := make([]byte, 32)
    if _, err := rand.Read(auxRand); err != nil {
        return nil, err
    }
    // Формируем tagged hash в стиле BIP340
    h := sha256.New()
    h.Write([]byte("BIP340/nonce"))
    h.Write(privKey)
    h.Write(auxRand)
    h.Write(message)
    nonce := h.Sum(nil)
    return nonce, nil
}

Key points:

A new auxRand is generated each time using a cryptographically secure generator.
Each signature has a unique nonce.
No reuse; the absence of duplicate nonces is guaranteed by the combination of the private key, a unique auxRand, and the message. blockstream+2

Check for nonce reuse

Add storage for used nonces to avoid duplication:

govar usedNonces = make(map[string]bool)

func IsNonceUsed(nonce []byte) bool {
    nonceStr := string(nonce)
    if usedNonces[nonceStr] {
        return true
    }
    usedNonces[nonceStr] = true
    return false
}

Integrate the call IsNonceUsed(nonce) into the generation and signing process—if the nonce already exists, block the signing operation. docs+1

Practical recommendations

Use only cryptographically secure entropy sources for aux_rand.
Never initialize aux_rand to a fixed value (e.g. all-zeroes).
In multi-signature schemes, exchange nonce commitments with other parties before the signing session begins and verify their uniqueness. blockstream
Hash the combination of private key, message, aux_rand to obtain a strong nonce.

Conclusion

A critical nonce reuse vulnerability in MuSig2 and similar protocols leads to complete disclosure of private keys and loss of funds unless deterministic and unique nonce generation protocols are implemented. Using BIP340/RFC6979-compliant deterministic generation code, continuous uniqueness validation, and secure memory erasure are the only effective methods for preventing nonce reuse attacks in modern multisig systems like Bitcoin and similar cryptographic technologies. delvingbitcoin+4

Final scientific conclusion

A critical cryptographic vulnerability related to nonce reuse in digital signatures in Bitcoin is a fundamental issue that threatens the security of the entire blockchain system. The attack, scientifically known as a Nonce Reuse Attack , creates a backdoor for an attacker: by obtaining two signatures with the same nonce for a single private key, an attacker can mathematically easily recover the owner’s private key and steal their funds. This threat is not theoretical—in the real history of Bitcoin, similar exploits have allowed hackers to steal hundreds of bitcoins .

What’s particularly dangerous is that the vulnerability arises not from a weak algorithm, but from errors or negligence on the part of developers, as well as from insufficiently stable entropy sources. Even a short repetition or predictability of the nonce in transactions leads to a complete compromise of cryptographic protection, the removal of the barrier between the user’s private and public key, and massive financial damage.

Blocking this attack at the development and protocol levels is not just a recommendation, but a critical necessity for the security of funds, user trust, and network stability. History and modern research clearly demonstrate that ensuring the uniqueness and secrecy of all nonces, as well as implementing modern randomness standards, is the only scientifically proven foundation for long-term cryptographic security in Bitcoin. habr+2

The bottom line:
Balancing scalability, privacy, and security in Bitcoin is impossible without strict control of the nonce—the slightest deviation from the uniqueness and secrecy of this parameter instantly turns any transaction into a potential victim of a fatal attack, threatening the entire cryptocurrency ecosystem.

Sources:

keyhunters.ru — Bitcoin Keyhunters Nonce Reuse Attack Analysis
aimspress.com — A research paper on deterministic nonce generation .
blog.blockstream.com — Verifiably Deterministic Nonces in MuSig blockstream
bitcoinops.org — A Practical Implementation of RFC6979 Bitcoin Security
docs.rs/musig2/latest/musig2 — Musig2 Documentation Rust docs
iacr.org — Official MuSig2: Two-Round Schnorr Multisignatures iacr paper
delvingbitcoin.org — Forum: How quickly is the key revealed when reusing a delvingbitcoin nonce?
bitcoindevs.xyz — Practical details of bitcoindevs nonce generation
btctranscripts.com — MuSig2 Security Protocol btctranscripts
halborn.com — Schnorr SDK Audit: Risks of Reuse Nonce halborn

Sources:

keyhunters.ru — Scientific examination of the Nonce Reuse Attack in Bitcoin keyhunters
aimspress.com — Research into Nonce Generation in Digital Signatures aimspress+1
access.redhat.com – CVE-2025-9288 access.redhat
feedly.com/cve/CVE-2015-6924 feedly
christian-rossow.de — Analysis of Bitcoin Key Leaks and Attacks christian-rossow
arxiv.org — Breaking ECDSA/Schnorr with Nonce Reuse arxiv
dl.acm.org – Security Aspects of Cryptocurrency Wallets acm
ishaana.com/blog – Deep Dive Into Nonce-Reuse During Bitcoin Transaction ishaana
fenefx.com/blog – What is Nonce? fenefx
nvlpubs.nist.gov — Notes on Threshold EdDSA/Schnorr Signatures nvlpubs.nist

Cryptanalysis