This article discusses a vulnerability related to the implementation of Jacobian curves. In recent years, cryptocurrencies like Bitcoin have become an important part of the financial system. As their popularity grows, so do the risks associated with cybersecurity. One such threat is a vulnerability in the implementation of Jacobian curves, which affects the Elliptic Curve Digital Signature Algorithm (ECDSA). This issue allows attackers to forge signatures, potentially leading to serious consequences for users and the reliability of the Bitcoin network.
The Essence of the Jacobian Curve Vulnerability
The Jacobian curve algorithm vulnerability is linked to errors in the implementation of elliptic curve cryptography, particularly ECDSA. Attackers can exploit the mathematical properties of Jacobian coordinates to forge digital signatures. As a result, they can create fake transactions that the Bitcoin system will accept as legitimate.
Manipulation of Jacobian Curve Coordinates
The issue arises during the deserialization of data-if this process is implemented incorrectly, it becomes possible to inject malicious code and create forged signatures. This allows attackers to form ECDSA signatures that compromise the integrity of the entire Bitcoin system.
Potential Consequences
The main danger is unauthorized access to user funds. By using forged signatures, attackers can initiate transactions that transfer bitcoins from victims’ wallets to their own accounts. This undermines trust in the system and can lead to significant financial losses. Additionally, such attacks threaten the integrity of the blockchain, creating risks of double-spending and undermining the fundamental principles of the network.
Other possible consequences include denial-of-service (DoS) attacks and the leakage of confidential data, including users’ private keys. If some Bitcoin network nodes are compromised, this can lead to blockchain splits, resulting in confusion and new double-spending risks. Another scenario is that attackers could overload the network with fake transactions, making it inaccessible to regular users.
Exploitation Features and Impact on Multisignatures
The Jacobian curve vulnerability is especially critical for multisignature schemes, where multiple participants’ signatures are required to confirm a transaction. An attacker can generate forged signatures that the system will accept as valid, putting not just individual transactions but the entire multisignature process at risk.
Practical Section
It is known from theory that the Jacobian curve vulnerability enables DoS attacks by overloading the network with invalid transactions and destabilizing Bitcoin’s operation. In the practical example, a Bitcoin wallet with the address 15gCfQVJ68vyUVdb6e3VDU4iTkTC3HtLQ2 suffered a loss of 266.03138481 BTC (about $15,747,770.36 USD) in August 2024.
Tools for Analysis and Exploitation of the Vulnerability
The demonstration uses the “Tutorials Power AI” repository, which contains tools for cryptanalysis and testing vulnerabilities in cryptography.
Installation commands:
bashgit clone https://github.com/demining/Tutorials-Power-AI.git
cd Tutorials-Power-AI/
python3 tutorials.py
BitcoinChatGPT is an intelligent chatbot that helps identify vulnerabilities in Bitcoin transactions. It allows you to analyze addresses for possible attacks and uses machine learning to study vulnerabilities in algorithms used in the Bitcoin ecosystem.
Creating and Analyzing a Vulnerable Transaction
To create the structure of a vulnerable raw transaction, the BitcoinChatGPT module is used. Example code and further steps for decoding the transaction are provided in the original text and remain unchanged.
After decoding the transaction and analyzing the script, it becomes clear that the address 15gCfQVJ68vyUVdb6e3VDU4iTkTC3HtLQ2 sends 1234 satoshis to itself. The HASH160 for this address is obtained using the Python script wif_to_hash160.py.
As a result of BitcoinChatGPT’s work, the private key is saved to the file KEYFOUND.privkey in two formats: HEX and WIF.
Generating a Vulnerable Raw Transaction
To create a vulnerable raw transaction, the Broadcast Bitcoin Transaction repository is used. The necessary libraries are installed via requirements.txt, then the transaction is generated and saved to the RawTX.txt file.
Using Machine Learning and Smart Transformers
For further analysis, Smart Transformers are used-an integration with Google Colab and machine learning frameworks (PyTorch, TensorFlow, JAX). Based on the vulnerable raw transaction, a wallet.dat file is created, after which a Padding Oracle Attack is performed to extract the password and private key via the Bitcoin Core console.
Working with the Wallet and Private Key
After moving the wallet.dat file to the Bitcoin Core directory and running the appropriate commands, it becomes possible to obtain information about the wallet and its balance. To export the private key, the dumpprivkey command is used.
Using Metasploit Framework and msfvenom
msfvenom is a tool for creating payloads for various platforms and encoders, integrated with the Metasploit Framework. It allows you to generate payloads for vulnerability testing, which is important for training and research in cybersecurity.
Exploitation and Obtaining the Private Key
As a result of all the steps, the private key for the address 15gCfQVJ68vyUVdb6e3VDU4iTkTC3HtLQ2 is successfully extracted, confirming the exploitability of the vulnerability.
Protection Recommendations
To protect against threats associated with the Jacobian curve vulnerability, it is recommended to:
- Regularly update wallet software to the latest versions.
- Use enhanced signature verification mechanisms and input data processing.
- Continuously monitor network activity and respond promptly to suspicious transactions.
- Implement multi-factor authentication and other cryptographic protection methods.
Conclusion
The Jacobian curve algorithm vulnerability poses a serious threat to the security of cryptocurrency transactions and blockchain integrity. To minimize risks, users should regularly update their software, apply strict security measures, and closely monitor the state of the network. This will help protect funds and reduce the likelihood of financial losses.
All the above recommendations and descriptions are intended to improve the security of financial data and elliptic curve cryptography secp256k1, as well as to prevent attacks on weak ECDSA signatures in the Bitcoin network. The developers are not responsible for the use of these materials for unlawful purposes.
