Elliptic curve cryptography (ECC) is widely used in modern cryptographic protocols due to its high efficiency and security. However, some types of curves, such as binary curves over GF(2^m) fields, have been found to be outdated and vulnerable to various attacks. In this article, we will look at the problems associated with the use of outdated binary curves and their potential impact on the security of private keys in Bitcoin wallets.
Binary Curves and Their Vulnerabilities
Binary curves over GF(2^m) fields initially attracted attention due to their relative simplicity of implementation and computational efficiency. However, they have several significant drawbacks:
- Vulnerability to MOV attack : Binary curves, especially supersingular ones, are vulnerable to the Menezes–Oka–Vanstone (MOV) attack, which reduces the discrete logarithm problem on a group of points of an elliptic curve over a field to the discrete logarithm problem on a finite field[3]. This significantly reduces the security of such curves.
- Implementation Issues : Implementing binary curves can be complex and error-prone, which can lead to additional vulnerabilities in cryptographic protocols.
Private Keys in Bitcoin Wallets
Bitcoin wallets are used to store and manage private keys, which are needed to access funds on the blockchain. Private keys in Bitcoin are typically generated using elliptic curve cryptography, specifically the secp256k1 curve. However, if outdated or mathematically incorrect curves were used, this could lead to serious security issues:
- Key Generation Vulnerabilities : If outdated or incorrect curves are used in the private key generation process, this can lead to vulnerabilities that allow attackers to gain access to private keys.
- Side-channel attacks : Using stale curves can make the system vulnerable to side-channel attacks, such as computational error attacks that can be used to obtain information about private keys[1].
Conclusion
The use of outdated binary curves over GF(2^m) fields in cryptography poses a significant risk to the security of private keys in Bitcoin wallets. Modern, secure curves and protocols must be used to ensure a high level of data protection. The transition to post-quantum cryptography is also an important step in ensuring the long-term security of cryptographic systems[3].
Recommendations
- Using modern curves : It is recommended to use well-tested and secure curves such as secp256k1 or Edwards-shaped curves to generate and manage private keys.
- Updating cryptographic protocols : Regularly update cryptographic protocols and libraries to avoid using outdated algorithms and curves.
- Post-quantum cryptography : Begin the transition to post-quantum cryptography to ensure long-term data security as quantum computing advances.[3]
Citations:
[1] https://ru.wikipedia.org/wiki/%D0%90%D1%82%D0%B0%D0%BA%D0%B0_%D0%BF%D0%BE_%D 0%BE%D1%88%D0%B8%D0%B1%D0%BA%D0%B0%D0%BC_%D0%B2%D1%8B%D1%87%D0%B8%D1%81%D0%BB %D0%B5%D0%BD%D0%B8%D0%B9_%D0%BD%D0%B0_%D1%8D%D0%BB%D0%BB%D0%B8%D0%BF%D1%82%D0 %B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B5_%D0%BA%D1%80%D0%B8%D0%B2%D1%8B%D0%B5, %D0%B8%D1%81%D0%BF%D0%BE%D0%BB%D1%8C%D0%B7%D1%83%D1%8E%D1%89%D0%B8%D0%B5 %D0%B0%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC_%D0%9C%D0%BE%D0%BD%D1%82%D0%B3%D0%BE%D0%BC%D0%B5%D1%80%D0%B8
[2] https://digitalcryptography.ru/news/novosti-otrasli/ustarevshie-kriptoalgoritmy-povlekut-katastrofu/
[3] https://habr.com/ru/companies/neobit/articles/332942/
[4] https://core.ac.uk/download/pdf/146445895.pdf
[5] https://blog.qrator.net/ru/ec-tls-13_60/
[6] https://habr.com/ru/companies/globalsign/articles/713512/
[7] https://www.ssl.com/ru/%D1%81%D1%82%D0%B0%D1%82%D1%8C%D1%8E/%D1%87%D1%82%D0%B E-%D1%82%D0%B0%D0%BA%D0%BE%D0%B5-%D0%BA%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D0%B3%D1 %80%D0%B0%D1%84%D0%B8%D1%8F-%D1%81-%D1%8D%D0%BB%D0%BB%D0%B8%D0%BF%D1%82%D0%B8 %D1%87%D0%B5%D1%81%D0%BA%D0%BE%D0%B9-%D0%BA%D1%80%D0%B8%D0%B2%D0%BE%D0%B9-ecc/
[8] https://cyberleninka.ru/article/n/kriptoanaliz-i-kriptografiya-istoriya-protivostoyaniya