Unlocking the Future of Digital Currency: A Comparative Study of ECDSA vs. EdDSA Signatures with Oblivious Transfer Protocol

Bitcoin, one of the most widely used digital currencies for private transactions, relies heavily on the security of its digital signature mechanisms. Previous research by Ko and Kwak identified vulnerabilities in Bitcoin's ECDSA-based digital signatures, specifically private key recovery attacks. In response, this research explores a modified Bitcoin transaction scheme utilizing EdDSA digital signatures and an Oblivious Transfer protocol. EdDSA is reputed to offer superior performance without compromising security, while Oblivious Transfer, a form of secure multi-party computation (SMPC), enhances security further. This study presents a prototype comparing three schemes: a traditional ECDSA-based Bitcoin transaction, a modified EdDSA-based transaction, and an EdDSA-based transaction combined with an Oblivious Transfer protocol. Performance and security analyses are conducted by comparing execution times and time complexity across these schemes. With 80 entities and $N$ == 350 for the Oblivious Transfer protocol, results show that the EdDSA and Oblivious Transfer-based scheme outperforms ECDSA in terms of both speed and security. In scenarios assuming private key recovery attacks, the use of inverse nonces in ECDSA introduces vulnerabilities that are effectively mitigated by the EdDSA modification and 1-out-of-N Oblivious Transfer protocol. The proposed scheme reduces the attack's success probability to 2:76’ offering significantly stronger resistance compared to ECDSA-based schemes. This research demonstrates that transitioning from ECDSA to EdDSA, paired with Oblivious Transfer, can significantly enhance the security and efficiency of Bitcoin transactions.