Nonce generation techniques in Schnorr multi-signatures: Exploring EdDSA-inspired approaches

This paper proposes a deterministic nonce generation technique to address the catastrophic issues associated with nonce reuse in message signing and to enhance the efficiency of Schnorr multi-signature schemes. Additionally, this research aims to reduce computational complexity and bandwidth requirements in digital and multi-signature schemes while maintaining robust security against common attacks. The proposed method was inspired by the EdDSA approach. The methodology includes a comprehensive mathematical analysis of digital signature algorithms and a rigorous examination of their vulnerabilities to well-known cryptographic attacks. This analysis evaluates the effectiveness and robustness of the proposed nonce generation technique within the frameworks of the Schnorr digital signature and the two-round MuSig schemes. Techniques and tools employed in this research involve deterministically generating nonces by hashing the private key and subsequently hashing the result with the message. Furthermore, it is proposed to exclude the public nonce R from the challenge calculations and to allow signers to directly prove possession of their secret keys through the aggregated public key, thereby eliminating the need for non-interactive zero-knowledge (NIZK) proofs. The findings demonstrate significant reductions in computational complexity and operational requirements, thereby improving bandwidth efficiency and making this method well-suited for resource-constrained devices. The approach also exhibits strong resistance to various attacks, including nonce reuse, key cancellation, rogue keys, and virtual machine rewinding.