Search

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. [ABSTRACT FROM AUTHOR]

Elliptic curve cryptography (ECC) is widely acknowledged as a method for implementing public key cryptography on devices with limited resources thanks to its use of small keys. A crucial and complex operation in ECC calculations is scalar point multiplication. To improve its execution time and computational complexity in low-power devices, such as embedded systems, several algorithms have been suggested for scalar point multiplication, with each featuring different techniques and mathematical formulas. In this research, we focused on combining some techniques to produce a scalar point multiplication algorithm for elliptic curves over finite fields. The employed methodology involved mathematical analysis to investigate commonly used point multiplication methods. The aim was to propose an efficient algorithm that combined the best computational techniques, resulting in lower computational requirements. The findings show that the proposed method can overcome certain implementation issues found in other multiplication algorithms. In certain scenarios, the proposed method offers a more efficient approach by reducing the number of point doubling and point addition operations on elliptic curves using the inverse of the targeted point. [ABSTRACT FROM AUTHOR]