RSA Blind Signature System Using Matrices Over Finite Field

This paper presents a novel Blind RSA Signature Scheme that enhances both security and anonymity by leveraging matrix operations over finite fields and semiring structures. Blind signatures—originally introduced by David Chaum—are critical for privacy-preserving applications such as electronic voting, digital cash, and anonymous authentication. Although conventional RSA-based blind signatures offer foundational security, they often fall short in terms of privacy, traceability, and computational efficiency, especially under emerging cryptographic challenges. To address these limitations, the proposed scheme incorporates Mersenne primes for robust key generation, structured matrix transformations, and cryptographic hash functions to achieve improved untraceability and support selective disclosure. This design significantly increases resistance to key recovery, forgery, unbinding, and man-in-the-middle attacks, enhancing the scheme’s robustness against both classical and quantum adversaries. Empirical evaluations indicate a measurable reduction in signing time compared to standard RSA implementations, while delivering a superior level of security. Keywords— Semiring, discrete logarithm problem, blind signature, digital signature, RSA, finite field, mersenne prime.