New simultaneous Diophantine attacks on generalized RSA key equations

Autor: Wan Nur Aqlili Ruzai, Muhammad Rezal Kamel Ariffin, Muhammad Asyraf Asbullah, Amir Hamzah Abd Ghafar
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Journal of King Saud University: Computer and Information Sciences, Vol 36, Iss 5, Pp 102074- (2024)
Druh dokumentu: article
ISSN: 1319-1578
DOI: 10.1016/j.jksuci.2024.102074
Popis: RSA stands as a widely adopted method within asymmetric cryptography, commonly applied for digital signature validation and message encryption. The security of RSA relies on the challenge of integer factorization, a problem considered either computationally infeasible or highly intricate, especially when dealing with sufficiently large security parameters. Effective exploits of the integer factorization problem in RSA can allow an adversary to assume the identity of the key holder and decrypt such confidential messages. The keys employed in secure hardware are particularly significant due to the typically greater value of the information they safeguard, such as in the context of securing payment transactions. In general, RSA faces various attacks exploiting weaknesses in its key equations. This paper introduces a new vulnerability that enables the concurrent factorization of multiple RSA moduli. By working with pairs (Ni,ei) and a fixed value y satisfying the Diophantine equation eixi2−y2ϕ(Ni)=zi, we successfully factorized these moduli simultaneously using the lattice basis reduction technique. Notably, our research expands the scope of RSA decryption exponents considered as insecure.
Databáze: Directory of Open Access Journals