Public key authentication scheme over quaternions

Authentication is one of the cryptographic primitives that allows one entity to convince to another of the truth of an assertion without revealing any information other than that the assertion is true. In this paper, public key authentication scheme over quaternions modulo an RSA composite n = pq, where p and q are primes of equal size is proposed. Security of the scheme relies on the root extraction problem together with the conjugacy search problem over quaternions modulo n. Furthermore, issues related to the security, space complexity and computational cost of the scheme are discussed.