Fast RSA-type cryptosystem modulo p k q

Abstract

We propose a cryptosystem modulo p k q based on the RSA cryptosystem. We choose an appropriate modulus p k q which resists two of the fastest factoring algorithms, namely the number field sieve and the elliptic curve method. We also apply the fast decryption algorithm modulo p k proposed in [22]. The decryption process of the proposed cryptosystems is faster than the RSA cryptosystem using Chinese remainder theorem, known as the Quisquater-Couvreur method [17]. For example, if we choose the 768-bit modulus p 2 q for 256-bit primes p and q, then the decryption process of the proposed cryptosystem is about 3 times faster than that of RSA cryptosystem using Quisquater-Couvreur method.Key wordsRSA cryptosystemQuisquater-Couvreur methodfast decryptionfactoring algorithm