Batch Private Keys Generation for RSA in Security Communication Systems

RSA public key cryptosystem is extensively used in information security systems. However, key generation for RSA cryptosystem requires multiplicative inversion over finite field, which has higher computational complexity, compared with either multiplication in common sense or modular multiplication over finite field. In order to improve the performance of key generation, we propose a batch private keys generation method in this paper. The method derives efficiency from cutting down multiplicative inversions over finite field. Theoretical analysis shows that the speed of batch private keys generation for s users is faster than that of s times solo private key generation. It is suitable for applications in those systems with large amount of users.