Refined Algorithm for Prime Number Generation in Embedded Security Systems

Large prime numbers are one of inevitable ingredients in the public key crypto-systems. However, the decision of the primality requires significant computational resources. In this paper, we proposed two efficient methods to generate large prime numbers. Firstly, an accelerating method by utilizing pre-installed modular multiplier which is used to calculate public key algorithm is proposed. Secondly, new improved algorithm which reduces computational resources is presented. In the latter algorithm, the requirement for the related parameters are reinforced in order to prevent generating random numbers with small prime factors. In addition, by slightly releasing the requirement for the parameters, it is possible to remove the unit generation procedure in Joye and Paillier´s scheme. Through these modifications, it is possible to obtain new efficient prime number generation algorithm.