New Methods of Generating Primes Secure against Both P-1 and P+1 Methods

Yoshizo SATO  Yasuyuki MURAKAMI  Masao KASAHARA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.10   pp.2161-2166
Publication Date: 1999/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Security
prime generation,  P-1 method,  P+1 method,  trial division method,  

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Since cryptosystem based on the problem of factoring the composite number N can be attacked with P-1 and P+1 methods, it is required that P-1 and P+1 should be difficult to be factored into many small primes, where we assume that the P is a factor of N. In this paper, first, we consider the distribution of secure primes against both P-1 and P+1 methods. Second, we propose two efficient algorithms for generating secure primes against both P-1 and P+1 methods by extending the trial division method.