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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
Publication Date: 1999/10/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
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.