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New Methods of Generating Primes Secure against Both P1 and P+1 Methods
Yoshizo SATO Yasuyuki MURAKAMI Masao KASAHARA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E82A
No.10
pp.21612166 Publication Date: 1999/10/25
Online ISSN:
DOI:
Print ISSN: 09168508 Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Security Keyword: prime generation, P1 method, P+1 method, trial division method,
Full Text: PDF(456.1KB)>>
Summary:
Since cryptosystem based on the problem of factoring the composite number N can be attacked with P1 and P+1 methods, it is required that P1 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 P1 and P+1 methods. Second, we propose two efficient algorithms for generating secure primes against both P1 and P+1 methods by extending the trial division method.

