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Probabilistic Analysis on the Optimal Combination of Trial Division and Probabilistic Primality Tests for Safe Prime Generation

Title
Probabilistic Analysis on the Optimal Combination of Trial Division and Probabilistic Primality Tests for Safe Prime Generation
Author
박희진
Keywords
safe prime; safe prime generation; trial division; miller-rabin test; cryptography; information security
Issue Date
2011-06
Publisher
Institute of Electronics, Information and Communication Engineers
Citation
IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS E SERIES D, 2011, 94(6), P.1210-1215
Abstract
A safe prime p is a prime such that (p-1)/2 is also a prime. A primality test or a safe primality test is normally a combination of trial division and a probabilistic primality test. Since the number of small odd primes used in the trial division affects the performance of the combination, researchers have studied how to obtain the optimal number of small odd primes to be used in the trial division and the expected running time of the combination for primality tests. However, in the case of safe primality tests, the analysis of the combination is more difficult, and thus no such results have been given. In this paper, we present the first probabilistic analysis on the expected running time and the optimal number of small odd primes to be used in the trial division for optimizing the tests. Experimental results show that our probabilistic analysis estimates the behavior of the safe primality tests very well.
URI
https://www.jstage.jst.go.jp/article/transinf/E94.D/6/E94.D_6_1210/_articlehttp://hdl.handle.net/20.500.11754/66683
ISSN
0916-8532
DOI
10.1587/transinf.E94.D.1210
Appears in Collections:
COLLEGE OF ENGINEERING[S](공과대학) > COMPUTER SCIENCE(컴퓨터소프트웨어학부) > Articles
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