Probabilistic analysis on the optimal combination of trial division and probabilistic primality tests for safe prime generation

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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.

Original languageEnglish
Pages (from-to)1210-1215
Number of pages6
JournalIEICE Transactions on Information and Systems
VolumeE94-D
Issue number6
DOIs
Publication statusPublished - 2011 Jun

Keywords

  • Cryptography
  • Information security
  • Miller-rabin test
  • Safe prime
  • Safe prime generation
  • Trial division

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