Presentation	2005-07-21 Comparison of Error Probabilities of The Miller-Rabin Test by Experimental Measurement Value and Theoretical Upper Bound Toshiya NAKAJIMA,
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Abstract(in English)	We compare theoretical upper bounds of error probability of the Miller-Rabin test(probability that a strong probable prime is a strong pseudoprime) with experimental results for randomly generated odd integers of 100-300 bitlength. The number of strong probable primes we test is the theory-conjectured number in which about sixteen strong pseudoprimes would be found for each bitlength. After the experiment, no strong pseudoprimes were found. Analyzing this result by statistical inference, we estimate with 95% upper confidence limit that the real error probability for the range of tested bitlength is less than 1/4 of the minimum theoretical upper bound.
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Keyword(in English)	primality proving / Miller-Rabin test / error probability / IEEE P1363
Paper #	ISEC2005-15,SITE2005-13
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Committee	ISEC
Conference Date	2005/7/14(1days)
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Paper Information
Registration To	Information Security (ISEC)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Comparison of Error Probabilities of The Miller-Rabin Test by Experimental Measurement Value and Theoretical Upper Bound
Sub Title (in English)
Keyword(1)	primality proving
Keyword(2)	Miller-Rabin test
Keyword(3)	error probability
Keyword(4)	IEEE P1363
1st Author's Name	Toshiya NAKAJIMA
1st Author's Affiliation	Fujitsu Laborartories Ltd.()
Date	2005-07-21
Paper #	ISEC2005-15,SITE2005-13
Volume (vol)	vol.105
Number (no)	193
Page	pp.pp.-
#Pages	6
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