[19126] in cryptography@c2.net mail archive
Re: Fermat's primality test vs. Miller-Rabin
daemon@ATHENA.MIT.EDU (Joseph Ashwood)
Tue Dec 6 12:07:31 2005
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From: "Joseph Ashwood" <ashwood@msn.com>
To: "Anton Stiglic" <astiglic@okiok.com>, <cryptography@metzdowd.com>
Date: Mon, 5 Dec 2005 14:03:17 -0800
----- Original Message -----
From: "Anton Stiglic" <astiglic@okiok.com>
Subject: RE: Fermat's primality test vs. Miller-Rabin
>
>>Ok after making that change, and a few others. Selecting only odd numbers
>>(which acts as a small seive) I'm not getting much useful information. It
>>appears to be such that at 512 bits if it passes once it passes 128 times,
>>and it appears to fail on average about 120-130 times, so the sieve
>>amplifies the values more than expected. Granted this is only a test of
>>the
>
>>generation of 128 numbers, but I got 128 primes (based on 128 MR rounds).
>
>
> O.k., so if I read this right, your new results concord with the analysis
> of
> Pomerance et al. That would make much more sense.
>
> When you say "on average about 120-130 times the test fails", out of how
> many is that?
I should've said that the the quantity of numbers that failed the first test
between each success was about 120-130. Apparently, even sieving based
solely on "is it odd" is enough to substantially influence the outcome.
Joe
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