> With regards to the claim made by VME, Brian Beesley and I asked them to
> produce a factor of M(727). They did not come up with a factor. Instead
> they came up with the following (mass) reply which I leave to everyone's
> own thoughts. They also attached a letter in .gif format which can be
> viewed at http://home.wxs.nl/~tha/Mersenne/endorse.gif
Before anyone believes anything from this company I would
strongly suggest reading the snake oil FAQ. One version is at
http://www.cs.uu.nl/wais/html/na-dir/cryptography-faq/snake-oil.html
If a strong pseudoprime test identifies a number as composite it
is definitely composite, otherwise it is a probable prime. The chance
that it returns prime when it is actually composite is bounded by 1/4
for each base. If a 100 bases are used then the chance of error is
(1/4)^100 = 6.2*10^-61. It would be more likely the calculation was
affected by cosmic radiation.
A probablistic primality test could be as fast as the timings given
by meganet on their deterministic primality test. Their claim of 5
minutes for a sparc II workstation for a probabilistic primality test
of a 1000 bit number is absurd.
In Dr. Milstein's endorsement of this primality test, he states "I
applied the assertions of the paper to a number of non-trivial values."
and "I did not develop rigorous proofs, but I did recast the proposed
techniques within a sound mathematical framework ... I also believe
that rigorous proofs are less important than validating the performance
of the algorithm."
I emailed Dr. Milstein and asked if he has not rigorously proved this
then is it possible that it could a probabilisitic primality test. This
is his response:
"The answer to your question is NO, I've formulated the raw material
given to me by Meganet as a clear mathematical representation, i.e.
Lemma, Theorem, Corollary etc. I've proven some results and 'convince
myself' after a serious analysis that there is merit to the claim of 'a
deterministic algorithm'. Moreover, I've checked specific cases were
other techniques identified pseudo primes as primes or skipped all
together a specific prime. My first choice at this time, is to exhibit a
working algorithm rather than generating an analytical proof (I might do
it in the future)."
Dr. Milstein states that there is "NO" possibility that this is a
probabilistic primality test, despite having no rigorous proof. I don't
know what technique would identify a pseudoprime as prime. I have some
doubts as to Dr. Milstein's ability or bias.
In my opinion Meganet is making fraudelent claims of its software.
Why would anyone trust an unproven unpublished algorithm especially for
cryptography and primality testing?
Meganet has sent me four emails about their claims, despite responding
with complaints they believe I had some interest. Others on this list
have also received their emails which leads me to believe they may have
taken addresses from the mail archive. So I have removed the zip files
from the web page.
From a traceroute Sprintlink appears to be the upstream provider of
Meganet. I have sent three complaints to [EMAIL PROTECTED]
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