> > I may have missed this, but was there any final judgment on the Meganet
> >Corp. claim that they had a "deterministic and polynomial-time" prime
> >test? There were some discussions on the list early this year when they
> >first made their claim. But I don't recall reading about any resolution.
> >Did this just fade away? Are they still holding to their claim? And if
> >they are, does it stand up to examination (if they are revealing enough
> >for examination)?
>
> These guys are snake-oil vendors. I don't know what type of prime test
> they are claiming to have or not have but from my exposure to their crypto
> claims I wouldn't trust anything from them without proof.
I'd say this is true in this case as well.
On their site they say things like:
>Those results are unheard of. The 1,000 bits test on a Sparc
> II workstation takes 5 Minutes and it is still only
> PROBABALISTIC. The gap in time is much greater for larger
> bit sizes.
Eh? The probable prime test on 10^999+7 took ~20 seconds on my PII/233. That's
a thousand digits, ~3000 bits.
(w/primeform)
>The major breakthrough is solving a 400 year old
> mathematical problem � how to positively identify a prime
> number without spending exponential time in dividing the
> number by all the primes up to its root.
This problem was solved by a primality testing algorithm that is based on
eliptic curves (it was not practical), but it was polynomial.
>The solution
> Meganet Corporation have developed is based on a newly
> designed Mathematical Sequence called the T-Sequence.
> Once a number is transformed to the T-Sequence, its
> quadratic residue has definitive characteristics if it�s a prime
> number that can be easily determined in polynomial time by
> performing a binary decomposition.
Ok, if it is a prime then a^p==a mod p, what's your point?
They don't even give a correct statment for their claims, they should say
if and only if...
>Meganet Corporation would like to emphasize that there is a
> 100% mathematical proof behind their T-Sequence, and
> further, it is a complete working product tested successfully
> on over 1.3 million numbers without a single mistake.
Ok, so proofs are measured in percent? Also, how many numbers are both a 2-spsp,
and a lucas psuedoprime ($620 prize). I'll bet that that combination has been
tested for a lot more than 1.3 million numbers without failure...
Besides, the name meganet is too remanisant of Homer simpson's name for
his internet company (on the Simpsons) I believe he called it something like
hyper-compu-global-meganet. (It was eventually bought out by bill gates for
fear of competition).
-Lucas
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