David McClain <dbm_at_refined-audiometrics.com> Subject: [sftalk] Re: generating self-contained dlls: sf or swiftx?

> No, it needs to be a 1024-bit prime P = 2*Q+1 with Q also prime. We
> want a maximal length subgroup of length P-1 so that we don't get
> trapped in a short-cycle subgroup a you would if Q were composite. P
> itself must be prime or the SRP-6 (which is using a variant of
> Diffie-Hellman) won't work properly. So if P is 1024 bits then Q is 1023
> bits, right?

Ai, first bug.

The MSB of Q must be 1, or Q may have many less bits than the 1023
required. So actually only 1022 bits to process.

> Miller-Rabin is a good start, but it is not definitive. You also need to
> test with a probabilistic Lucas test, which tests for the probability
> that a number is composite -- goes the other way from Miller-Rabin, see?

Probabilities both ways -- that's why I asked how sure you want to
be and how long it is allowed to take. Absolutely sure can take very long!

[..]

> So that Bignum arithmetic, plus the need for platform independence, plus
> the need for a "portable dialect" (heh!) of Forth, probably is gonna
> stop you in your track pretty quickly.

Actually I do have all of that already, including Lucas-Lehmer, on Windows,
Linux and OSX, for 32/64-bit Forths. But as my bignums use a tiny bit of
assembler that part may not be directly portable to other 64-bit Forths.

-marcel

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Received on Sun Jan 31 2010 - 04:04:29 PST