# RSA

brian moore bem at cmc.net
Sat Feb 12 14:18:16 CET 2000

```On Sat, Feb 12, 2000 at 02:04:23PM +0000, Simpson, Sam wrote:
> Hi Brian,

Hello.

> > Well, you can't really generate a random prime.  In order to do that,
> > you'd have to be factoring really large numbers, which is generally
> > impracticle (the whole point of RSA is based on the hardness of
> > factoring).
>
> Not true...It is possible to deterministically check to see if a number is
> prime and the workload is FAR less than testing a primes up to the square
> root.

Got an algorithm?

> > You'll have to do it the way everyone else does: generate a really big
> > number, check it against a few low primes (ie, 2,3,5, etc, maybe up to
> > 1000 or so) and then use probability to determine whether
> > it's -likely- > to be a prime or not.
>
> Erm, not true.  It is quicker to use probalistic methods, but if 100%
> assurance is required then it is still feasible (on a PC - maybe not in
> constrained environments) to produce a number that is *certainly* a prime
> with a "deterministic method".  See for example Silvermans posts to
> sci.crypt
> (http://x28.deja.com/[ST_rn=ps]/getdoc.xp?AN=564819271&CONTEXT=950363781.265
> 224197&hitnum=2)

I don't see an algorithm cited there, just "algorithms exist".

(The algorithm at the end of the cited post is not proven -- it's still
a matter of statistics.  There's a huge difference between "well, we
haven't seen a non-prime pass this gauntlet" and "a non-prime cannot
pass this".)

--
Brian Moore                       | Of course vi is God's editor.
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Netscum, Bane of Elves.

```