FORTRAN 77 on PDP-11

[Jerome H. Fine]

 >Paul Koning wrote:

>Depending on how deep you want to dig, if you like primes, you should
>get yourself some cryptography textbooks.  A good primer, without a
>lot of serious math, is Bruce Schneier's "Applied Cryptography".  If
>you want to understand the math in depth, get "Handbook of Applied
>Cryptography" (I think that's the correct title) by Menezes et al.  I
>have both, though I'm stuck at around chapter 2 in the latter because
>the math goes beyond what I know.
>
>I think Knuth has a discussion of the M-R test -- surely you have
>Knuth, right?  If not, you need to fix that.
>
>The M-R test is a "probabilistic primality test" -- a fast way of
>testing a number for being prime that has a certain probability of
>giving the wrong answer.  You can do the test repeatedly, and if the
>tests are done right so they are independent, the test will become
>more and more accurate.  This test is generally used in crypto
>programs because it is fast.
>
>There are also tests for primality that are exact rather than
>probabilistic -- those are MUCH slower.  For multi-thousand-bit
>numbers, people use M-R unless they absolutely, positively require a
>guarantee of primality and can afford the hours or days of CPU time
>investment.  An example: the Diffie-Hellman parameters for the IKE key
>exchange protocol (part of IPsec) were subjected to the full primality
>test, not just M-R.
>
Jerome Fine replies:

Interesting - THANK  YOU!!  I did a google on the
topic.  While my interest at the moment is really
limited to small primes (currently defined as less
than 1000 digits although at present I will initially
limit myself to 32 bits), I might want to look elsewhere
in the future.  I had sort of noticed the M-R in
looking at google for the very largest primes which
are currently almost 10 million decimal digits, but
had not attempted to really understand the M-R test.

Sincerely yours,

Jerome Fine
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