RE: [Algorithms] Message signature in token ring

[Tony C. <to...@mi...>]

>How do people generate these really prime large numbers and relative
primes, anyway? Simple brute=20
>force? Does the choice of prime numbers affect the security of the
algorithm? (Does their magnitude >affect the security?)

Actually, they don't. Confirming for certain that you have a prime
number is a very hard problem. However, you can determine that the
probability of your number being composite is below any given threshold
you like (there are well-known algorithms for this), the longer you run
for, the more sure you can be. Once your probability of having a
composite falls below one in
age-of-universe/protons-in-galaxy/days-until-Duke-Nukem-Forever-ships/yo
ur-big-number-of-choice, you're happy with it.

If you're interested, some quick Googling should reveal some
implementations of RSA, including key generation, which will give you
the idea (but please don't trust random code you trawled from the net,
even if not malicious, it may be buggy in subtle ways not immediately
obvious).

The magnitude of one of the primes in RSA is a factor in the security of
the system (because that's effectly what dictates the size of the number
an attacker would have to factor to break the system).

However, I would like to very strongly restate my observation that you
really really really shouldn't be doing this yourself. It's easy to get
wrong even for an expert in crypto algorithms (and, no offense, but it
doesn't sound like you are an expert). Any decent OS will provide
perfectly good implementations of these core algorithms (for example,
the Crypto API in Windows), I highly recommend you use them.

Tony Cox - Development Lead, Hockey
Microsoft Games Studios - Sports