Subject: Re: [stella] 7800 development From: "Frank Palazzolo" <palazzol@xxxxxxxx> Date: Wed, 8 Aug 2001 00:25:44 0400 
Heh, Keith, I still have your C code for this stuff on my hard disk from 1997 :) It looks like p and q are the fabled "factors of N", i.e. N=p*q. Apparently, calculating the X in: X^2 mod N = Y is now easy. (Which means authorizing carts) Unfortunately, I don't know the algorithm, but quoting from "Applied Cryptography" by Bruce Schnier: "If n is the product of two primes, then the ability to calculate square roots mod n is computationally equivalent to the ability to factor n [724]. In other words, someone who knows the prime factors of n can easily compute the square roots of a number mod n, but for everyone else the computation has been proven to be as hard as computing the prime factors of n." The reference [724] is: M.O.Rabin, "Digital Signatures and PublicKey Functions as Intractable as Factorization," MIT Laboratory of Computer Science, Technical Report, MIT/LCS/TR212, Jan 1979. I found this paper here: http://ncstrl.mit.edu/Dienst/UI/2.0/Describe/ncstrl.mit_lcs%2fMIT%2fLCS%2fT R212 I haven't grokked it yet, but it sounds like it describes the technique. I've been wanting to bone up on my number theory anyways... If we come up with an understanding of that paper, we'll finally have code to sign a7800 carts just like Atari did, but using a modern PC. Very cool! Frank  Archives (includes files) at http://www.biglist.com/lists/stella/archives/ Unsub & more at http://www.biglist.com/lists/stella/
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