Subject: Re: [stella] 7800 development From: "Frank Palazzolo" <palazzol@xxxxxxxx> Date: Wed, 8 Aug 2001 23:42:25 0400 
Hey guys, Woohoo!  I'm generating 7800 signatures now in a C++ program! Keith, your formula was almost perfect, I just fixed it by following the analysis on page 6 and 7 in that paper I cited earlier. I've attached my code as it is, for reference. BTW, I'm using the library "Crypto++", which has all the algorithms you'd ever need. I don't have the 7800 checksum algorithm integrated into it yet. I've only tested it on Pole Position but it seems to be correct. All those numbers in the Atari ST program come from p and q. p and q were chosen with the following properties: p and q must be prime p (mod 4) = 3 q (mod 4) = 3 of course...n = p*q and... pexp = (p+1)/4 qexp = (q+1)/4 ap and aq can be determined using something called the Chinese Remainder Theorem: ap can be calculated based on ap (mod p) = 1, and ap (mod q) = 0 aq can be calculated based on aq (mod p) = 0, and aq (mod q) = 1 The only funny part is in the hash calculation. The final step of setting of byte 4 to zero is not part of the hash algorithm. It's just a little extra to trip you up. So, it works like this: Atari:  Compute Full Hash of cart (as in MungeCart(), but do not set that byte to zero) Use formula to compute sig from cart: sig = [ap * (hash^((p+1)/4)(mod p))) + aq * ((hash^((q+1)/4))(mod q))](mod n) Give the sig to the cart maker Console:  Compute a hash from sig: sig_hash = (sig^2)(mod n) Tweak hash before compare (set byte to zero) Compute a hash from the cart Tweak cart_hash before compare (set byte to zero) Compare the two tweaked hashes. Frank
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Re: [stella] 7800 development, Keith Gerdes  Thread  Re: [stella] 7800 development, Eckhard Stolberg 
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