Wow, what a coincidence to hear from the original author!
I never looked at (or even located) the actual password generation code, but only worked on the password verification code,
as it's way easier to do it in that direction. What I initially did was to use the PCSX emulator's cheat finder feature
to locate the memory address of the variable that holds the length of the entered password, then placed a memory breakpoint on that
address in the NO$PSX emulator, which then lead to the discovery of the virtual machine.
After some reverse engineering of the VM's instruction set and programming the VM tracer, as I knew
the address of the VM instruction that incremented the password length counter, I could mash
one button for 24 times, and then look at the differences in the instruction traces when the final password character was entered.
The function make() in the JS is my implementation of the password generator, i.e. inverse of check(), which
wasn't too hard to figure out. I never did bother to find a closed-form expression for the inverse of `mixAndPermute()` function,
so maybe that's where the modular exponentiation hides, but I personally don't have enough number theory-fu to crack that.
Interesting... it looks from your code like maybe I broke the bitmap into chunks and separately permuted each chunk -- probably to make things faster on the (incredibly slow) PS1 CPU.
It's a weird experience for me to try to figure out what I did 20 years ago, without access to the original source. You have almost certainly put more time and thought into reverse engineering it than I did in writing it, and at this point probably know more than I do about how it works. :) Somebody at Naughty Dog must have the code -- maybe they can post a snippet...
(I also play the Crash games with my kids and hardly remember even the levels I worked on... it's like playing a new game! Maybe I am just amnesiac...)
mixAndPermute is actually 'RSA' encryption; the modulus factors as 43 * 47 and the public exponent is 5. Inverting it is a matter of computing x^773 mod 2021.
I never looked at (or even located) the actual password generation code, but only worked on the password verification code, as it's way easier to do it in that direction. What I initially did was to use the PCSX emulator's cheat finder feature to locate the memory address of the variable that holds the length of the entered password, then placed a memory breakpoint on that address in the NO$PSX emulator, which then lead to the discovery of the virtual machine. After some reverse engineering of the VM's instruction set and programming the VM tracer, as I knew the address of the VM instruction that incremented the password length counter, I could mash one button for 24 times, and then look at the differences in the instruction traces when the final password character was entered.
The function `check()` in https://github.com/dezgeg/crash-bandicoot-password-cracking/... is a bit cleaned-up version of the verification function written in JavaScript, mentally translated from this trace dump: https://github.com/dezgeg/crash-bandicoot-password-cracking/... . All the cryptic variable names in the JS come directly from the virtual machine's "registers".
The function make() in the JS is my implementation of the password generator, i.e. inverse of check(), which wasn't too hard to figure out. I never did bother to find a closed-form expression for the inverse of `mixAndPermute()` function, so maybe that's where the modular exponentiation hides, but I personally don't have enough number theory-fu to crack that.