[ykehjiqq] 129-bit AES

start with AES with a 128-bit key and add extra bit to specify whether the cipher is to be used in the decoding or encoding direction.  if it is the least significant bit, then cipher direction is determined by whether the key is even or odd.

pick a decimal number 0 through 680564733841876926926749214863536422911 (= 2^129-1) as the puzzle number.

or make it the most significant bit and convert to decimal by two's complement.  opposite directions have opposite sign (counting zero as positive) but typically have very different absolute values.

of course, this is a "related key", but I'm not sure where that would make protocols that use a block cipher go wrong.