Check out the modular multiplicative inverse. This is the equivalent of division modulo some number. Implementing it using the EEA can be tricky, though there is a shortcut.

Also, as Frob says, you have the wrong decryption function. You're trying to get "x" back, not "a". Look through it again.

Also, for bonus points, implement a message decryption function without using "a" nor "b".

**Edited by Bacterius, 04 March 2013 - 01:20 AM.**

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

- *Pessimal Algorithms and Simplexity Analysis*