P ҉r ҉o ҉g ҉

1. Implement a homomorphic encryption function for beta reduction
50 points

2. Implement said scheme in a compiler for your favorite language
30 points

3. Create an anonymous peer to peer secure grid computing framework
20 points

Due date: before your death.

>>6
Equivalent points will be rewarded for a holomorphic encryption function for brainfuck.

>>9
If it makes things easier you can assume a finite bound on the complexity of the expressions, but the solution would no longer be turing complete, so it would be partial credit. If your encryption function can only encrypt a finite number of values, then you can always consider arbitrary length tuples of these values. Very long lambda strings can be partitioned into blocks and each block can be encrypted separately/sequentially/however-you-want-to-do-it. Of course there would need to be some preservation of structure in order to have an encrypted eval function, but not enough preservation to give away what it is...

>>10
Yeah, it might be easier to just work off of the turing machine model instead.