Matthew J Ghio suggested an encryption scheme based on polynomials mod P. I haven't looked at this too thoroughly yet, but a quick read seemed to suggest that it relies on the intractability of solving polynomial equations mod P. If so, realize that this is a very tractable problem with efficient (polynomial time) algorithms given by e.g. Knuth. If anyone wants more info I'll post the reference. It's in his sections on computer arithmetic. The algorithm was discovered by a researcher at Bell Labs as I recall; the name escapes me.