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I'm looking for public key algorithms that are not based on the difficulty of prime factorization. In particular, there are rumblings about the prime factorizations being solved in some state security apparatus with a combination of better algorithms and the horsepower for brute forcing.

I remember reading a few years back about alternative algorithms based on other equally difficult problems that won't be easily solved if P <> NP.

What are the most promising research avenues in security and encryption that do not rely on prime factorization?

Vinay Paradox
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Elliptic Curve is big these days. The math is pretty mind boggling, though.

McEliece is another alternative that meets your description.

Beyond that, you can just wander the wikipedia public key encryption references.

tbroberg
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