Non-Prime Factorization Public Key Algorithms and Code?
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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?