In addition to McEliece (already mentioned by Mike), there's also Hard Based Signatures (such as this one); these are signature algorithms that is based only on some security assumptions of a hash function (and typical hash functions as about as far from numeric-theoretical problems as you can get)

In addition to McEliece (already mentioned by Mike), there's also Hash Based Signatures (such as this one); these are signature algorithms that is based only on some security assumptions of a hash function (and typical hash functions as about as far from numeric-theoretical problems as you can get)