There is one cryptosystem that uses an NP-hard problem for its security: the McEliece cryptosystem. The problem used here is decoding a generalized version of an error correcting code, which can be made both NP-hard in theory and in practice if you use the right kind of code. It is reliant on using very specific algorithmic parameters to stay hard, though. However, the versions that are not broken are likely post-quantum ready.