Abstract:  Quantum computers present challenges to cryptographers. Not only do quantum computers have a quadratic advantage on NP-complete problems, they can factor and computer discrete log efficiently. Even without quantum computers, there is a risk that a single discrete log algorithm could break most cryptosystems. We show a primitive for establishing sets that doesn't seem to be susceptible to quantum attack. Black-box quantum algorithms have a lower bound of Omega(2^{n/3}) for the intersection of NP and coNP necessitating 384-bit keys for the post-quantum model. We have a cipher whose keys may range from 256-bits to 1024-bits.