Leonard Schulman: Cryptography from tensor problems

Abstract

We describe a new cryptosystem which (conjecturally) provides both a
trap-door one-way function and a signature scheme. The new system is a
type of "multivariate quadratic" cryptosystem, but is based on a
different trap-door from existing methods, and is simpler.

Known quantum algorithms do not appear to help an adversary attack
this cryptosystem (beyond the asymptotic square-root-speedup which
applies to all oracle search problems).