Public-Key Encryption Schemes with Auxiliary Inputs. Theory of Cryptography

Abstract

We construct public-key cryptosystems that remain secure even when the adversary is given any computationally uninvertible function of the secret key as auxiliary input (even one that may reveal the secret key information-theoretically). Our schemes are based on the decisional Diffie-Hellman (DDH) and the Learning with Errors (LWE) problems. As an independent technical contribution, we extend the Goldreich-Levin theorem to provide a hard-core (pseudorandom) value over large fields.