Arithmetic Cryptography

Abstract

We study the possibility of computing cryptographic primitives in a fully-black-box arithmetic model over a finite field $\F$. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits which make only a black-box use of the underlying field, and the adversary has a full (non-black-box) access to the field. This model captures many standard information-theoretic constructions.