On a FPGA-based method for authentication using Edwards curves

Abstract

Modern cryptographic authentication protocols have a wide range of real world applications to gain assurance about the identity of a potential communication partner. For example they are used as wireless keys to gain access to an otherwise restricted place, e.g. a closed door or a car. Widely used challenge-response authentication protocols have very often a shared secret, such that the a prover can convince a verifier about his identity by using this secret. The major drawback of this scheme is, that the prover and the verifier both know the shared secret, and thus the distribution of the secret is problematic. This problem can be solved by using asymmetric cryptography and adapting suitable existing protocols to the used cryptographic primitive. This paper evaluates the Schnorr protocol for FPGA implementations and adopts twisted Edwards curves, a variant of elliptic curves, for this study. Both a theoretical introduction and a thorough practical part is provided and in this way the suitability of this combination for hardware implementations is shown.