A post-quantum key exchange protocol from the intersection of quadric surfaces

Abstract

In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded in a large ambient space by means of the Veronese embedding and public keys given by hyperplanes containing the embedded quadrics. Both of them reconstruct the isomorphism class of the intersection which is a curve of genus 1, and is uniquely determined by the j-invariant. An eavesdropper, to find this j-invariant, has to solve problems which are conjecturally quantum resistant.