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

TL;DR

This paper introduces a post-quantum secure key exchange protocol based on the intersection of quadric surfaces and hyperplanes, leveraging algebraic geometry to ensure resistance against quantum attacks.

Contribution

It proposes a novel cryptographic scheme using algebraic geometry, specifically quadric surfaces and their intersections, for secure key exchange in the post-quantum era.

Findings

Protocol is conjecturally quantum resistant.

Reconstructs isomorphism class via the $j$-invariant of genus 1 curves.

Uses Veronese embedding for embedding quadrics.

Abstract

In this paper we present a 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, which is uniquely determined by the $j$-invariant. An eavesdropper, to find this $j$-invariant, has to solve problems which are conjecturally quantum resistant.