A post-quantum key exchange protocol from the intersection of quadric surfaces
This work addresses the need for secure communication in a post-quantum era, offering a novel cryptographic protocol, though it appears incremental as it builds on existing mathematical constructs.
The authors tackled the problem of designing a post-quantum key exchange protocol by using quadric surfaces and Veronese embeddings, resulting in a method where Alice and Bob reconstruct a curve's j-invariant as a shared secret, with security based on conjectured quantum-resistant problems.
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.