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In this paper we present a key exchange protocol in which Alice and Bob havesecret keys given by quadric surfaces embedded in a large ambient space bymeans of the Veronese embedding and public keys given by hyperplanes containingthe embedded quadrics. Both of them reconstruct the isomorphism class of theintersection which is a curve of genus 1, which is uniquely determined by the$j$-invariant. An eavesdropper, to find this $j$-invariant, has to solveproblems which are conjecturally quantum resistant.

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