  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.
