Key exchange based on three-dimensional Segre products and their projections

In this paper we present a key exchange protocol in which Alice and Bob use a three-dimensional Segre product embedded in a large projective space by mean of the Veronese embedding. Public keys are given by hyperplanes cutting pairs of Segre products containing a common plane. Alice and Bob consider the residual curve which is projectively equivalent to a smooth plane curve of genus 1, whose j-invariant is the exchanged key. When the dimension of the above projective space increases very much, HPC capabilities are required.