  The point of this paper is to use affine automorphisms from algebraic
geometry to build cryptographic multivariate mappings. We will construct groups
G,H, both isomorphic to the cyclic group with a prime number of elements and
multilinear pairings from the k-fold product of G to H. The construction is
reminiscent of techniques in multivariate encryption. We display several
different versions of the discrete logarithm problem for these groups. We show
that the efficient solution of some of these problems result in efficient
algorithms for inverting systems of multivariate polynomials corresponding to
affine automorphisms, which implies that such problems are as computationally
difficult as breaking multivariate encryption.
