Constructing Cryptographic Multilinear Maps Using Affine Automorphisms
This work addresses cryptographic security for applications like encryption and key exchange, but it appears incremental as it builds on existing multivariate encryption techniques.
The paper tackles the problem of constructing cryptographic multilinear maps by using affine automorphisms from algebraic geometry, resulting in groups and pairings that relate to the discrete logarithm problem and show computational difficulty comparable to breaking multivariate encryption.
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.