Paper 2024/1793

On the Jordan-Gauss graphs and new multivariate public keys

Abstract

We suggest two families of multivariate public keys defined over arbitrary finite commutative ring \(K\) with unity. The first one has quadratic multivariate public rule, this family is an obfuscation of previously defined cryptosystem defined in terms of well known algebraic graphs \(D(n, K)\) with the partition sets isomorphic to \(K^n\). Another family of cryptosystems uses the combination of Eulerian transformation of \(K[x_1, x_2, \ldots, x_n]\) sending each variable \(x_i\) to a monomial term with the quadratic encryption map of the first cryptosystem. The resulting map has unbounded degree and the density \(O(n^4)\) like the cubic multivariate map. The space of plaintexts of the second cryptosystem is the variety \((K^*)^n\) and the space of ciphertexts is the affine space \(K^n\).