On algebraic graph theory and non-bijective multivariate maps in cryptography

Abstract

Special family of non-bijective multivariate maps Fn of Zmⁿ into itself is constructed for n=2,3,… and composite m. The map Fn is injective on Ωn={x|x₁+x₂+…xn ∈ Zm∗} and solution of the equation Fn(x)=b,x∈Ωn can be reduced to the solution of equation zr=α, z∈Zm∗, (r,ϕ(m))=1. The ``hidden RSA cryptosystem'' is proposed. Similar construction is suggested for the case Ωn=Zm∗ⁿ.