A public key system with signature and master key functions

Abstract

Let K be a finite field of 2m elements. Let Ø4Ø3Ø2Ø1be tame automorphisms of the n + r-dimensional affine space Kn+r . Let the composition Ø4Ø3Ø2Ø1 be π. The automorphism π and some of the Ø i ’S will be hidden. Let the component expression of π be . Let the restriction of π to a subspace be as . The field K and the polynomial map will be announced as the public key. Given a plaintext , then the ciphertext will be . Given Ø i and , it is easy to find . Therefore the plaintext can be recovered by . The private key will be the set of maps Ø4Ø3Ø2Ø1. The security of the system rests in part on the difficulty of finding the map π from the partial informations provided by the map and the factorization of the map π into a product (i.e., composition) of tame automorphisms Ø i 's.