A new Shamir’s three pass random matrix ciphering mechanism

Abstract

A new Shamir’s three pass random matrix ciphering mechanism. This new random matrix ciphering mechanism uses a three-pass protocol with encryption operators that are random commutative matrices. The three-pass protocol, at the same time, allows the authentication of the participants in the transaction (Alice and Bob as usual). The novelty of this mechanism is that it uses two encryption matrices for Alice [AC1] and [AC2] and for Bob [BC1] and [BC2], which "encapsulate" the message matrix [M]. For example, the data flow from Bob to Alice is the product of five matrices: [BC1][AC1][M][AC2][BC2] in which the possibility for Alice to delete her encryption matrices [AC1] and [AC2], implies that the matrices: [BC1] and [AC1] and also [AC2] and [BC2] be commutative, therefore randomly generated in the same eigenvector spaces. This is made possible because a non-singular matrix [G] can be put in the following form: [G] = [C] [D] [C]-1 in which the matrix [C] is related to the eigenvector space of the matrix [G], the diagonal matrix [D] being its eigenvalues. This equation then makes it possible to write an infinity of encryption commutative matrices [G] belonging to this eigenvector space, each having different eigenvalues [D] generated randomly by the mechanism. The proposed mechanism is based on this equation. The authentication process consists of a pseudo-random permutation module, embedded in the mechanism, generating permutation matrices which are unique identifiers of Alice and Bob. These permutation matrices also "encapsulate" the data stream exchanged between Alice and Bob.