Matrix Representation of Virus Machines and an Application to the Discrete Logarithm Problem.

Abstract

Virus machines, which develop models of computation inspired by biological processes and the spread of viruses among hosts, deviate from the traditional methods. These virus machines are recognized for their computational power (functioning as algorithms) and their ability to tackle computationally difficult problems. In this paper, we introduce a new extension of the matrix-based representation of virus machines. In this way, hosts, the number of viruses and the instructions to control virus transmission are represented as vectors and matrices, describing the computations of virus machines by linear algebra operations. We also use our matrix representation to show invariants, useful in the proofs, of such machines. In addition, an explicit example is shown to clarify the computation and invariants using the representation. That is, a virus machine that computes the discrete logarithm, which relies on the presumed intractability of cryptosystems such the digital signature algorithm.