Comment on 'A Framework for Modelling Trojans and Computer Virus Infection'

Abstract

Thimbleby et al. [1] have recently introduced a framework for modelling computer viruses and other malicious programs. They also criticized the use of Turing machine (TM) models for the same purpose. This note (re-)introduces a universal Turing machine (UTM) model which originally appeared in [2] and discusses its properties in the light of Thimbleby et al.’s critique. We show that their points are not valid in the case of models using UTMs. We show that (universal) TMs can serve as a basis of a model illustrating the properties of viruses and other malicious programs. An obvious benefit of our model is that TMs and their properties are so widely known. This gives a considerable ‘competitive advantage’ to our model and compensates for the fact that TM models are a bit clumsy. A typical model using TMs is presented by Cohen [3]. The concept of viral sets is essential in the model. A viral set is a pair (M,W) where M is a TM and W is a set of strings over its tape alphabet. Each string w in W has the property that when M , being in its start state, starts reading w it always writes another string w′ of W to somewhere else in its tape. Hence, each w in W is a virus and when M (i.e. ‘a computer’) reads it, another virus will appear somewhere in its tape (i.e. in its ‘memory’). Cohen’s model allows us to directly apply the well-known undecidability results for TMs, e.g. it follows from the halting problem of TMs that it is undecidable whether or not a given pair (M, {w}) is a viral set. The shortcomings of Cohen’s model are discussed in [2]. Most of the critiques of Thimbleby et al. [1] are appropriate in the case of Cohen’s model. Instead of a TM we use the UTM as a model of a computer. Viruses are then descriptions of TMs causing other descriptions to be written to the tape of the UTM. In Cohen’s model the set of viruses depends on the TM on which they are interpreted. In our modification the set of viruses depends on the rules according to which the descriptions of TMs are written.