The Foundational Work of Harrison-Ruzzo-Ullman Revisited

The work by Harrison, Ruzzo, and Ullman (the HRU paper) on safety in the context of the access matrix model is widely considered to be foundational work in access control. In this paper, we address two errors we have discovered in the HRU paper. To our knowledge, these errors have not been previously reported in the literature. The first error regards a proof that shows that safety analysis for mono-operational HRU systems is in NP. The error stems from a faulty assumption that such systems are monotonic for the purpose of safety analysis. We present a corrected proof in this paper. The second error regards a mapping from one version of the safety problem to another that is presented in the HRU paper. We demonstrate that the mapping is not a reduction, and present a reduction that enables us to infer that the second version of safety introduced in the HRU paper is also undecidable for the HRU scheme. These errors lead us to ask whether the notion of safety as defined in the HRU paper is meaningful. We introduce other notions of safety that we argue have more intuitive appeal, and present the corresponding safety analysis results for the HRU scheme.