Tsüklite eemaldamine krüptograafiliste protokollide analüsaatori protokolliesitusest

Abstract

Käesolev töö käsitleb ühte võimalust Peeter Laua ja Ilja Tšahhirovi loodud krüptograafiliste protokollide analüsaatori protokolliesitusest tsüklite eemaldamiseks. Protokolliesituseks kasutatakse analüsaatoris sõltuvusgraafe, millesse transformatsioonide tulemusel võivad tekkida tsüklid. Analüsaatoris on olemas teisendused, mis võimaldavad eemaldada tsükleid, kus on maksimaalselt üks mitterange tipp. Lahendada on vaja rohkemaid mitterangeid tippe sisaldavate tsüklite eemaldamise ülesanne.

The aim of this paper was to describe a cryptographic protocol analyser, specially its protocol representation, and implement a transformation to simplify protocol representation. The analyser was first described in the doctoral thesis of Ilja Tšahhirov and was afterwards implemented by Peeter Laud and Ilja Tšahhirov. The analyser is designed for static protocol analysis to check confidentiality and integrity of secret messages. All cryptographic primitives used in the protocols have to be strong in computational model in order for the analysis to be correct. Protocols are represented by dependency flow graphs that indicate possible data and control flows in protocol execution. Like any directed graphs, they may contain directed cycles that make understanding and drawing graphs more difficult. In general, all nodes in graph can be divided to two groups - strict and non-strict nodes. Strict nodes only compute their value if they have received all their inputs, on the other hand, non-strict nodes compute their value as soon as they have sufficient inputs to do so. All cycles in graph can be divided to groups depending on which non-strict nodes they contain and how many of them are present. The analyser already has transformations to cut cycles with none or just one non-strict nodes. This paper described a way based on depth-first search trees to find all cycles and transform them so that they contain only one non-strict node and can therefore be removed by cutting an edge in the cycle.