Analyzing Security Protocols Using Time-Bounded Task-PIOAs

Abstract

This paper presents the time-bounded task-PIOA modeling framework, an extension of the probabilistic input/output automata (PIOA) framework that can be used for modeling and verifying security protocols. Time-bounded taskPIOAs can describe probabilistic and nondeterministic behavior, as well as timebounded computation. Together, these features support modeling of important aspects of security protocols, including secrecy requirements and limitations on the computational power of adversarial parties. Discrete Event Dyn Syst (2008) 18:111-159 verification using methods that are compatible with less formal approaches used in the computational cryptography research community. We illustrate the use of our framework by outlining a proof of functional correctness and security properties for a well-known oblivious transfer protocol.

Computational indistinguishability logic

“…In particular, they develop a proof system for bisimulation for their process algebra. Segala et al [13,34] develop a model of probabilistic I/O-automata adapted to security proofs and a corresponding approximated bounded probabilistic simulation relations.…”

Specification Theories for Probabilistic and Real-Time Systems

“…They are used as semantic model for formalisms such as probabilistic process algebra [28] and a probabilistic variant of Harel's statecharts [20]. An input-output version of PA is the basis of PIOA and variants thereof [4,7]. PA have been enriched with notions such as weak and strong (bi)simulations [30], decision algorithms for these notions [6] and a statistical testing theory [8].…”

Automatic Verification of Simulatability in Security Protocols

“…The wide adoption of complex cryptographic protocols in open environments stimulates the elaboration of more and more sophisticated models for the security analysis of such protocols [1,5,7,13]. In turn, the complexity of the security proofs obtained in these models has recently attracted much effort to mechanize such proofs [2,4,11,15].…”

“…In this paper, we outline a new technique for obtaining tool-supported security proofs in the task-PIOA framework of Canetti et al [7] that permits the modeling of both probabilistic and nondeterministic choices, resulting in security notions incomparable to those obtained in pure probabilistic models (as shown in [8]). …”

“…In the task-PIOA framework, this indistinguishability notion is captured by a series of implementation relations, ≤ 0 , ≤ δ , and ≤ neg,pt , that capture perfect, statistical, and computational indistinguishability, respectively, [7,10].…”