Towards Incrementalization of Holistic Hyperproperties

Abstract

Abstract.A hyperproperty is a set of sets of finite or infinite traces over some fixed alphabet and can be seen as a very generic system specification. In this work, we define the notions of holistic and incremental hyperproperties. Systems specified holistically tend to be more intuitive but difficult to reason about, whereas incremental specifications have a straightforward verification approach. Since most interesting securityrelated hyperproperties are in the syntactic class of holistic hyperproperties, we introduce the process of incrementalization to convert holistic specifications into incremental ones. We then present three incrementalizable classes of holistic hyperproperties and a respective verification method.

Temporal Logics for Hyperproperties

“…There is a manual verification methodology for IL [44], but no automated decision procedure. -Another incremental hyperproperty logic IL k µ , a fragment of polyadic modal µ-calculus [3] that permits at most one quantifier alternation (a greatest fixed-point followed by a least fixed-point).…”

“…Other program logics could already express observational determinism or closely related policies [7,33,45]. Milushev and Clarke [44][45][46] have even proposed other logics for hyperproperties, which we discuss in Section 8. But HyperLTL provides a simple and unifying logic in which many information-flow security policies can be directly expressed.…”

Many-to-many information flow policies

“…We mention, e.g., hyperproperties [5] and their logics (e.g. [4,15]). Our policies can be easily integrated in logic-based languages to obtain a richer policy language.…”

Incremental Hyperproperty Model Checking via Games

“…Unfortunately, hyperproperties lack a generic verification methodology: for instance, there is no such verification methodology for possibilistic information flow hyperproperties [3]. In order to make a step towards such a methodology, in recent work [15] we proposed an incremental approach to both system and hyperproperty specification and verification. As a result, systems can be seen as potentially infinite trees and hyperproperties as coinductive predicates on ktuples of trees expressed in a logic called IL.…”

“…As a result, systems can be seen as potentially infinite trees and hyperproperties as coinductive predicates on ktuples of trees expressed in a logic called IL. Specifications defined in such a manner are called incremental hyperproperties (IHPs) and we argued that they have a clear and feasible verification methodology [15]. Given a hyperproperty H, an IHP H is the greatest fixed point of a monotone function over k-tuples of trees such that H implies or is equivalent to H. We also introduced Hsimulation relations which correspond to a monotone operator whose greatest fixed point is the coinductive tree predicate H .…”