Universal Composability is Secure Compilation

Universal composability is a framework for the specification and analysis of cryptographic protocols with a strong compositionality guarantee: UC protocols are secure even when composed with other protocols. Secure compilation tells whether compiled programs are as secure as their source-level counterparts, no matter what target-level code they interact with. These two disciplines are studied in isolation, but we believe there is a deeper connection between them with benefits from both worlds to reap. This paper outlines the connection between universal composability and robust compilation, the latest of secure compilation theories. We show how to read the universal composability theorem in terms of a robust compilation theorem and vice-versa. This, in turn, shows which elements of one theory corresponds to which element in the other theory. We believe this is the first step towards understanding how can secure compilation theories be used in universal composability settings and vice-versa

Toward an Algebraic Theory of Systems

We propose the concept of a system algebra with a parallel composition operation and an interface connection operation, and formalize composition-order invariance, which postulates that the order of composing and connecting systems is irrelevant, a generalized form of associativity. Composition-order invariance explicitly captures a common property that is implicit in any context where one can draw a figure (hiding the drawing order) of several connected systems, which appears in many scientific contexts. This abstract algebra captures settings where one is interested in the behavior of a composed system in an environment and wants to abstract away anything internal not relevant for the behavior. This may include physical systems, electronic circuits, or interacting distributed systems. One specific such setting, of special interest in computer science, are functional system algebras, which capture, in the most general sense, any type of system that takes inputs and produces outputs depending on the inputs, and where the output of a system can be the input to another system. The behavior of such a system is uniquely determined by the function mapping inputs to outputs. We consider several instantiations of this very general concept. In particular, we show that Kahn networks form a functional system algebra and prove their composition-order invariance. Moreover, we define a functional system algebra of causal systems, characterized by the property that inputs can only influence future outputs, where an abstract partial order relation captures the notion of "later". This system algebra is also shown to be composition-order invariant and appropriate instantiations thereof allow to model and analyze systems that depend on time