We consider the problem of basing Oblivious Transfer (OT) and Bit Commitment (BC), with information theoretic security, on seemingly weaker primitives. We introduce a general model for describing such primitives, called Weak Generic Transfer (WGT). This model includes as important special cases Weak Oblivious Transfer (WOT), where both the sender and receiver may learn too much about the other party’s input, and a new, more realistic model of noisy channels, called unfair noisy channels. An unfair noisy channel has a known range of possible noise levels; protocols must work for any level within this range against adversaries who know the actual noise level. We give a precise characterization for when one can base OT on WOT. When the deviation of the WOT from the ideal is above a certain threshold, we show that no information-theoretic reductions from OT (even against passive adversaries) and BC exist; when the deviation is below this threshold, we give a reduction from OT (and hence BC) that is information-theoretically secure against active adversaries. For unfair noisy channels we show a similar threshold phenomenon for bit commitment. If the upper bound on the noise is above a threshold (given as a function of the lower bound) then no information-theoretic reduction from OT (even against passive adversaries) or BC exist; when it is below this threshold we give a reduction from BC. As a partial result, we give a reduction from OT to UNC for smaller noise intervals.

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We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. The open map bisimulation is shown to coincide with the extended bisimulation of Hennessy and Stirling. Finally we formulate Milners operational semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation

The meaning and mathematical consequences of linear-ity (managing without a presumed ability to copy) are studied for a path-based model of processes which is also amodel of affine-linear logic. This connection yields an affine-linear language for processes, automatically respect-ing open-map bisimulation, in which a range of process operations can be expressed. An operational semantics isprovided for the tensor fragment of the language. Different ways to make assemblies of processes lead to differentchoices of exponential, some of which respect bisimulation.

This thesis is concerned with formal semantics and models for concurrent computational systems, that is, systems consisting of a number of parallel computing sequential systems, interacting with each other and the environment. A formal semantics gives meaning to computational systems by describing their behaviour in a mathematical model. For concurrent systems the interesting aspect of their computation is often how they interact with the environment during a computation and not in which state they terminate, indeed they may not be intended to terminate at all. For this reason they are often referred to as reactive systems, to distinguish them from traditional calculational systems, as e.g. a program calculating your income tax, for which the interesting behaviour is the answer it gives when (or if) it terminates, in other words the (possibly partial) function it computes between input and output. Church's thesis tells us that regardless of whether we choose the lambda calculus, Turing machines, or almost any modern programming language such as C or Java to describe calculational systems, we are able to describe exactly the same class of functions. However, there is no agreement on observable behaviour for concurrent reactive systems, and consequently there is no correspondent to Church's thesis. A result of this fact is that an overwhelming number of di#erent and often competing notions of observable behaviours, primitive operations, languages and mathematical models for describing their semantics, have been proposed in the litterature on concurrency.

The category of event structures is known to embed fully and faithfully in the category of presheaves over pomsets. Here a characterisation of the presheaves represented by event structures is presented. The proof goes via a characterisation of the presheaves represented by event structures when the morphisms on event structures are "strict" in that they preserve the partial order of causal dependency. 1

The copying of processes is limited in the context of distributed computation, either as a fact of life, often because remote networks are simply too complicated to have control over, or deliberately, as in the design of security protocols. Roughly, linearity is about how to manage without a presumed ability to copy. The meaning and mathematical consequences of linearity are studied for path-based models of processes which are also models of affine-linear logic. This connection yields an affine-linear language for processes in which processes are typed according to the kind of computation paths they can perform. One consequence is that the affine-linear language automatically respects open-map bisimulation. A range of process operations (from CCS, CCS with process-passing, mobile ambients, and dataflow) can be expressed within the affine-linear language showing the ubiquity of linearity. Of course, process code can be sent explicitly to be copied. Following the discipline of linear logic, suitable nonlinear maps are obtained as linear maps whose domain is under an exponential. Different ways to make assemblies of processes lead to different choices of exponential; the nonlinear maps of only some of which will respect bisimulation.

We show that the extensional collapse of the relational model of linear logic is the model of prime-algebraic complete lattices, a natural extension to linear logic of the well known Scott semantics of the lambda-calculus.

We present a presheaf model for the observation of infinite as well as finite computations. We apply it to give a denotational semantics of SCCS with finite delay, in which the meanings of recursion are given by final coalgebras and meanings of finite delay by initial algebras of the process equations for delay. This can be viewed as a first step in representing fairness in presheaf semantics. We give a concrete representation of the presheaf model as a category of generalised synchronisation trees and show that it is coreflective in a category of generalised transition systems, which are a special case of the general transition systems of Hennessy and Stirling. The open map bisimulation is shown to coincide with extended bisimulation of Hennessy and Stirling, which is essentially fair CTL*-bisimulation. Finally we formulate Milners operation semantics of SCCS with finite delay in terms of generalised transition systems and prove that the presheaf semantics is fully abstract with respect to extended bisimulation.