Dominic J. D. Hughes

Information hiding, anonymity and privacy: a modular approach

We propose a new specification framework for information hiding properties such as anonymity and privacy. The framework is based on the concept of a function view, which is a concise representation of the attackers partial knowledge about a function. We describe system behavior as a set of functions, and formalize different information hiding properties in terms of views of these functions. We present an extensive case study, in which we use the function view framework to systematically classify and rigorously define a rich domain of identity-related properties, and to demonstrate that privacy and anonymity are independent. The key feature of our approach is its modularity. It yields precise, formal specifications of information hiding properties for any protocol formalism and any choice of the attacker model as long as the latter induce an observational equivalence relation on protocol instances. In particular, specifications based on function views are suitable for any cryptographic process calculus that defines some form of indistinguishability between processes. Our definitions of information hiding properties take into account any feature of the security model, including probabilities, random number generation, timing, etc., to the extent that it is accounted for by the formalism in which the system is specified. Partially supported by ONR grants N00014-02-1-0109 and N00014-01-1-0837 and DARPA contract N66001-00-C-8015.

Proof nets for unit-free multiplicative-additive linear logic

A cornerstone of the theory of proof nets for unit-free multiplicative linear logic (MLL) is the abstract representation of cut-free proofs modulo inessential rule commutation. The only known extension to additives, based on monomial weights, fails to preserve this key feature: a host of cut-free monomial proof nets can correspond to the same cut-free proof. Thus, the problem of finding a satisfactory notion of proof net for unit-free multiplicative-additive linear logic (MALL) has remained open since the inception of linear logic in 1986. We present a new definition of MALL proof net which remains faithful to the cornerstone of the MLL theory.

The automatic measurement of facial beauty

We develop an automatic facial beauty scoring system based on ratios between facial features. After isolating the face, eyes, eyebrows and mouth in a portrait photograph, we represent a face abstractly as an 8-element vector of ratios between these features. We use a variant of the K-nearest neighbor algorithm, in the context of a parameterized metric space optimized using a genetic algorithm, to learn a beauty assignment function from a training set of photographs rated by humans. We assess performance on a test set of photographs, concluding that when facial ratios are accurately extracted in the computer vision phase, the results of the program are highly correlated with median-human ratings of beauty.

Proof nets for unit-free multiplicative-additive linear logic (extended abstract)

A cornerstone of the theory of proof nets for unit-freemultiplicative linear logic (MLL) is the abstract representation of cut-freeproofs modulo inessential commutations of rules. The only knownextension to additives, based on monomial weights, fails topreserve this key feature: a host of cut-free monomial proof nets cancorrespond to the same cut-free proof. Thus the problem offinding a satisfactory notion of proof net for unit-freemultiplicative-additive linear logic (MALL) has remained open since theincep-tion of linear logic in 1986. We present a new definition of MALLproof net which remains faithful to the cornerstone of the MLLtheory.

Towards Hilbert's 24th Problem: Combinatorial Proof Invariants

Proofs Without Syntax [Hughes, D.J.D. Proofs Without Syntax. Annals of Mathematics 2006 (to appear), http://arxiv.org/abs/math/0408282 (v3). August 2004 submitted version also available: [35]] introduced polynomial-time checkable combinatorial proofs for classical propositional logic. This sequel approaches Hilberts 24^t^hProblem with combinatorial proofs as abstract invariants for sequent calculus proofs, analogous to homotopy groups as abstract invariants for topological spaces. The paper lifts a simple, strongly normalising cut elimination from combinatorial proofs to sequent calculus, factorising away the mechanical commutations of structural rules which litter traditional syntactic cut elimination. Sequent calculus fails to be surjective onto combinatorial proofs: the paper extracts a semantically motivated closure of sequent calculus from which there is a surjection, pointing towards an abstract combinatorial refinement of Herbrands theorem.

Intensional Double Glueing, Biextensional Collapse, and the Chu Construction

The superficial similarity between the Chu construction and the Hyland-Tan double glueing construction G has been observed widely. This paper establishes a more formal mathematical relationship between the two. We show that double glueing on relations subsumes the Chu construction on sets: we present a full monoidal embedding of the category chu(Set, K) of biextensional Chu spaces over K into G(Rel^K), and a full monoidal embedding of the category Chu(Set, K) of Chu spaces over K into IG(Rel^K ), where we define IG, the intensional double glueing construction, by substituting multisets for sets in G. We define a biextensional collapse from IG to G which extends the familiar notion on Chu spaces. This yields a new interpretation of the monic specialisation implicit in G as a form of biextensionality.

A minimal classical sequent calculus free of structural rules

Abstract Gentzen’s classical sequent calculus LK has explicit structural rules for contraction and weakening. They can be absorbed (in a right-sided formulation) by replacing the axiom P , ¬ P by Γ , P , ¬ P for any context Γ , and replacing the original disjunction rule with Γ , A , B implies Γ , A ∨ B . This paper presents a classical sequent calculus which is also free of contraction and weakening, but more symmetrically: both contraction and weakening are absorbed into conjunction, leaving the axiom rule intact. It uses a blended conjunction rule, combining the standard context-sharing and context-splitting rules: Γ , Δ , A and Γ , Σ , B implies Γ , Δ , Σ , A ∧ B . We refer to this system M as minimal sequent calculus. We prove a minimality theorem for the propositional fragment Mp : any propositional sequent calculus S (within a standard class of right-sided calculi) is complete if and only if S contains Mp (that is, each rule of Mp is derivable in S ). Thus one can view M as a minimal complete core of Gentzen’s LK .