15,468 research outputs found
Relating Strand Spaces and Distributed Temporal Logic for Security Protocol Analysis
In previous work, we introduced a version of distributed temporal logic that is well-suited both for verifying security protocols and as a metalogic for reasoning about, and relating, different security protocol models. In this paper, we formally investigate the relationship between our approach and strand spaces, which is one of the most successful and widespread formalisms for analyzing security protocols. We define translations between models in our logic and strand-space models of security protocols, and we compare the results obtained with respect to the level of abstraction that is inherent in each of the formalisms. This allows us to clarify different aspects of strand spaces that are often left implicit, as well as pave the way to transfer results, techniques and tools across the two approache
Structure Attacks in Cryptographic Protocols
Cryptographic protocols are in general difficult to analyze, and complicated attacks exposing security flaws have remained hidden years after a protocol is developed. Recently developed tools such as strand spaces and inductive logical proofs provide mechanical procedures for analyzing protocols. The key to these methods is that a generous upper bound on the activity of a malicious penetrator is often much easier to work with than a tighter bound. However, these formalizations make strong assumptions about the algebraic structure of the cryptosystem that are never met in a real application. In this work, we show that an extended form of the strand space machinery can be used to analyze protocols which contain nontrivial algebraic structure, specifically that which arises from the XOR operation. This work also serves as one of the first steps in reconciling computational and formal methods of analyzing cryptographic security
Hilbert schemes and -ification of Khovanov-Rozansky homology
We define a deformation of the triply graded Khovanov-Rozansky homology of a
link depending on a choice of parameters for each component of ,
which satisfies link-splitting properties similar to the Batson-Seed invariant.
Keeping the as formal variables yields a link homology valued in triply
graded modules over . We conjecture that
this invariant restores the missing symmetry of the
triply graded Khovanov-Rozansky homology, and in addition satisfies a number of
predictions coming from a conjectural connection with Hilbert schemes of points
in the plane. We compute this invariant for all positive powers of the full
twist and match it to the family of ideals appearing in Haiman's description of
the isospectral Hilbert scheme
Canonical bases and higher representation theory
This paper develops a general theory of canonical bases, and how they arise
naturally in the context of categorification. As an application, we show that
Lusztig's canonical basis in the whole quantized universal enveloping algebra
is given by the classes of the indecomposable 1-morphisms in a categorification
when the associated Lie algebra is finite type and simply laced. We also
introduce natural categories whose Grothendieck groups correspond to the tensor
products of lowest and highest weight integrable representations. This
generalizes past work of the author's in the highest weight case.Comment: 55 pages; DVI may not compile correctly, PDF is preferred. v2: added
section on dual canonical bases. v3: improved exposition in line with new
version of 1309.3796. v4: final version, to appear in Compositio Mathematica.
v5: corrected references for proof of Theorem 4.
The Future of Science Governance: A review of public concerns, governance and institutional response
Attack analysis of cryptographic protocols using strand spaces
Security protocols make use of cryptographic techniques to achieve goals such as confidentiality, authentication and integrity. However, the fact that strong cryptographic algorithms exist does not guarantee the security of a communications system. In fact, it is recognised that the engineering of security protocols is a challenging task, since protocols that appear secure can contain subtle flaws that attackers can exploit. A number of techniques exist for the analysis of security protocol specifications. Individually they are not capable of detecting every possible flaw or attack against a protocol. However, when combined, these techniques all complement each other, allowing a protocol engineer to obtain a more accurate overview of the security of a protocol that is being designed. This is the rationale for multi-dimensional security protocol engineering, a concept introduced by previous projects of ours over several years. We propose an attack construction approach to security protocol analysis within a multi-dimensional context. This analysis method complements the existing inference construction analysis tools developed earlier in the group. We give a brief overview of the concepts associated with the project, including a summary of existing security protocol analysis techniques, and a description of the strand space model, which is the intended formalism for the analysis
On the Connectivity of Cobordisms and Half-Projective TQFT's
We consider a generalization of the axioms of a TQFT, so called
half-projective TQFT's, with an anomaly, , in the composition law.
is a coboundary on the cobordism categories with non-negative, integer
values. The element of the ring over which the TQFT is defined does not
have to be invertible. In particular, it may be 0. This modification makes it
possible to extend quantum-invariants, which vanish on , to
non-trivial TQFT's. (A TQFT in the sense of Atiyah with this property has to be
trivial all together). Under a few natural assumptions the notion of a
half-projective TQFT is shown to be the only possible generalization. Based on
separate work with Lyubashenko on connected TQFT's, we construct a large class
of half-projective TQFT's with . Their invariants vanish on , and they coincide with the Hennings invariant for non-semisimple Hopf
algebras. Several toplogical tools that are relevant for vanishing properties
of such TQFT's are developed. They are concerned with connectivity properties
of cobordisms, as for example maximal non-separating surfaces. We introduce in
particular the notions of ``interior'' homotopy and homology groups, and of
coordinate graphs, which are functions on cobordisms with values in the
morphisms of a graph category. For applications we will prove that
half-projective TQFT's with vanish on cobordisms with infinite interior
homology, and we argue that the order of divergence of the TQFT on a cobordism
in the ``classical limit'' can be estimated by the rank of its maximal free
interior group.Comment: 55 pages, Late
Tensor product algebras, Grassmannians and Khovanov homology
We discuss a new perspective on Khovanov homology, using categorifications of
tensor products. While in many ways more technically demanding than Khovanov's
approach (and its extension by Bar-Natan), this has distinct advantage of
directly connecting Khovanov homology to a categorification of
\$(\mathbb{C}^2)^{\otimes \ell}\$, and admitting a direct generalization to
other Lie algebras.
While the construction discussed is a special case of that given in previous
work of the author, this paper contains new results about the special case of
\$\mathfrak{sl}_2\$ showing an explicit connection to Bar-Natan's approach to
Khovanov homology, to the geometry of Grassmannians, and to the categorified
Jones-Wenzl projectors of Cooper and Krushkal. In particular, we show that the
colored Jones homology defined by our approach coincides with that of Cooper
and Krushkal.Comment: v2: 37 pages. The paper has been extended at several points, and
various small issues corrected following referee reports. Final published
versio
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