Homomorphic encryption and some black box attacks

This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic encryption schemes, and that homomorphic encryption is an area of research where cryptography and black box algebra may benefit from exchange of ideas

Geometric Expression Invariant 3D Face Recognition using Statistical Discriminant Models

Currently there is no complete face recognition system that is invariant to all facial expressions. Although humans find it easy to identify and recognise faces regardless of changes in illumination, pose and expression, producing a computer system with a similar capability has proved to be particularly di cult. Three dimensional face models are geometric in nature and therefore have the advantage of being invariant to head pose and lighting. However they are still susceptible to facial expressions. This can be seen in the decrease in the recognition results using principal component analysis when expressions are added to a data set. In order to achieve expression-invariant face recognition systems, we have employed a tensor algebra framework to represent 3D face data with facial expressions in a parsimonious space. Face variation factors are organised in particular subject and facial expression modes. We manipulate this using single value decomposition on sub-tensors representing one variation mode. This framework possesses the ability to deal with the shortcomings of PCA in less constrained environments and still preserves the integrity of the 3D data. The results show improved recognition rates for faces and facial expressions, even recognising high intensity expressions that are not in the training datasets. We have determined, experimentally, a set of anatomical landmarks that best describe facial expression e ectively. We found that the best placement of landmarks to distinguish di erent facial expressions are in areas around the prominent features, such as the cheeks and eyebrows. Recognition results using landmark-based face recognition could be improved with better placement. We looked into the possibility of achieving expression-invariant face recognition by reconstructing and manipulating realistic facial expressions. We proposed a tensor-based statistical discriminant analysis method to reconstruct facial expressions and in particular to neutralise facial expressions. The results of the synthesised facial expressions are visually more realistic than facial expressions generated using conventional active shape modelling (ASM). We then used reconstructed neutral faces in the sub-tensor framework for recognition purposes. The recognition results showed slight improvement. Besides biometric recognition, this novel tensor-based synthesis approach could be used in computer games and real-time animation applications

Tensor-based trapdoors for CVP and their application to public key cryptography

We propose two trapdoors for the Closest-Vector-Problem in lattices (CVP) related to the lattice tensor product. Using these trapdoors we set up a lattice-based cryptosystem which resembles to the McEliece scheme

Recognising the Suzuki groups in their natural representations

Under the assumption of a certain conjecture, for which there exists strong experimental evidence, we produce an efficient algorithm for constructive membership testing in the Suzuki groups Sz(q), where q = 2^{2m + 1} for some m > 0, in their natural representations of degree 4. It is a Las Vegas algorithm with running time O{log(q)} field operations, and a preprocessing step with running time O{log(q) loglog(q)} field operations. The latter step needs an oracle for the discrete logarithm problem in GF(q). We also produce a recognition algorithm for Sz(q) = . This is a Las Vegas algorithm with running time O{|X|^2} field operations. Finally, we give a Las Vegas algorithm that, given ^h = Sz(q) for some h in GL(4, q), finds some g such that ^g = Sz(q). The running time is O{log(q) loglog(q) + |X|} field operations. Implementations of the algorithms are available for the computer system MAGMA

Connected components of compact matrix quantum groups and finiteness conditions

We introduce the notion of identity component of a compact quantum group and that of total disconnectedness. As a drawback of the generalized Burnside problem, we note that totally disconnected compact matrix quantum groups may fail to be profinite. We consider the problem of approximating the identity component as well as the maximal normal (in the sense of Wang) connected subgroup by introducing canonical, but possibly transfinite, sequences of subgroups. These sequences have a trivial behaviour in the classical case. We give examples, arising as free products, where the identity component is not normal and the associated sequence has length 1. We give necessary and sufficient conditions for normality of the identity component and finiteness or profiniteness of the quantum component group. Among them, we introduce an ascending chain condition on the representation ring, called Lie property, which characterizes Lie groups in the commutative case and reduces to group Noetherianity of the dual in the cocommutative case. It is weaker than ring Noetherianity but ensures existence of a generating representation. The Lie property and ring Noetherianity are inherited by quotient quantum groups. We show that A_u(F) is not of Lie type. We discuss an example arising from the compact real form of U_q(sl_2) for q<0.Comment: 43 pages. Changes in the introduction. The relation between our and Wang's notions of central subgroup has been clarifie