Algebraic attacks over GF(q)

Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of f ^{q – 1} – 1. In this case, many such low degree multiples exist.

On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.

On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

Generalized pseudo-likelihood estimates for markov random fields on lattice

In this paper we generalize Besag's pseudo-likelihood function for spatial statistical models on a region of a lattice. The correspondingly defined maximum generalized pseudo-likelihood estimates (MGPLEs) are natural extensions of Besag's maximum pseudo-likelihood estimate (MPLE). The MGPLEs connect the MPLE and the maximum likelihood estimate. We carry out experimental calculations of the MGPLEs for spatial processes on the lattice. These simulation results clearly show better performances of the MGPLEs than the MPLE, and the performances of differently defined MGPLEs are compared. These are also illustrated by the application to two real data sets.

Deconstructing diversity discourses in the fields of educationnal management and leadership

Discourses of diversity have supplanted those of equal opportunity or social justice in many Western democratic societies. While the notion of diversity is seemingly empowering through its recognition of cultural, religious, racial and gender difference within nation states, the emergence of this discourse during the 1990s has been in the context of neoliberal managerialist discourses that assume social action is fully explicable through theories of maximizing self interest. Thus notions of diversity, while originating in collective demands of social movements of feminism, anti racism and multiculturalism of the 1970s and 1980s, have in recent times privileged learning and leadership as an individual accomplishment and not a collective practice. Thus the dominant discourse of diversity is more in alignment with the deregulatory aspects of the increasingly managerial and market orientation of schooling, decentring earlier discourses of more transformatory notions premised upon reducing inequality and discrimination and developing ‘inclusivity’ in and through schooling. This paper provides a contextual and conceptual framework through which to explore the intersections and divergences of discourses of diversity in schools and their practical application.

MRD hashing

We propose two new classes of hash functions which are motivated by Maximum Rank Distance (MRD) codes. We analise the security of these schemes. The system setup phase is computationally expensive for general field extensions. To overcome this limitation we derive an algebraic solution which avoids computations in special extension fields in the intended operational range of the hash functions.

Algebraic attacks on clock-controlled stream ciphers

We present an algebraic attack approach to a family of irregularly clock-controlled bit-based linear feedback shift register systems. In the general set-up, we assume that the output bit of one shift register controls the clocking of other registers in the system and produces a family of equations relating the output bits to the internal state bits. We then apply this general theory to four specific stream ciphers: the (strengthened) stop-and-go generator, the alternating step generator, the self-decimated generator and the step1/step2 generator. In the case of the strengthened stop-and-go generator and of the self-decimated generator, we obtain the initial state of the registers in a significantly faster time than any other known attack. In the other two situations, we do better than or as well as all attacks but the correlation attack. In all cases, we demonstrate that the degree of a functional relationship between the registers can be bounded by two. Finally, we determine the effective key length of all four systems.

Algebraic attacks on clock-controlled cascade ciphers

In this paper, we mount the first algebraic attacks against clock controlled cascade stream ciphers. We first show how to obtain relations between the internal state bits and the output bits of the Gollmann clock controlled cascade stream ciphers. We demonstrate that the initial states of the last two shift registers can be determined by the initial states of the others. An alternative attack on the Gollmann cascade is also described, which requires solving quadratic equations. We then present an algebraic analysis of Pomaranch, one of the phase two proposals to eSTREAM. A system of equations of maximum degree four that describes the full cipher is derived. We also present weaknesses in the filter functions of Pomaranch by successfully computing annihilators and low degree multiples of the functions.

The influence of magnetic fields exposure on neurite outgrowth in PC12 rat pheochromocytoma cells

The aim of present work was to investigate the influence of magnetic fields exposure on neurite outgrowth in PC12 cells. The neurite number per cell, length of neurites and directions of neurite growth with respect to the direction of the magnetic field were analyzed after exposure to 50 Hz electromagnetic field for 96 h. A promotion was observed under a weak field (0.23 mT), as the average number of neurites per cell increased to 2.38±0.06 compared to 1.91±0.07 neurites/cell of the control dishes, while inhibition and directional outgrowth was evident under a relatively stronger field (1.32 mT). Our work shows that biological systems can be very sensitive to the strength of electromagnetic field.

Controlling the relative orientation between the two magnetic fields of a synchronous motor

A simple and reliable method for controlling the relative orientation between the two magnetic fields of a permanent magnet synchronous motor is presented. Finding the initial (at motor powering-up time) value of this relative location is essential for the proper operation of the motor. The feedback control loop used finds this initial relative orientation quickly. Further, using the proposed method allows considerable cost saving, as a transducer that is usually used for this purpose can be eliminated. The cost saving is most obvious in the case of linear motors and angle motors with large diameters. The way the problem is posed is an essential part of this work and it is the reason behind the apparent simplicity of the solution. The method relied upon a single sensor, and it has been tested when a relative encoder was used

An algebraic approach for delay-independent and delay-dependent stability of linear time-delay systems

This paper addresses the problem of asymptotic stability of a linear system with many delay units. A novel algebraic test is proposed for the delay-independent stability of the system, based on the root distribution of the system's characteristic equation. If the system is only stable dependent of delay, the whole stable regions of the system can be perfectly obtained. Two algorithms are derived to examine the delay-independent stability, and to compute the whole stable regions if the system is of delay-dependent stability. These algorithms are computationally efficient and applicable to both certain and uncertain systems. Some illustrative examples demonstrate the validity of the approach.

Mutually clock-controlled feedback shift registers provide resistance to algebraic attacks

Algebraic attacks have been applied to several types of clock-controlled stream ciphers. However, to date there are no such attacks in the literature on mutually clock-controlled ciphers. In this paper, we present a preliminary step in this direction by giving the first algebraic analysis of mutually clock-controlled feedback shift register stream ciphers: the bilateral stop-and-go generator, A5/1, Alpha 1 and the MICKEY cipher. We show that, if there are no regularly clocked shift registers included in the system, mutually clock-controlled feedback shift register ciphers appear to be highly resistant to algebraic attacks. As a demonstration of the weakness inherent in the presence of a regularly clocked shift register, we present a simple algebraic attack on Alpha 1 based on only 29 keystream bits.