Algebraic analysis of small Scale LEX-BES

This work examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this article, experiments were conducted to find solutions of equation systems describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the authors know, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

A different algebraic analysis of the ZUC stream cipher

Existing algebraic analyses of the ZUC cipher indicate that the cipher should be secure against algebraic attacks. In this paper, we present an alternative algebraic analysis method for the ZUC stream cipher, where a combiner is used to represent the nonlinear function and to derive equations representing the cipher. Using this approach, the initial states of ZUC can be recovered from 2^97 observed words of keystream, with a complexity of 2^282 operations. This method is more successful when applied to a modified version of ZUC, where the number of output words per clock is increased. If the cipher outputs 120 bits of keystream per clock, the attack can succeed with 219 observed keystream bits and 2^47 operations. Therefore, the security of ZUC against algebraic attack could be significantly reduced if its throughput was to be increased for efficiency.

Algebraic analysis of the SSS stream cipher

Both the SSS and SOBER-t32 stream cipher designs use a single word-based shift register and a nonlinear filter function to produce keystream. In this paper we show that the algebraic attack method previously applied to SOBER-t32 is prevented from succeeding on SSS by the use of the key dependent substitution box (SBox) in the nonlinear filter of SSS. Additional assumptions and modifications to the SSS cipher in an attempt to enable algebraic analysis result in other difficulties that also render the algebraic attack infeasible. Based on these results, we conclude that a well chosen key-dependent substitution box used in the nonlinear filter of the stream cipher provides resistance against such algebraic attacks.

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the approach of Berbain et al. to Trivium-like ciphers and perform new algebraic analyses on them, namely Trivium and its reduced versions: Trivium-N, Bivium-A and Bivium-B. In doing so, we answer an open question in the literature. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques which use the F4 algorithm to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analysis. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail.

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the algebraic attack approach of Berbain et al. to Trivium-like ciphers and perform new analyses on them. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analyses. We also answer an open question posed by Berbain et al. on the feasibility of applying their technique on Trivium-like ciphers. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail. Analysis of Bivium-B and Trivium-N are omitted from this manuscript. The full paper is available on the IACR ePrint Archive.

Social Media Analytics : Ein interdisziplinärer Ansatz und seine Implikationen für die Wirtschaftsinformatik [Social Media Analytics - An Interdisciplinary Approach and Its Implications for Information Systems]

Social Media Analytics ist ein neuer Forschungsbereich, in dem interdisziplinäre Methoden kombiniert, erweitert und angepasst werden, um Social-Media-Daten auszuwerten. Neben der Beantwortung von Forschungsfragen ist es ebenfalls ein Ziel, Architekturentwürfe für die Entwicklung neuer Informationssysteme und Anwendungen bereitzustellen, die auf sozialen Medien basieren. Der Beitrag stellt die wichtigsten Aspekte des Bereichs Social Media Analytics vor und verweist auf die Notwendigkeit einer fächerübergreifenden Forschungsagenda, für deren Erstellung und Bearbeitung der Wirtschaftsinformatik eine wichtige Rolle zukommt.

An algebraic approach for determination of DG parameters to support voltage profiles in radial distribution networks

Rapidly increasing electricity demands and capacity shortage of transmission and distribution facilities are the main driving forces for the growth of Distributed Generation (DG) integration in power grids. One of the reasons for choosing a DG is its ability to support voltage in a distribution system. Selection of effective DG characteristics and DG parameters is a significant concern of distribution system planners to obtain maximum potential benefits from the DG unit. This paper addresses the issue of improving the network voltage profile in distribution systems by installing a DG of the most suitable size, at a suitable location. An analytical approach is developed based on algebraic equations for uniformly distributed loads to determine the optimal operation, size and location of the DG in order to achieve required levels of network voltage. The developed method is simple to use for conceptual design and analysis of distribution system expansion with a DG and suitable for a quick estimation of DG parameters (such as optimal operating angle, size and location of a DG system) in a radial network. A practical network is used to verify the proposed technique and test results are presented.

An algebraic analysis of trivium ciphers based on the boolean satisfiability problem

Trivium is a stream cipher candidate of the eStream project. It has successfully moved into phase three of the selection process under the hardware category. No attacks faster than the exhaustive search have so far been reported on Trivium. Bivium-A and Bivium-B are simplified versions of Trivium that are built on the same design principles but with two registers. The simplified design is useful in investigating Trivium type ciphers with a reduced complexity and provides insight into effective attacks which could be extended to Trivium. This paper focuses on an algebraic analysis which uses the boolean satisfiability problem in propositional logic. For reduced variants of the cipher, this analysis recovers the internal state with a minimal amount of keystream observations.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering

This paper presents algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. For unstuttered SOBER-t32, two different attacks are implemented. In the first attack, we obtain multivariate equations of degree 10. Then, an algebraic attack is developed using a collection of output bits whose relation to the initial state of the LFSR can be described by low-degree equations. The resulting system of equations contains 2^69 equations and monomials, which can be solved using the Gaussian elimination with the complexity of 2^196.5. For the second attack, we build a multivariate equation of degree 14. We focus on the property of the equation that the monomials which are combined with output bit are linear. By applying the Berlekamp-Massey algorithm, we can obtain a system of linear equations and the initial states of the LFSR can be recovered. The complexity of attack is around O(2^100) with 2^92 keystream observations. The second algebraic attack is applicable to SOBER-t16 without stuttering. The attack takes around O(2^85) CPU clocks with 2^78 keystream observations.

On algebraic immunity and annihilators

Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function f^c called the algebraic complement of f. This motivates us to examine AI(f ^c ). We define the extended algebraic immunity of f as AI *(f)= min {AI(f), AI(f^c )}. We prove that 0≤AI(f)–AI *(f)≤1. Since AI(f)–AI *(f)= 1 holds for a large number of cases, the difference between AI(f) and AI *(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI *(f).

An algebraic theory of functional and multivalued dependencies in relational databases

Computation of the dependency basis is the fundamental step in solving the membership problem for functional dependencies (FDs) and multivalued dependencies (MVDs) in relational database theory. We examine this problem from an algebraic perspective. We introduce the notion of the inference basis of a set M of MVDs and show that it contains the maximum information about the logical consequences of M. We propose the notion of a dependency-lattice and develop an algebraic characterization of inference basis using simple notions from lattice theory. We also establish several interesting properties of dependency-lattices related to the implication problem. Founded on our characterization, we synthesize efficient algorithms for (a): computing the inference basis of a given set M of MVDs; (b): computing the dependency basis of a given attribute set w.r.t. M; and (c): solving the membership problem for MVDs. We also show that our results naturally extend to incorporate FDs also in a way that enables the solution of the membership problem for both FDs and MVDs put together. We finally show that our algorithms are more efficient than existing ones, when used to solve what we term the ‘generalized membership problem’.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Algebraic characterization of decentralized fixed modes

An input-output, frequency-domain characterization of decentralized fixed modes is given in this paper, using only standard block-diagram algebra, well-known determinantal expansions and the Binet-Cauchy formula.