Improved algebraic cryptanalysis of QUAD, Bivium and Trivium via graph partitioning on equation systems

We present a novel approach for preprocessing systems of polynomial equations via graph partitioning. The variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the corresponding system of equations can be split into smaller ones that can be solved individually. This can provide a tremendous speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting certain vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations would be separated into smaller systems of near-equal sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach in algebraic cryptanalysis on symmetric ciphers are presented: For the QUAD family of stream ciphers, we show how a malicious party can manufacture conforming systems that can be easily broken. For the stream ciphers Bivium and Trivium, we nachieve significant speedups in algebraic attacks against them, mainly in a partial key guess scenario. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method. These results may open a new avenue for evaluating the security of symmetric ciphers against algebraic attacks.

State cycles, initialization and the Trivium stream cipher

Trivium is a keystream generator for a binary additive synchronous stream cipher. It was selected in the final portfolio for the Profile 2 category of the eSTREAM project. The keystream generator is constructed using bit- based shift registers. In this paper we present an alternate representation of Trivium using word-based shift registers, with a word size of three bits. This representation is useful for determining cycles of internal state values. Under this representation it is clear that the state space can be partitioned into subspaces and that over some of these subspaces the state update function is effectively linear. The role of the initialization process is critical in ensuring the states used for generating keystream are updated nonlinearly at some point, as the state update function alone does not provide this.

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.

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.

Algebraic attacks on clock-controlled stream ciphers

Stream ciphers are encryption algorithms used for ensuring the privacy of digital telecommunications. They have been widely used for encrypting military communications, satellite communications, pay TV encryption and for voice encryption of both fixed lined and wireless networks. The current multi year European project eSTREAM, which aims to select stream ciphers suitable for widespread adoptation, reflects the importance of this area of research. Stream ciphers consist of a keystream generator and an output function. Keystream generators produce a sequence that appears to be random, which is combined with the plaintext message using the output function. Most commonly, the output function is binary addition modulo two. Cryptanalysis of these ciphers focuses largely on analysis of the keystream generators and of relationships between the generator and the keystream it produces. Linear feedback shift registers are widely used components in building keystream generators, as the sequences they produce are well understood. Many types of attack have been proposed for breaking various LFSR based stream ciphers. A recent attack type is known as an algebraic attack. Algebraic attacks transform the problem of recovering the key into a problem of solving multivariate system of equations, which eventually recover the internal state bits or the key bits. This type of attack has been shown to be effective on a number of regularly clocked LFSR based stream ciphers. In this thesis, algebraic attacks are extended to a number of well known stream ciphers where at least one LFSR in the system is irregularly clocked. Applying algebriac attacks to these ciphers has only been discussed previously in the open literature for LILI-128. In this thesis, algebraic attacks are first applied to keystream generators using stop-and go clocking. Four ciphers belonging to this group are investigated: the Beth-Piper stop-and-go generator, the alternating step generator, the Gollmann cascade generator and the eSTREAM candidate: the Pomaranch cipher. It is shown that algebraic attacks are very effective on the first three of these ciphers. Although no effective algebraic attack was found for Pomaranch, the algebraic analysis lead to some interesting findings including weaknesses that may be exploited in future attacks. Algebraic attacks are then applied to keystream generators using (p; q) clocking. Two well known examples of such ciphers, the step1/step2 generator and the self decimated generator are investigated. Algebraic attacks are shown to be very powerful attack in recovering the internal state of these generators. A more complex clocking mechanism than either stop-and-go or the (p; q) clocking keystream generators is known as mutual clock control. In mutual clock control generators, the LFSRs control the clocking of each other. Four well known stream ciphers belonging to this group are investigated with respect to algebraic attacks: the Bilateral-stop-and-go generator, A5/1 stream cipher, Alpha 1 stream cipher, and the more recent eSTREAM proposal, the MICKEY stream ciphers. Some theoretical results with regards to the complexity of algebraic attacks on these ciphers are presented. The algebraic analysis of these ciphers showed that generally, it is hard to generate the system of equations required for an algebraic attack on these ciphers. As the algebraic attack could not be applied directly on these ciphers, a different approach was used, namely guessing some bits of the internal state, in order to reduce the degree of the equations. Finally, an algebraic attack on Alpha 1 that requires only 128 bits of keystream to recover the 128 internal state bits is presented. An essential process associated with stream cipher proposals is key initialization. Many recently proposed stream ciphers use an algorithm to initialize the large internal state with a smaller key and possibly publicly known initialization vectors. The effect of key initialization on the performance of algebraic attacks is also investigated in this thesis. The relationships between the two have not been investigated before in the open literature. The investigation is conducted on Trivium and Grain-128, two eSTREAM ciphers. It is shown that the key initialization process has an effect on the success of algebraic attacks, unlike other conventional attacks. In particular, the key initialization process allows an attacker to firstly generate a small number of equations of low degree and then perform an algebraic attack using multiple keystreams. The effect of the number of iterations performed during key initialization is investigated. It is shown that both the number of iterations and the maximum number of initialization vectors to be used with one key should be carefully chosen. Some experimental results on Trivium and Grain-128 are then presented. Finally, the security with respect to algebraic attacks of the well known LILI family of stream ciphers, including the unbroken LILI-II, is investigated. These are irregularly clock- controlled nonlinear filtered generators. While the structure is defined for the LILI family, a particular paramater choice defines a specific instance. Two well known such instances are LILI-128 and LILI-II. The security of these and other instances is investigated to identify which instances are vulnerable to algebraic attacks. The feasibility of recovering the key bits using algebraic attacks is then investigated for both LILI- 128 and LILI-II. Algebraic attacks which recover the internal state with less effort than exhaustive key search are possible for LILI-128 but not for LILI-II. Given the internal state at some point in time, the feasibility of recovering the key bits is also investigated, showing that the parameters used in the key initialization process, if poorly chosen, can lead to a key recovery using algebraic attacks.

Key derivation function : the SCKDF scheme

A key derivation function is used to generate one or more cryptographic keys from a private (secret) input value. This paper proposes a new method for constructing a generic stream cipher based key derivation function. We show that our proposed key derivation function based on stream ciphers is secure if the underlying stream cipher is secure. We simulate instances of this stream cipher based key derivation function using three eStream finalist: Trivium, Sosemanuk and Rabbit. The simulation results show these stream cipher based key derivation functions offer efficiency advantages over the more commonly used key derivation functions based on block ciphers and hash functions.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

Key derivation function based on stream ciphers

A key derivation function (KDF) is a function that transforms secret non-uniformly random source material together with some public strings into one or more cryptographic keys. These cryptographic keys are used with a cryptographic algorithm for protecting electronic data during both transmission over insecure channels and storage. In this thesis, we propose a new method for constructing a generic stream cipher based key derivation function. We show that our proposed key derivation function based on stream ciphers is secure if the under-lying stream cipher is secure. We simulate instances of this stream cipher based key derivation function using three eStream nalist: Trivium, Sosemanuk and Rabbit. The simulation results show these stream cipher based key derivation functions offer efficiency advantages over the more commonly used key derivation functions based on block ciphers and hash functions.

Modellbildung in der algebraischen Kryptoanalyse

In der algebraischen Kryptoanalyse werden moderne Kryptosysteme als polynomielle, nichtlineare Gleichungssysteme dargestellt. Das Lösen solcher Gleichungssysteme ist NP-hart. Es gibt also keinen Algorithmus, der in polynomieller Zeit ein beliebiges nichtlineares Gleichungssystem löst. Dennoch kann man aus modernen Kryptosystemen Gleichungssysteme mit viel Struktur generieren. So sind diese Gleichungssysteme bei geeigneter Modellierung quadratisch und dünn besetzt, damit nicht beliebig. Dafür gibt es spezielle Algorithmen, die eine Lösung solcher Gleichungssysteme finden. Ein Beispiel dafür ist der ElimLin-Algorithmus, der mit Hilfe von linearen Gleichungen das Gleichungssystem iterativ vereinfacht. In der Dissertation wird auf Basis dieses Algorithmus ein neuer Solver für quadratische, dünn besetzte Gleichungssysteme vorgestellt und damit zwei symmetrische Kryptosysteme angegriffen. Dabei sind die Techniken zur Modellierung der Chiffren von entscheidender Bedeutung, so das neue Techniken entwickelt werden, um Kryptosysteme darzustellen. Die Idee für das Modell kommt von Cube-Angriffen. Diese Angriffe sind besonders wirksam gegen Stromchiffren. In der Arbeit werden unterschiedliche Varianten klassifiziert und mögliche Erweiterungen vorgestellt. Das entstandene Modell hingegen, lässt sich auch erfolgreich auf Blockchiffren und auch auf andere Szenarien erweitern. Bei diesen Änderungen muss das Modell nur geringfügig geändert werden.

Corrupción y delitos contra la administración pública especial referencia a los delitos cometidos en la contratación

La corrupción sigue siendo uno de los principales problemas del Estado de Derecho en el siglo XXI. Su incidencia reduce la eficacia de la inversión, aumenta el valor de los bienes y servicios, reduce la competitividad de las empresas, vulnera la confianza de los ciudadanos en el ordenamiento jurídico y sobre todo condena a la miseria a quienes deben ser destinatarios de las políticas públicas.Sin embrago, la lucha que han realizado muchos gobiernos y funcionarios judiciales contra este fenómeno ha modificado sus formas de aparición, pues es cada vez menos frecuente la apropiación directa de los caudales públicos o la entrega de sobornos a los funcionarios, prefiriéndose métodos mucho más sutiles como los sobrecostos, la subcontratación masiva o la constitución de complicadas sociedades, en las cuales tienen participación los funcionarios públicos o sus familias.Este libro constituye un esfuerzo por el estudio jurídico y criminológico de la corrupción y los delitos contra la administración pública en Europa y Latinoamérica y reúne la selección de los temas penales más relevantes de la tesis doctoral del profesor Carlos Guillermo Castro Cuenca, denominada Aproximación a la Corrupción en la contratación pública y defendida en la universidad de Salamanca en febrero de 2008, con lo cual obtuvo la calificación de sobresaliente por unanimidad.

La contratación Estatal: teoría general : perspectiva comparada y regulación internacional

Por medio de esta obra se pretende exponer una teoría general de la contratación pública enfocada a la elaboración de los principios generales que la desarrollan. Para ello, se realiza un estudio multidisciplinario desde la óptica del derecho administrativo, el derecho constitucional y el derecho internacional para lograr una visión más amplia sobre las temáticas abordadas. En el primer capítulo se establece la relación entre la contratación pública y la administración pública, exponiéndose la influencia de la primera en la formación paulatina de un concepto materia de la administración pública. El segundo capítulo, tiene por objeto la determinación del concepto de la contratación pública y su evolución, lo cual será el punto de partida para la construcción de la obra. El tercer capítulo examina los principios de la función pública y los principios de la contratación pública; en este capítulo se hace un especial énfasis en un estudio jurisprudencial del alcance de cada uno de los principios y sus consecuencias jurídicas concretas.

Matemáticas en la música.

Los pitagóricos crearon una división del currículo conocida como quadrivium (aritmética, música, geometría y astronomía) y trivium (gramática, retórica y dialéctica). El artículo se centra especialmente en la relación entre matemáticas y música. La relación entre ritmo y números o armonía y divisibilidad son algunas de las diferentes relaciones analizadas.

Un nuevo código deontológico para la profesión docente.

Monográfico con el título: 'Profesorado y calidad de la educación'. El presente artículo fue publicado en el número 12 de la revista Trivium, noviembre de 2010. Resumen basado en el de la publicación.

Rhetorical theory of public relations: opening the door to semiotic and pragmatism approaches

The 2001 Handbook of Public Relations edited by Robert Heath contains a prominent article advocating the use of rhetorical theory or ‘rhetorical enactment rational’ as a fruitful way of advancing theoretical understandings of public relations. In 2004 Heath and Dan Millar edited: Responding to Crisis: A Rhetorical Approach to Crisis Communication. These are the latest excursions into a perspective on public relations reflecting the extensive study of rhetoric in North America. Other examples are Public Relations Inquiry as Rhetorical Criticism (Elwood, 1995); Rhetorical and Critical Approaches to Public Relations (Toth and Heath, 1992); and a chapter Public Relations? No, Relations with Publics: A Rhetorical-Organisational Approach to Contemporary Corporate Communication (Cheney and Dionisopoulos, in Botan and Hazleton (Eds.) 1989).

The conventional notion of rhetoric is argumentation and persuasion stemming from the ancient Greek sophists, such as Aristotle, and from the Romans, particularly Cicero and Quintillion. Rhetoric became a fundamental plank of the trivium of ancient and medieval education: grammar, logic and rhetoric. Then in the 20th century Kenneth Burke, Stephen Toulmin and Chaim Perelman with Lucie Olbrechts-Tyteca extended Aristotle’s suggestion that: “Rhetoric is the counterpart of dialectic” Aristotle (trans. 1991). To use the rhetorical approach to argue that rational discourse cannot describe the world on its own. Instead living, enculturated human beings have to perceive ‘their’ truths. They take a perceptual ‘position’ on reason.

Public relations, is an industry for influencing perceptual ‘positions’. But the study of perception and attempts to influence perception cannot be claimed by rhetorical scholars alone. Semioticians and linguists who take the perspective of linguistic pragmatics also claim this field. This paper takes the example of ‘public relations’ as a focus for the confluence of rhetorical, semiotic and pragmatism approaches to the ‘problematic’ of understanding and truth.