11 research outputs found

    Algorithm 959: VBF: A Library of C plus plus Classes for Vector Boolean Functions in Cryptography

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    VBF is a collection of C++ classes designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This implementation uses the NTL library from Victor Shoup, adding new modules that call NTL functions and complement the existing ones, making it better suited to cryptography. The class representing a vector Boolean function can be initialized by several alternative types of data structures such as Truth Table, Trace Representation, and Algebraic Normal Form (ANF), among others. The most relevant cryptographic criteria for both block and stream ciphers as well as for hash functions can be evaluated with VBF: it obtains the nonlinearity, linearity distance, algebraic degree, linear structures, and frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions are presented. Finally, three real applications of the library are described: the first one analyzes the KASUMI block cipher, the second one analyzes the Mini-AES cipher, and the third one finds Boolean functions with very high nonlinearity, a key property for robustness against linear attacks

    Stream ciphers

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    Design of Stream Ciphers and Cryptographic Properties of Nonlinear Functions

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    Block and stream ciphers are widely used to protect the privacy of digital information. A variety of attacks against block and stream ciphers exist; the most recent being the algebraic attacks. These attacks reduce the cipher to a simple algebraic system which can be solved by known algebraic techniques. These attacks have been very successful against a variety of stream ciphers and major efforts (for example eSTREAM project) are underway to design and analyze new stream ciphers. These attacks have also raised some concerns about the security of popular block ciphers. In this thesis, apart from designing new stream ciphers, we focus on analyzing popular nonlinear transformations (Boolean functions and S-boxes) used in block and stream ciphers for various cryptographic properties, in particular their resistance against algebraic attacks. The main contribution of this work is the design of two new stream ciphers and a thorough analysis of the algebraic immunity of Boolean functions and S-boxes based on power mappings. First we present WG, a family of new stream ciphers designed to obtain a keystream with guaranteed randomness properties. We show how to obtain a mathematical description of a WG stream cipher for the desired randomness properties and security level, and then how to translate this description into a practical hardware design. Next we describe the design of a new RC4-like stream cipher suitable for high speed software applications. The design is compared with original RC4 stream cipher for both security and speed. The second part of this thesis closely examines the algebraic immunity of Boolean functions and S-boxes based on power mappings. We derive meaningful upper bounds on the algebraic immunity of cryptographically significant Boolean power functions and show that for large input sizes these functions have very low algebraic immunity. To analyze the algebraic immunity of S-boxes based on power mappings, we focus on calculating the bi-affine and quadratic equations they satisfy. We present two very efficient algorithms for this purpose and give new S-box constructions that guarantee zero bi-affine and quadratic equations. We also examine these S-boxes for their resistance against linear and differential attacks and provide a list of S-boxes based on power mappings that offer high resistance against linear, differential, and algebraic attacks. Finally we investigate the algebraic structure of S-boxes used in AES and DES by deriving their equivalent algebraic descriptions

    Algebraic graph theoretic applications to cryptography.

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    Master of Science in Mathematics. University of KwaZulu-Natal, Durban, 2015.Abstract available in PDF file

    The Complexity of Reliable and Secure Distributed Transactions

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    The use of transactions in distributed systems dates back to the 70's. The last decade has also seen the proliferation of transactional systems. In the existing transactional systems, many protocols employ a centralized approach in executing a distributed transaction where one single process coordinates the participants of a transaction. The centralized approach is usually straightforward and efficient in the failure-free setting, yet the coordinator then turns to be a single point of failure, undermining reliability/security in the failure-prone setting, or even be a performance bottleneck in practice. In this dissertation, we explore the complexity of decentralized solutions for reliable and secure distributed transactions, which do not use a distinguished coordinator or use the coordinator as little as possible. We show that for some problems in reliable distributed transactions, there are decentralized solutions that perform as efficiently as the classical centralized one, while for some others, we determine the complexity limitations by proving lower and upper bounds to have a better understanding of the state-of-the-art solutions. We first study the complexity on two aspects of reliable transactions: atomicity and consistency. More specifically, we do a systematic study on the time and message complexity of non-blocking atomic commit of a distributed transaction, and investigate intrinsic limitations of causally consistent transactions. Our study of distributed transaction commit focuses on the complexity of the most frequent executions in practice, i.e., failure-free, and willing to commit. Through our systematic study, we close many open questions like the complexity of synchronous non-blocking atomic commit. We also present an effective protocol which solves what we call indulgent atomic commit that tolerates practical distributed database systems which are synchronous "most of the time", and can perform as efficiently as the two-phase commit protocol widely used in distributed database systems. Our investigation of causal transactions focuses on the limitations of read-only transactions, which are considered the most frequent in practice. We consider "fast" read-only transactions where operations are executed within one round-trip message exchange between a client seeking an object and the server storing it (in which no process can be a coordinator). We show two impossibility results regarding "fast" read-only transactions. By our impossibility results, when read-only transactions are "fast", they have to be "visible", i.e., they induce inherent updates on the servers. We also present a "fast" read-only transaction protocol that is "visible" as an upper bound on the complexity of inherent updates. We then study the complexity of secure transactions in the model of secure multiparty computation: even in the face of malicious parties, no party obtains the computation result unless all other parties obtain the same result. As it is impossible to achieve without any trusted party, we focus on optimism where if all parties are honest, they can obtain the computation result without resorting to a trusted third party, and the complexity of every optimistic execution where all parties are honest. We prove a tight lower bound on the message complexity by relating the number of messages to the length of the permutation sequence in combinatorics, a necessary pattern for messages in every optimistic execution

    Dickens and science: Summaries of contibutions related to science in "Household Words" and "All the Year Round" with an introduction

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    The study is an attempt to find a reasonable basis on which to form an estimate of Dickens's knowledge of science as far as it can be seen in his two weekly journals, Household Words and All the Year Round. Some recent and influential criticism on Dickens by commentators such as George Levine, Gillian Beer and their followers, has pioneered the study of Dickens and Science, and their ideas have also been popularised by Peter Ackroyd, Dickens's major biographer currently in print. They argue or imply that Dickens's knowledge of science was considerable, and that science is part of the very form of his novels, including Bleak Home, Little Dorrit, Our Mutual Friend and Great Expectations. However their assertion that Dickens's understanding of the second law of thermodynamics, "entropy," and Darwin's evolutionary theories in his Origin of Species (1859) have influenced his writing is highly questionable, and there is the need to examine what evidence there is for Dickens's knowledge of science in his life, letters, speeches, his library and the journals he edited. A preliminary survey of the scientific works in Dickens's library was undertaken for my M. Litt. The present study continues this work by investigating science in Dickens's journals, and by offering brief summaries of their articles on scientific subjects. An introduction discusses questions about the extent of Dickens's supervision. It looks at reasons for doubting whether it was as close as has sometimes been thought, the problems of inferring Dickens's own views on scientific subjects, and how we can decide whether the articles reflect his personal ideas about creation, man and the universe. The introduction also looks at some of the writers who contributed scientific articles; it shows that, with few exceptions, they were journalists or laymen, and examines how they conveyed to general readers accounts of the new discoveries in astronomy, geology, chemistry and physics. The relationship between Dickens's journals and his fiction is of critical significance. This cross-boundary exploration of Dickens and his journals in relation to science aims to find a reliable methodology for studying Victorian periodicals based on actual reading of them

    fast discrete fourier spectra attacks on stream ciphers

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    In this paper, some new results are presented on the selective discrete Fourier spectra attack introduced first as the RnjomHelleseth attack and the modifications due to Rnjom, Gong, and Helleseth. The first part of this paper fills some gaps in the theory of analysis in terms of the discrete Fourier transform (DFT). The second part introduces the new fast selective DFT attacks, which are closely related to the fast algebraic attacks in the literature. However, in contrast to the classical view that successful algebraic cryptanalysis of LFSR-based stream cipher depends on the degree of certain annihilators, the analysis in terms of the DFT spectral properties of the sequences generated by these functions is far more refined. It is shown that the selective DFT attack is more efficient than known methods for the case when the number of observed consecutive bits of a filter generator is less than the linear complexity of the sequence. Thus, by utilizing the natural representation imposed by the underlying LFSRs, in certain cases, the analysis in terms of DFT spectra is more efficient and has more flexibility than classical and fast algebraic attacks. Consequently, the new attack imposes a new criterion for the design of cryptographic strong Boolean functions, which is defined as the spectral immunity of a sequence or a Boolean function. © 2011 IEEE
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