226 research outputs found

    Large substitution boxes with efficient combinational implementations

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    At a fundamental level, the security of symmetric key cryptosystems ties back to Claude Shannon\u27s properties of confusion and diffusion. Confusion can be defined as the complexity of the relationship between the secret key and ciphertext, and diffusion can be defined as the degree to which the influence of a single input plaintext bit is spread throughout the resulting ciphertext. In constructions of symmetric key cryptographic primitives, confusion and diffusion are commonly realized with the application of nonlinear and linear operations, respectively. The Substitution-Permutation Network design is one such popular construction adopted by the Advanced Encryption Standard, among other block ciphers, which employs substitution boxes, or S-boxes, for nonlinear behavior. As a result, much research has been devoted to improving the cryptographic strength and implementation efficiency of S-boxes so as to prohibit cryptanalysis attacks that exploit weak constructions and enable fast and area-efficient hardware implementations on a variety of platforms. To date, most published and standardized S-boxes are bijective functions on elements of 4 or 8 bits. In this work, we explore the cryptographic properties and implementations of 8 and 16 bit S-boxes. We study the strength of these S-boxes in the context of Boolean functions and investigate area-optimized combinational hardware implementations. We then present a variety of new 8 and 16 bit S-boxes that have ideal cryptographic properties and enable low-area combinational implementations

    Additive Autocorrelation of Resilient Boolean Functions

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    Abstract. In this paper, we introduce a new notion called the dual func-tion for studying Boolean functions. First, we discuss general properties of the dual function that are related to resiliency and additive autocor-relation. Second, we look at preferred functions which are Boolean func-tions with the lowest 3-valued spectrum. We prove that if a balanced preferred function has a dual function which is also preferred, then it is resilient, has high nonlinearity and optimal additive autocorrelation. We demonstrate four such constructions of optimal Boolean functions using the Kasami, Dillon-Dobbertin, Segre hyperoval and Welch-Gong Transformation functions. Third, we compute the additive autocorrela-tion of some known resilient preferred functions in the literature by using the dual function. We conclude that our construction yields highly non-linear resilient functions with better additive autocorrelation than the Maiorana-McFarland functions. We also analysed the saturated func-tions, which are resilient functions with optimized algebraic degree and nonlinearity. We show that their additive autocorrelation have high peak values, and they become linear when we fix very few bits. These potential weaknesses have to be considered before we deploy them in applications.

    C-DIFFERENTIALS AND GENERALIZED CRYPTOGRAPHIC PROPERTIES OF VECTORIAL BOOLEAN AND P-ARY FUNCTIONS

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    This dissertation investigates a newly defined cryptographic differential, called a c-differential, and its relevance to the nonlinear substitution boxes of modern symmetric block ciphers. We generalize the notions of perfect nonlinearity, bentness, and avalanche characteristics of vectorial Boolean and p-ary functions using the c-derivative and a new autocorrelation function, while capturing the original definitions as special cases (i.e., when c=1). We investigate the c-differential uniformity property of the inverse function over finite fields under several extended affine transformations. We demonstrate that c-differential properties do not hold in general across equivalence classes typically used in Boolean function analysis, and in some cases change significantly under slight perturbations. Thus, choosing certain affine equivalent functions that are easy to implement in hardware or software without checking their c-differential properties could potentially expose an encryption scheme to risk if a c-differential attack method is ever realized. We also extend the c-derivative and c-differential uniformity into higher order, investigate some of their properties, and analyze the behavior of the inverse function's second order c-differential uniformity. Finally, we analyze the substitution boxes of some recognizable ciphers along with certain extended affine equivalent variations and document their performance under c-differential uniformity.Commander, United States NavyApproved for public release. Distribution is unlimited

    On the Design and Analysis of Stream Ciphers

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    This thesis presents new cryptanalysis results for several different stream cipher constructions. In addition, it also presents two new stream ciphers, both based on the same design principle. The first attack is a general attack targeting a nonlinear combiner. A new class of weak feedback polynomials for linear feedback shift registers is identified. By taking samples corresponding to the linear recurrence relation, it is shown that if the feedback polynomial has taps close together an adversary to take advantage of this by considering the samples in a vector form. Next, the self-shrinking generator and the bit-search generator are analyzed. Both designs are based on irregular decimation. For the self-shrinking generator, it is shown how to recover the internal state knowing only a few keystream bits. The complexity of the attack is similar to the previously best known but uses a negligible amount of memory. An attack requiring a large keystream segment is also presented. It is shown to be asymptotically better than all previously known attacks. For the bit-search generator, an algorithm that recovers the internal state is given as well as a distinguishing attack that can be very efficient if the feedback polynomial is not carefully chosen. Following this, two recently proposed stream cipher designs, Pomaranch and Achterbahn, are analyzed. Both stream ciphers are designed with small hardware complexity in mind. For Pomaranch Version 2, based on an improvement of previous analysis of the design idea, a key recovery attack is given. Also, for all three versions of Pomaranch, a distinguishing attack is given. For Achterbahn, it is shown how to recover the key of the latest version, known as Achterbahn-128/80. The last part of the thesis introduces two new stream cipher designs, namely Grain and Grain-128. The ciphers are designed to be very small in hardware. They also have the distinguishing feature of allowing users to increase the speed of the ciphers by adding extra hardware

    Améliorations des transmissions VLC (Visible Light Communication) sous contrainte d'éclairage : études théoriques et expérimentations

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    Abstract : Indoor visible light communication (VLC) networks based on light-emitting diodes (LEDs) currently enjoy growing interest thanks in part to their robustness against interference, wide license-free available bandwidth, low cost, good energy efficiency and compatibility with existing lighting infrastructure. In this thesis, we investigate spectral-efficient modulation techniques for the physical layer of VLC to increase throughput while considering the quality of illumination as well as implementation costs. Numerical and experimental studies are performed employing pulse amplitude modulation (PAM) and carrierless amplitude and phase (CAP) modulation under illumination constraints and for high modulation orders. Furthermore, the impact of LED nonlinearity is investigated and a postdistortion technique is evaluated to compensate these nonlinear effects. Within this framework, transmission rates in the order of a few hundred Mb/s are achieved using a test bench made of low-cost components. In addition, an imaging multiple input multiple-output (MIMO) system is developed and the impact on performance of imaging lens misalignment is theoretically and numerically assessed. Finally, a polynomial matrix decomposition technique based on the classical LU factorization method is studied and applied for the first time to MIMO VLC systems in large space indoor environments.Les rĂ©seaux de communication en lumiĂšre visible (VLC) s’appuyant sur l’utilisation de diodes Ă©lectroluminescentes (LED) bĂ©nĂ©ficient actuellement d’un intĂ©rĂȘt grandissant, en partie grĂące Ă  leur robustesse face aux interfĂ©rences Ă©lectromagnĂ©tiques, leur large bande disponible non-rĂ©gulĂ©e, leur faible coĂ»t, leur bonne efficacitĂ© Ă©nergĂ©tique, ainsi que leur compatibilitĂ© avec les infrastructures d’éclairage dĂ©jĂ  existantes. Dans cette thĂšse, nous Ă©tudions des techniques de modulation Ă  haute efficacitĂ© spectrale pour la couche physique des VLC pour augmenter les dĂ©bits tout en considĂ©rant la qualitĂ© de l’éclairage ainsi que les coĂ»ts d’implĂ©mentation. Des Ă©tudes numĂ©riques et expĂ©rimentales sont rĂ©alisĂ©es sur la modulation d’impulsion d’amplitude (PAM) et sur la modulation d’amplitude et de phase sans porteuse (CAP) sous des contraintes d’éclairage et pour des grands ordres de modulation. De plus, l’impact des non-linĂ©aritĂ©s de la LED est Ă©tudiĂ© et une technique de post-distorsion est Ă©valuĂ©e pour corriger ces effets non-linĂ©aires. Dans ce cadre, des dĂ©bits de plusieurs centaines de Mb/s sont atteints en utilisant un banc de test rĂ©alisĂ© Ă  partir de composants Ă  bas coĂ»ts. Par ailleurs, un systĂšme multi-entrĂ©es multi-sorties (MIMO) imageant est Ă©galement dĂ©veloppĂ© et l’impact du dĂ©saxage de l’imageur sur les performances est Ă©tudiĂ©. Finalement, une technique de dĂ©composition polynomiale basĂ©e sur la mĂ©thode de factorisation classique LU est Ă©tudiĂ©e et appliquĂ©e aux systĂšmes MIMO VLC dans des grands espaces intĂ©rieurs

    D.STVL.7 - Algebraic cryptanalysis of symmetric primitives

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    The recent development of algebraic attacks can be considered an important breakthrough in the analysis of symmetric primitives; these are powerful techniques that apply to both block and stream ciphers (and potentially hash functions). The basic principle of these techniques goes back to Shannon's work: they consist in expressing the whole cryptographic algorithm as a large system of multivariate algebraic equations (typically over F2), which can be solved to recover the secret key. Efficient algorithms for solving such algebraic systems are therefore the essential ingredients of algebraic attacks. Algebraic cryptanalysis against symmetric primitives has recently received much attention from the cryptographic community, particularly after it was proposed against some LFSR- based stream ciphers and against the AES and Serpent block ciphers. This is currently a very active area of research. In this report we discuss the basic principles of algebraic cryptanalysis of stream ciphers and block ciphers, and review the latest developments in the field. We give an overview of the construction of such attacks against both types of primitives, and recall the main algorithms for solving algebraic systems. Finally we discuss future research directions

    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
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