The Experts below are selected from a list of 15486 Experts worldwide ranked by ideXlab platform
Claude Carlet - One of the best experts on this subject based on the ideXlab platform.
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constructing low weight d th order Correlation immune boolean functions through the fourier hadamard transform
IEEE Transactions on Information Theory, 2018Co-Authors: Claude Carlet, Xi ChenAbstract:The Correlation Immunity of Boolean functions is a property related to cryptography, to error correcting codes, to orthogonal arrays (in combinatorics), and in a slightly looser way to sequences. Correlation-immune Boolean functions (in short, CI functions) have the property of keeping the same output distribution when some input variables are fixed. They have been widely used as combiners in stream ciphers to allow resistance to the Siegenthaler Correlation attack. Very recently, a new use of CI functions has appeared in the framework of side channel attacks (SCA). To reduce the cost overhead of counter-measures to SCA, CI functions need to have low Hamming weights. This actually poses new challenges since the known constructions which are based on properties of the Walsh–Hadamard transform, do not allow to build unbalanced CI functions. In this paper, we propose constructions of low-weight $d$ th-order CI functions based on the Fourier–Hadamard transform, while the known constructions of resilient functions are based on the Walsh–Hadamard transform. These two transforms are closely related but the resulting constructions are very different. We first prove a simple but powerful result, which makes that one only need to consider the case where $d$ is odd in further research. Then, we investigate how constructing low Hamming weight CI functions through the Fourier–Hadamard transform (which behaves well with respect to the multiplication of Boolean functions). We use the characterization of CI functions by the Fourier–Hadamard transform and introduce a related general construction of CI functions by multiplication. By using the Kronecker product of vectors, we obtain more constructions of low-weight $d$ -CI Boolean functions. Furthermore, we present a method to construct low-weight d-CI Boolean functions by making additional restrictions on the supports built from the Kronecker product.
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evolutionary approach for finding Correlation immune boolean functions of order t with minimal hamming weight
TPNC 2015 Proceedings of the Fourth International Conference on Theory and Practice of Natural Computing - Volume 9477, 2015Co-Authors: Stjepan Picek, Sylvain Guilley, Claude Carlet, Domagoj Jakobovic, Julian F MillerAbstract:The role of Boolean functions is prominent in several areas like cryptography, sequences and coding theory. Therefore, various methods to construct Boolean functions with desired properties are of direct interest. When concentrating on Boolean functions and their role in cryptography, we observe that new motivations and hence new properties have emerged during the years. It is important to note that there are still many design criteria left unexplored and this is where Evolutionary Computation can play a distinct role. One combination of design criteria that has appeared recently is finding Boolean functions that have various orders of Correlation Immunity and minimal Hamming weight. Surprisingly, most of the more traditionally used methods for Boolean function generation are inadequate in this domain. In this paper, we concentrate on a detailed exploration of several evolutionary algorithms and their applicability for this problem. Our results show that such algorithms are a viable choice when evolving Boolean functions with minimal Hamming weight and certain order of Correlation Immunity. This approach is also successful in obtaining Boolean functions with several values that were known previously to be theoretically optimal, but no one succeeded in finding actual Boolean functions with such values.
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Correlation Immunity of boolean functions an evolutionary algorithms perspective
Genetic and Evolutionary Computation Conference, 2015Co-Authors: Stjepan Picek, Claude Carlet, Domagoj Jakobovic, Julian F Miller, Lejla BatinaAbstract:Boolean functions are essential in many stream ciphers. When used in combiner generators, they need to have sufficiently high values of Correlation Immunity, alongside other properties. In addition, Correlation immune functions with small Hamming weight reduce the cost of masking countermeasures against side-channel attacks. Various papers have examined the applicability of evolutionary algorithms for evolving cryptographic Boolean functions. However, even when authors considered Correlation Immunity, it was not given the highest priority. Here, we examine the effectiveness of three different EAs, namely, Genetic Algorithms, Genetic Programming (GP) and Cartesian GP for evolving Correlation immune Boolean functions. Besides the properties of balancedness and Correlation Immunity, we consider several other relevant cryptographic properties while maintaining the optimal trade-offs among them. We show that evolving Correlation immune Boolean functions is an even harder objective than maximizing nonlinearity.
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Achieving side-channel high-order Correlation Immunity with leakage squeezing
Journal of Cryptographic Engineering, 2014Co-Authors: Claude Carlet, Sylvain Guilley, Jean-luc Danger, Houssem Maghrebi, Emmanuel ProuffAbstract:This article deeply analyzes high-order (HO) Boolean masking countermeasures against side-channel attacks in contexts where the shares are manipulated simultaneously and the Correlation coefficient is used as a statistical distinguisher. The latter attacks are sometimes referred to as zero-offset high-order Correlation power analysis (HO-CPA). In particular, the main focus is to get the most out of a single mask (i.e., for masking schemes with two shares). The relationship between the leakage characteristics and the attack efficiency is thoroughly studied. Our main contribution is to link the minimum attack order (called HO-CPA Immunity) to the amount of information leaked. Interestingly, the HO-CPA Immunity can be much larger than the number of shares in the masking scheme. This is made possible by the leakage squeezing. It is a variant of the Boolean masking where masks are recoded relevantly by bijections. This technique and others from the state-of-the-art (namely leak-free masking and wire-tap codes) are overviewed, and put in perspective.
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on the construction of balanced boolean functions with a good algebraic Immunity
International Symposium on Information Theory, 2005Co-Authors: Claude Carlet, Philippe GaboritAbstract:In this paper, we study the algebraic Immunity of Boolean functions and consider in particular the problem of constructing Boolean functions with a good algebraic Immunity. We first give heuristic arguments which seem to indicate that the algebraic Immunity of a random Boolean function on n variables is at least lfloorn/2rfloor with a very high probability (while the upper bound is lceiln/2rceil, the "ceiling" of n/2). We give an upper bound, under a reasonable assumption, on the algebraic Immunity of Boolean functions constructed through Maiorana-MacFarland construction. At last we give examples of balanced functions with optimal algebraic Immunity and a good nonlinearity and of balanced functions with a good algebraic Immunity, a good nonlinearity and a good Correlation Immunity, which can be used for cryptographic purposes
Yongzhuang Wei - One of the best experts on this subject based on the ideXlab platform.
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maximum autoCorrelation analysis of nonlinear combining functions in stream ciphers
International Symposium on Information Theory, 2007Co-Authors: Yongzhuang WeiAbstract:This paper investigates two new design rules of nonlinear combining functions in stream ciphers. It is shown that a combining function with high nonlinearity and high order Correlation Immunity is still not enough to prevent the divide and conquer attack and the BAA attack (or the best affine approximation attack) since the autoCorrelation function of the combining function may also be leaked much more information about the input of the combining function. To measure the strength of nonlinear combining functions, the notion of maximum autoCorrelation is introduced, which is based on the Correlation between linear functions of input and the autoCorrelation function of a combining function. The relationship between the maximum autoCorrelation coefficient and the mutual information of the autoCorrelation function of the combining function is discussed. Moreover, the upper bound of maximum autoCorrelation coefficient is presented by using Walsh transform.
Stjepan Picek - One of the best experts on this subject based on the ideXlab platform.
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evolutionary approach for finding Correlation immune boolean functions of order t with minimal hamming weight
TPNC 2015 Proceedings of the Fourth International Conference on Theory and Practice of Natural Computing - Volume 9477, 2015Co-Authors: Stjepan Picek, Sylvain Guilley, Claude Carlet, Domagoj Jakobovic, Julian F MillerAbstract:The role of Boolean functions is prominent in several areas like cryptography, sequences and coding theory. Therefore, various methods to construct Boolean functions with desired properties are of direct interest. When concentrating on Boolean functions and their role in cryptography, we observe that new motivations and hence new properties have emerged during the years. It is important to note that there are still many design criteria left unexplored and this is where Evolutionary Computation can play a distinct role. One combination of design criteria that has appeared recently is finding Boolean functions that have various orders of Correlation Immunity and minimal Hamming weight. Surprisingly, most of the more traditionally used methods for Boolean function generation are inadequate in this domain. In this paper, we concentrate on a detailed exploration of several evolutionary algorithms and their applicability for this problem. Our results show that such algorithms are a viable choice when evolving Boolean functions with minimal Hamming weight and certain order of Correlation Immunity. This approach is also successful in obtaining Boolean functions with several values that were known previously to be theoretically optimal, but no one succeeded in finding actual Boolean functions with such values.
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Correlation Immunity of boolean functions an evolutionary algorithms perspective
Genetic and Evolutionary Computation Conference, 2015Co-Authors: Stjepan Picek, Claude Carlet, Domagoj Jakobovic, Julian F Miller, Lejla BatinaAbstract:Boolean functions are essential in many stream ciphers. When used in combiner generators, they need to have sufficiently high values of Correlation Immunity, alongside other properties. In addition, Correlation immune functions with small Hamming weight reduce the cost of masking countermeasures against side-channel attacks. Various papers have examined the applicability of evolutionary algorithms for evolving cryptographic Boolean functions. However, even when authors considered Correlation Immunity, it was not given the highest priority. Here, we examine the effectiveness of three different EAs, namely, Genetic Algorithms, Genetic Programming (GP) and Cartesian GP for evolving Correlation immune Boolean functions. Besides the properties of balancedness and Correlation Immunity, we consider several other relevant cryptographic properties while maintaining the optimal trade-offs among them. We show that evolving Correlation immune Boolean functions is an even harder objective than maximizing nonlinearity.
Julian F Miller - One of the best experts on this subject based on the ideXlab platform.
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evolutionary approach for finding Correlation immune boolean functions of order t with minimal hamming weight
TPNC 2015 Proceedings of the Fourth International Conference on Theory and Practice of Natural Computing - Volume 9477, 2015Co-Authors: Stjepan Picek, Sylvain Guilley, Claude Carlet, Domagoj Jakobovic, Julian F MillerAbstract:The role of Boolean functions is prominent in several areas like cryptography, sequences and coding theory. Therefore, various methods to construct Boolean functions with desired properties are of direct interest. When concentrating on Boolean functions and their role in cryptography, we observe that new motivations and hence new properties have emerged during the years. It is important to note that there are still many design criteria left unexplored and this is where Evolutionary Computation can play a distinct role. One combination of design criteria that has appeared recently is finding Boolean functions that have various orders of Correlation Immunity and minimal Hamming weight. Surprisingly, most of the more traditionally used methods for Boolean function generation are inadequate in this domain. In this paper, we concentrate on a detailed exploration of several evolutionary algorithms and their applicability for this problem. Our results show that such algorithms are a viable choice when evolving Boolean functions with minimal Hamming weight and certain order of Correlation Immunity. This approach is also successful in obtaining Boolean functions with several values that were known previously to be theoretically optimal, but no one succeeded in finding actual Boolean functions with such values.
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Correlation Immunity of boolean functions an evolutionary algorithms perspective
Genetic and Evolutionary Computation Conference, 2015Co-Authors: Stjepan Picek, Claude Carlet, Domagoj Jakobovic, Julian F Miller, Lejla BatinaAbstract:Boolean functions are essential in many stream ciphers. When used in combiner generators, they need to have sufficiently high values of Correlation Immunity, alongside other properties. In addition, Correlation immune functions with small Hamming weight reduce the cost of masking countermeasures against side-channel attacks. Various papers have examined the applicability of evolutionary algorithms for evolving cryptographic Boolean functions. However, even when authors considered Correlation Immunity, it was not given the highest priority. Here, we examine the effectiveness of three different EAs, namely, Genetic Algorithms, Genetic Programming (GP) and Cartesian GP for evolving Correlation immune Boolean functions. Besides the properties of balancedness and Correlation Immunity, we consider several other relevant cryptographic properties while maintaining the optimal trade-offs among them. We show that evolving Correlation immune Boolean functions is an even harder objective than maximizing nonlinearity.
Jakub Husa - One of the best experts on this subject based on the ideXlab platform.
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designing Correlation immune boolean functions with minimal hamming weight using various genetic programming methods
Genetic and Evolutionary Computation Conference, 2019Co-Authors: Jakub HusaAbstract:In this paper, we search for Boolean functions with properties useful in cryptography for preventing side-channel attacks. We use three genetic programming methods including linear genetic programming, which has not been used to design these functions before. Our results aim to provide a fair comparison by performing parameter optimization for each individual method, and deliver an insight into how well they cope with the demand for growing number of function inputs and higher degrees of Correlation Immunity.
