The Experts below are selected from a list of 4932 Experts worldwide ranked by ideXlab platform
Sumanta Sarkar - One of the best experts on this subject based on the ideXlab platform.
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On the Triple-Error-Correcting Cyclic Codes with Zero Set {1, 2^i + 1, 2^j + 1}
2011Co-Authors: Vincent Herbert, Sumanta SarkarAbstract:We consider a class of 3-error-correcting cyclic codes of length 2^m −1 over the two-element field F2 . The generator polynomial of a code of this class has zeroes α, α^(2^i +1) and α^(2^j +1) , where α is a primitive element of the field F2^m . In short, {1, 2^i + 1, 2^j + 1} refers to the zero set of these codes. Kasami in 1971 and Bracken and Helleseth in 2009, showed that cyclic codes with zeroes {1, 2^l + 1, 2^(3l) + 1} and {1, 2^l + 1, 2^(2l) + 1} respectively are 3-error correcting, where gcd(l , m) = 1. We present a sufficient condition so that the zero set {1, 2^l + 1, 2^(pl) + 1}, gcd( l, m) = 1 gives a 3-error-correcting cyclic code. The question for p > 3 is open. In addition, we determine all the 3-error-correcting cyclic codes in the class {1, 2^i + 1, 2^j + 1} for m < 20. We investigate their weight distribution via their duals and observe that they have the same weight distribution as 3-error-correcting BCH codes for m < 14. Further our experiment shows that these codes are not equivalent to the 3-error-correcting BCH code in general. We also study the Schaub algorithm which determines a lower bound of the minimum distance of a cyclic code. We introduce a pruning strategy to improve the Schaub algorithm. Finally we study the Cryptographic Property of a Boolean function, called spectral immunity which is directly related to the minimum distance of cyclic codes over F2m . We apply the improved Schaub algorithm in order to find a lower bound of the spectral immunity of a Boolean function related to the zero set {1, 2^i + 1, 2^j + 1}.
Vincent Herbert - One of the best experts on this subject based on the ideXlab platform.
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On the Triple-Error-Correcting Cyclic Codes with Zero Set {1, 2^i + 1, 2^j + 1}
2011Co-Authors: Vincent Herbert, Sumanta SarkarAbstract:We consider a class of 3-error-correcting cyclic codes of length 2^m −1 over the two-element field F2 . The generator polynomial of a code of this class has zeroes α, α^(2^i +1) and α^(2^j +1) , where α is a primitive element of the field F2^m . In short, {1, 2^i + 1, 2^j + 1} refers to the zero set of these codes. Kasami in 1971 and Bracken and Helleseth in 2009, showed that cyclic codes with zeroes {1, 2^l + 1, 2^(3l) + 1} and {1, 2^l + 1, 2^(2l) + 1} respectively are 3-error correcting, where gcd(l , m) = 1. We present a sufficient condition so that the zero set {1, 2^l + 1, 2^(pl) + 1}, gcd( l, m) = 1 gives a 3-error-correcting cyclic code. The question for p > 3 is open. In addition, we determine all the 3-error-correcting cyclic codes in the class {1, 2^i + 1, 2^j + 1} for m < 20. We investigate their weight distribution via their duals and observe that they have the same weight distribution as 3-error-correcting BCH codes for m < 14. Further our experiment shows that these codes are not equivalent to the 3-error-correcting BCH code in general. We also study the Schaub algorithm which determines a lower bound of the minimum distance of a cyclic code. We introduce a pruning strategy to improve the Schaub algorithm. Finally we study the Cryptographic Property of a Boolean function, called spectral immunity which is directly related to the minimum distance of cyclic codes over F2m . We apply the improved Schaub algorithm in order to find a lower bound of the spectral immunity of a Boolean function related to the zero set {1, 2^i + 1, 2^j + 1}.
Feng Ke-qin - One of the best experts on this subject based on the ideXlab platform.
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On Algebraic Immunity of Symmetric Boolean Functions
Chinese Journal of Engineering Mathematics, 2008Co-Authors: Feng Ke-qinAbstract:In the stream and the block cipher systems,we need to construct the Boolean functions with nice Cryptographic properties as keys to resist the existing efficient attacks.In recent years a new (algebraic) attack has been investigated and a new Cryptographic Property- algebraic immunity-has proposed to resist the algebraic attack.In this survey paper we review basic conceptions and main problems on algebraic immunity and some developments on algebraic immunity of symmetric Boolean functions.
Jiansheng Guo - One of the best experts on this subject based on the ideXlab platform.
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Quantum Cryptographic Property testing of multi-output Boolean functions
Quantum Information Processing, 2019Co-Authors: Jingyi Cui, Jiansheng GuoAbstract:Compared with Boolean functions, multi-output Boolean functions (a.k.a. vectorial Boolean functions) are commonly used in classical cryptography. More generally, many Cryptographic primitives can be treated as multi-output Boolean functions. Hence, the research on Property testing of multi-output Boolean functions is meaningful for the design and cryptanalysis of symmetric cryptography. This paper mainly focuses on the Cryptographic Property testing of multi-output Boolean functions in the quantum world. Firstly, the generalized Deutsch–Jozsa algorithm is proposed to distinguish balanced multi-output Boolean functions from constant ones with a single query. This algorithm has a wider scope of applications with arbitrary ancillary inputs. The first generalized Bernstein–Vazirani algorithm suitable for multi-output Boolean functions is presented to recover the linear coefficients of linear functions. Then, combined with the generalized Deutsch–Jozsa algorithm, the quantum algorithm for estimating Walsh coefficients of multi-output Boolean functions is proposed with the same idea of quantum approximate counting algorithm, accompanied with an algorithm for computing the Walsh coefficient at a specified point based on quantum exact counting algorithm. Finally, with the usage of algorithms mentioned above, the Cryptographic Property testing of multi-output Boolean functions is studied. In order to describe the distances from having the certain properties, Euclidean distance and Manhattan distance are introduced as complements of Hamming distance. According to the definition, the first balance testing of multi-output Boolean functions is presented by testing the uniformity of images. The second algorithm exploits the relationship between balance and the Walsh coefficients at the point 0 which could be easily extended to k-order resiliency testing. We also briefly analyze the query complexities of strict avalanche criterion testing and k-order propagation criteria testing. The linearity testing algorithm for multi-output Boolean functions based on the generalized Bernstein–Vazirani algorithm can be adapted to Boolean functions achieving a further speedup. The non-junta testing algorithm is proposed with lower query complexity.
Zhuo Wang - One of the best experts on this subject based on the ideXlab platform.
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On Algebraic Immunity of Weight Symmetric H Boolean Functions
Applied Mechanics and Materials, 2014Co-Authors: Jing Lian Huang, Zhuo WangAbstract:Using the derivative of Boolean functions and the e-derivative defined by ourselves as research tools, we discuss the relationship among a variety of Cryptographic properties of the weight symmetric H Boolean functions in the range of the weight with the existence of H Boolean functions. We also study algebraic immunity and correlation immunity of the weight symmetric H Boolean functions and the balanced H Boolean functions. We obtain that the weight symmetric H Boolean function should have the same algebraic immunity, correlation immunity, propagation degree and nonlinearity. Besides, we determine that there exist several kinds of H Boolean functions with resilient, algebraic immunity and optimal algebraic immunity. The above results not only provide a theoretical basis for reducing nearly half of workload when studying the Cryptographic properties of H Boolean function, but also provide a new research method for the study of secure Cryptographic Property of Boolean functions. Such researches are important in Cryptographic primitive designs.