Results 161 to 170 of about 568,049 (193)
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On the Construction of Boolean Functions With Optimal Algebraic Immunity
IEEE Transactions on Information Theory, 2008In this correspondence, we introduce a method to construct Boolean functions in any number of variables, with optimal algebraic immunity. Remarkably, all functions of this type with an odd number of variables can be obtained in this way. We study some cryptographic properties, such as balancedness, algebraic degree of the constructed functions ...
Longjiang Qu
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Revised Algorithms for Computing Algebraic Immunity against Algebraic and Fast Algebraic Attacks
2014Given a Boolean function with n variables, a revised algorithm for computing the algebraic immunity d against conventional algebraic attacks in O(D 2±e ) complexity is described for \(D=\sum _{i = 0}^d {n \choose i}\) and a small e, which corrects and clarifies the most efficient algorithm so far at Eurocrypt 2006.
Lin Jiao, Bin Zhang, Mingsheng Wang
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Applied Mechanics and Materials, 2013
Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we study the Effects of e-derivative on algebraic immunity, correlation immunity and algebraic degree of H Boolean functions with the Hamming weight .
Jing Lian Huang, Zhuo Wang, Jing Zhang
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Using the derivative of the Boolean function and the e-derivative defined by ourselves as research tools, we study the Effects of e-derivative on algebraic immunity, correlation immunity and algebraic degree of H Boolean functions with the Hamming weight .
Jing Lian Huang, Zhuo Wang, Jing Zhang
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IEEE Transactions on Information Theory, 2017
In 2013, Tang, Carlet, and Tang [IEEE TIT 59(1): 653–664, 2013] presented two classes of Boolean functions. The functions in the first class are unbalanced and the functions in the second one are balanced. Both of those two classes of functions have high nonlinearity, high algebraic degree, optimal algebraic immunity, and high fast algebraic immunity ...
Zhengchun Zhou +2 more
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In 2013, Tang, Carlet, and Tang [IEEE TIT 59(1): 653–664, 2013] presented two classes of Boolean functions. The functions in the first class are unbalanced and the functions in the second one are balanced. Both of those two classes of functions have high nonlinearity, high algebraic degree, optimal algebraic immunity, and high fast algebraic immunity ...
Zhengchun Zhou +2 more
exaly +3 more sources
Algebraic Immunity of Boolean Functions
2016Algebraic immunity is a cryptographic measure about the resistance against algebraic attack which was first proposed by Courtois in 2003 for stream ciphers. This chapter studies some basic properties of algebraic immunity of Boolean functions, including the construction of annihilators of Boolean functions, upper and lower bounds of algebraic immunity,
Chuan-Kun Wu, Dengguo Feng
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Cyclic codes and algebraic immunity of Boolean functions
2015 IEEE Information Theory Workshop (ITW), 2015Since 2003, algebraic attacks have received a lot of attention in the cryptography literature. In this context, algebraic immunity quantifies the resistance of a Boolean function to the standard algebraic attack of the pseudo-random generators using it as a nonlinear Boolean function.
Sihem Mesnager, Gérard D. Cohen
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A Process Algebra Model of the Immune System
2004Current models of the immune system have proven capable of reproducing the dynamics of the immune system response. However, they lack of formalisms (including semantics) to understand general laws of immune system behaviour. This paper introduces a process algebra with which we can model the immune system and make this model subjected to formal ...
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Group Algebras and Correlation Immune Functions
2005In this paper we consider functions $F : {\mathbb F}^{m}_{2} \rightarrow {\{\pm\}}$ which satisfy certain linear and differential properties. The investigation of these properties is motivated by applications in cryptography. The linear property that we are interested in is “correlation immunity”, the differential properties are known under the name
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Constructing balanced functions with optimum algebraic immunity
2007 IEEE International Symposium on Information Theory, 2007Because of the algebraic attacks, a high algebraic immunity is now an absolutely necessary (but not sufficient) property for Boolean functions used in stream ciphers. A difference of only 1 between the algebraic immunities of two functions can make a crucial difference with respect to algebraic attacks.
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Exact relation between nonlinearity and algebraic immunity
Discrete Mathematics and Applications, 2006We sharpen some lower bounds on the higher order nonlinearity of a Boolean function in terms of the value of its algebraic immunity and obtain new tight bounds. We prove a universal tight lower bound, which enables us to reduce the problem of estimating higher order nonlinearity to finding the dimension of certain linear subspaces in the space of ...
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