Fast correlation attacks on stream ciphers
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Fast Correlation Attacks through Reconstruction of Linear Polynomials
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Information Security and Cryptology --- ICISC 2008
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Designs, Codes and Cryptography
Construction and analysis of boolean functions of 2t+1 variables with maximum algebraic immunity
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
On the algebraic immunity of symmetric boolean functions
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Weight distributions of the cosets of the (32,6) Reed-Muller code
IEEE Transactions on Information Theory
The covering radius of the (128,8) Reed-Muller code is 56 (Corresp.)
IEEE Transactions on Information Theory
The covering radius of the Reed-Muller code is at least 16276
IEEE Transactions on Information Theory
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
On the Construction of Boolean Functions With Optimal Algebraic Immunity
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
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To resist fast correlation attacks, Boolean functions used in stream ciphers should have high nonlinearity. n-variable bent functions have the maximum nonlinearity. However, they are not balanced and their algebraic degrees are at most n2. Therefore, they cannot be used directly as filter functions. In this paper, we give a new method to construct cryptographically significant Boolean functions. As an example, based on bent functions, we construct an infinite class of functions with good cryptographic properties: balancedness, optimum algebraic degree, almost optimum algebraic immunity and an almost optimum nonlinearity (higher than all other infinite classes of balanced functions with high algebraic immunity).