Fast correlation attacks on stream ciphers
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Cryptanalysis of Block Ciphers with Overdefined Systems of Equations
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Asymptotic Nonlinearity of Boolean Functions
Designs, Codes and Cryptography
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Maximal values of generalized algebraic immunity
Designs, Codes and Cryptography
Improved fast correlation attacks using parity-check equations of weight 4 and 5
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
Using wiedemann's algorithm to compute the immunity against algebraic and fast algebraic attacks
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
Open problems related to algebraic attacks on stream ciphers
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
On the higher order nonlinearities of algebraic immune functions
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient computation of algebraic immunity for algebraic and fast algebraic attacks
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity
IEEE Transactions on Information Theory
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
A New Upper Bound on the Block Error Probability After Decoding Over the Erasure Channel
IEEE Transactions on Information Theory
A New Attack on the Filter Generator
IEEE Transactions on Information Theory
A Note on Symmetric Boolean Functions With Maximum Algebraic Immunity in Odd Number of Variables
IEEE Transactions on Information Theory
On the Construction of Boolean Functions With Optimal Algebraic Immunity
IEEE Transactions on Information Theory
Algebraic immunity of S-boxes and augmented functions
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
IWCC '09 Proceedings of the 2nd International Workshop on Coding and Cryptology
A New Construction of Boolean Functions with Maximum Algebraic Immunity
ISC '09 Proceedings of the 12th International Conference on Information Security
Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity
Information Security Applications
Designs, Codes and Cryptography
Z4-Nonlinearity of a constructed quaternary cryptographic functions class
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
On the nonlinearity of discrete logarithm in F2n
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
On a conjecture about binary strings distribution
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
Upper bound for algebraic immunity on a subclass of Maiorana McFarland class of bent functions
Information Processing Letters
Construction of 1-resilient boolean functions with optimal algebraic immunity and good nonlinearity
Journal of Computer Science and Technology
Designs, Codes and Cryptography
Results on the immunity of Boolean functions against probabilistic algebraic attacks
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
A note on fast algebraic attacks and higher order nonlinearities
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
On equivalence classes of boolean functions
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Boolean functions optimizing most of the cryptographic criteria
Discrete Applied Mathematics
Cryptography and Communications
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Security and Communication Networks
Attack based on direct sum decomposition against the nonlinear filter generator
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
On the resistance of boolean functions against fast algebraic attacks
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
On the aperiodic hamming correlation of frequency-hopping sequences from norm functions
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Perfect algebraic immune functions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Designs, Codes and Cryptography
A new method to construct Boolean functions with good cryptographic properties
Information Processing Letters
Secondary constructions of Boolean functions with maximum algebraic immunity
Cryptography and Communications
On the immunity of rotation symmetric Boolean functions against fast algebraic attacks
Discrete Applied Mathematics
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After the improvement by Courtois and Meier of the algebraic attacks on stream ciphers and the introduction of the related notion of algebraic immunity, several constructions of infinite classes of Boolean functions with optimum algebraic immunity have been proposed. All of them gave functions whose algebraic degrees are high enough for resisting the Berlekamp-Massey attack and the recent Rønjom-Helleseth attack, but whose nonlinearities either achieve the worst possible value (given by Lobanov's bound) or are slightly superior to it. Hence, these functions do not allow resistance to fast correlation attacks. Moreover, they do not behave well with respect to fast algebraic attacks. In this paper, we study an infinite class of functions which achieve an optimum algebraic immunity. We prove that they have an optimum algebraic degree and a much better nonlinearity than all the previously obtained infinite classes of functions. We check that, at least for small values of the number of variables, the functions of this class have in fact a very good nonlinearity and also a good behavior against fast algebraic attacks.