The complexity of Boolean functions
The complexity of Boolean functions
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Using Strassen's algorithm to accelerate the solution of linear systems
The Journal of Supercomputing
Higher order correlation attacks, XL algorithm and cryptanalysis of Toyocrypt
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Results on algebraic immunity for cryptographically significant boolean functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
IEEE Transactions on Information Theory
Information Security and Cryptology
On the Higher Order Nonlinearities of Boolean Functions and S-Boxes, and Their Generalizations
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
Some lower bounds on the algebraic immunity of functions given by their trace forms
Problems of Information Transmission
Improved lower bound on the number of balanced symmetric functions over GF(p)
Information Sciences: an International Journal
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
Further properties of several classes of Boolean functions with optimum algebraic immunity
Designs, Codes and Cryptography
Constructing symmetric boolean functions with maximum algebraic immunity
IEEE Transactions on Information Theory
Probabilistic versus deterministic algebraic cryptanalysis: a performance comparison
IEEE Transactions on Information Theory
Efficient computation of algebraic immunity of symmetric boolean functions
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Enumeration of balanced symmetric functions over GF(p)
Information Processing Letters
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
On extended algebraic immunity
Designs, Codes and Cryptography
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
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
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
Cryptography and Communications
Reducing the number of homogeneous linear equations in finding annihilators
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
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
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Security and Communication Networks
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
S-box construction from non-permutation power functions
Proceedings of the 6th International Conference on Security of Information and Networks
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In this paper, we analyze the algebraic immunity of symmetric Boolean functions. The algebraic immunity is a property which measures the resistance against the algebraic attacks on symmetric ciphers. We identify a set of lowest degree annihilators for symmetric functions and propose an efficient algorithm for computing the algebraic immunity of a symmetric function. The existence of several symmetric functions with maximum algebraic immunity is proven. In this way, we have found a new class of functions which have good implementation properties and maximum algebraic immunity.