Combinatorial theory and statistical design
Combinatorial theory and statistical design
On the bent boolean functions that are symmetric
European Journal of Combinatorics
On integral zeros of Krawtchouk polynomials
Journal of Combinatorial Theory Series A
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
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Results on algebraic immunity for cryptographically significant boolean functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
Maximum nonlinearity of symmetric Boolean functions on odd number of variables
IEEE Transactions on Information Theory
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
A New Construction of Boolean Functions with Maximum Algebraic Immunity
ISC '09 Proceedings of the 12th International Conference on Information Security
Constructing symmetric boolean functions with maximum algebraic immunity
IEEE Transactions on Information Theory
Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity
Information Security Applications
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
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
A class of Boolean functions with four-valued Walsh spectra
APCC'09 Proceedings of the 15th Asia-Pacific conference on Communications
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
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
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
Boolean functions optimizing most of the cryptographic criteria
Discrete Applied Mathematics
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Cryptography and Communications
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
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
Designs, Codes and Cryptography
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So far there is no systematic attempt to construct Boolean functions with maximum annihilator immunity. In this paper we present a construction keeping in mind the basic theory of annihilator immunity. This construction provides functions with the maximum possible annihilator immunity and the weight, nonlinearity and algebraic degree of the functions can be properly calculated under certain cases. The basic construction is that of symmetric Boolean functions and applying linear transformation on the input variables of these functions, one can get a large class of non-symmetric functions too. Moreover, we also study several other modifications on the basic symmetric functions to identify interesting non-symmetric functions with maximum annihilator immunity. In the process we also present an algorithm to compute the Walsh spectra of a symmetric Boolean function with O(n2) time and O(n) space complexity.