Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Designs and their codes
Two new classes of bent functions
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
A construction of bent function
FFA '95 Proceedings of the third international conference on Finite fields and applications
Journal of Combinatorial Theory Series A
ICICS '99 Proceedings of the Second International Conference on Information and Communication Security
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Fast Correlation Attacks Based on Turbo Code Techniques
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
A Larger Class of Cryptographic Boolean Functions via a Study of the Maiorana-McFarland Construction
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
On Resilient Boolean Functions with Maximal Possible Nonlinearity
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
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
Journal of Complexity - Special issue on coding and cryptography
Concatenating Indicators of Flats for Designing Cryptographic Functions
Designs, Codes and Cryptography
Piecewise Constructions of Bent and Almost Optimal Boolean Functions
Designs, Codes and Cryptography
Hyper-bent functions and cyclic codes
Journal of Combinatorial Theory Series A
Construction of bent functions via Niho power functions
Journal of Combinatorial Theory Series A
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
More correlation-immune and resilient functions over Galois fields and Galois rings
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Improved fast correlation attacks on stream ciphers via convolutional codes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Construction of nonlinear boolean functions with important cryptographic properties
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
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
Normal extensions of bent functions
IEEE Transactions on Information Theory
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
New cyclic difference sets with Singer parameters
Finite Fields and Their Applications
Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions
Finite Fields and Their Applications
Z4-Nonlinearity of a constructed quaternary cryptographic functions class
SETA'10 Proceedings of the 6th international conference on Sequences and their applications
On immunity profile of boolean functions
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
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Security and Communication Networks
A note on vectorial bent functions
Information Processing Letters
Hi-index | 0.00 |
Since the introduction of the notions of nonlinearity in the mid-70’s (the term has been in fact introduced later), of correlation immunity and resiliency in the mid-80’s, and of algebraic immunity recently, the problem of efficiently constructing Boolean functions satisfying, at high levels, one or several of these criteria has received much attention. Only few primary constructions are known, and secondary constructions are also necessary to obtain functions achieving or approaching the best possible cryptographic characteristics. After recalling the background on cryptographic criteria and making some general observations, we try to give a survey of all these constructions and their properties. We then show that a nice and simple property of Boolean functions leads to a general secondary construction building an n-variable function from three known n-variable functions. This construction generalizes secondary constructions recently obtained for Boolean bent functions and also leads to secondary constructions of highly nonlinear balanced or resilient functions, with potentially better algebraic immunities than the three functions used as building blocks.