On constructions and nonlinearity of correlation immune functions
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques 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
Fast Correlation Attacks through Reconstruction of Linear Polynomials
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
A Generalized Birthday Problem
CRYPTO '02 Proceedings of the 22nd 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 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
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
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Information Security and Cryptology
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
When stream cipher analysis meets public-key cryptography
SAC'06 Proceedings of the 13th international conference on Selected areas in cryptography
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
On the security of the LILI family of stream ciphers against algebraic attacks
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Note: On homogeneous rotation symmetric bent functions
Discrete Applied Mathematics
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On extended algebraic immunity
Designs, Codes and Cryptography
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
Upper bound for algebraic immunity on a subclass of Maiorana McFarland class of bent functions
Information Processing Letters
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
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
Enumeration of 9-variable rotation symmetric boolean functions having nonlinearity 240
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
On bent and highly nonlinear balanced/resilient functions and their algebraic immunities
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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
Computing the algebraic immunity efficiently
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Reducing the number of homogeneous linear equations in finding annihilators
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Partially perfect nonlinear functions and a construction of cryptographic 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
On algebraic immunity and annihilators
ICISC'06 Proceedings of the 9th international conference on Information Security and Cryptology
Characterisations of extended resiliency and extended immunity of s-boxes
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Perfect algebraic immune functions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
| Hi-index | 0.12 |
Recently algebraic attack has received a lot of attention in cryptographic literature. It has been observed that a Boolean function f, interpreted as a multivariate polynomial over GF(2), should not have low degree multiples when used as a cryptographic primitive. In this paper we show that high nonlinearity is a necessary condition to resist algebraic attack and explain how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attack) of a Boolean function. Next we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity.