Fast correlation attacks on stream ciphers
Lecture Notes in Computer Science on Advances in Cryptology-EUROCRYPT'88
Fast Correlation Attacks through Reconstruction of Linear Polynomials
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Probabilistic Higher Order Differential Attack and Higher Order Bent Functions
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
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
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
Non-linear approximations in linear cryptanalysis
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Fast low order approximation of cryptographic functions
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
Designs, Codes and Cryptography
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
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
On the higher order nonlinearities of algebraic immune functions
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
IEEE Transactions on Information Theory
A New Attack on the Filter Generator
IEEE Transactions on Information Theory
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
On equivalence classes of boolean functions
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
On the second-order nonlinearities of some bent functions
Information Sciences: an International Journal
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In this note, we deduce a bound between fast algebraic immunity and higher order nonlinearity (it is the first time that a bound between these two cryptographic criteria is given), and find that a Boolean function should have high r-order nonlinearity to resist fast algebraic attacks. As a corollary, we find that no matter how much effort we make, the Tu-Deng functions cannot be repaired in a standard way to behave well against fast algebraic attacks. Therefore, we should give up repairing this class of Boolean functions and try to find other classes of functions with good cryptographic properties or to prove that the Carlet-Feng function behaves well.