Analysis and design of stream ciphers
Analysis and design of stream ciphers
Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A fast correlation attack on nonlinearly feedforward filtered shift-register sequences
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Handbook of Applied Cryptography
Handbook of Applied Cryptography
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
Low Order Approximation of Cipher Functions
Proceedings of the International Conference on Cryptography: Policy and Algorithms
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
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
New approaches to the design of self-synchronizing stream ciphers
EUROCRYPT'91 Proceedings of the 10th annual 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
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
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
Results on algebraic immunity for cryptographically significant boolean functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
On immunity profile of boolean functions
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
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
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
A New Upper Bound on the Block Error Probability After Decoding Over the Erasure Channel
IEEE Transactions on Information Theory
Improving the Upper Bounds on the Covering Radii of Binary Reed–Muller Codes
IEEE Transactions on Information Theory
Sequences, DFT and Resistance against Fast Algebraic Attacks
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
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
Further properties of several classes of Boolean functions with optimum algebraic immunity
Designs, Codes and Cryptography
Best affine and quadratic approximations of particular classes of Boolean functions
IEEE Transactions on Information Theory
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
Discrete Applied Mathematics
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
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
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One of the most basic requirements concerning Boolean functions used in cryptosystems is that they must have high algebraic degrees. This simple criterion is not always well adapted to the concrete situation in which Boolean functions are used in symmetric cryptography, since changing one or several output bits of a Boolean function considerably changes its algebraic degree while it may not change its robustness. The proper characteristic is the r-th order nonlinearity profile (which includes the first-order nonlinearity). However, studying it is difficult and almost no paper, in the literature, has ever been able to give general effective results on it. The values of the nonlinearity profile are known for very few functions and these functions have little cryptographic interest. A recent paper has given a lower bound on the nonlinearity profile of functions, given their algebraic immunity. We improve upon it, and we deduce that it is enough, for a Boolean function, to have high algebraic immunity, for having non-weak low order nonlinearity profile (even when it cannot be evaluated), except maybe for the first order.