Linear Cryptanalysis Using Multiple Approximations
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Quadratic Relation of S-box and Its Application to the Linear Attack of Full Round DES
CRYPTO '98 Proceedings of the 18th 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
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
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
An improved list decoding algorithm for the second order Reed---Muller codes and its applications
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
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
Constructing single- and multi-output boolean functions with maximal algebraic immunity
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
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
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
Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Propagation characteristics of x→ x-1 and Kloosterman sums
Finite Fields and Their Applications
Finite Fields and Their Applications
An Upper Bound for the Extended Kloosterman Sums over Galois Rings
Finite Fields and Their Applications
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
| Hi-index | 0.00 |
The r-th order nonlinearity of a Boolean function $f:F_2^n\to F_2$ is its minimum Hamming distance to all functions of algebraic degrees at most r, where ris a positive integer. The r-th order nonlinearity of an S-box $F:F_2^n\to F_2^m$ is the minimum r-th order nonlinearity of its component functions v·F, $v\in F_2^m\setminus \{0\}$. The role of this cryptographic criterion against attacks on stream and block ciphers has been illustrated by several papers. Its study is also interesting for coding theory and is related to the covering radius of Reed-Muller codes (i.e. the maximum multiplicity of errors that have to be corrected when maximum likelihood decoding is used on a binary symmetric channel). We give a survey of what is known on this parameter, including the bounds involving the algebraic immunity of the function, the bounds involving the higher order nonlinearities of its derivatives, and the resulting bounds on the higher order nonlinearities of the multiplicative inverse functions (used in the S-boxes of the AES). We show an improvement, when we consider an S-box instead of a Boolean function, of the bounds on the higher order nonlinearity expressed by means of the algebraic immunity. We study a generalization (for S-boxes) of the notion and we give new results on it.