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
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
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
Maximal values of generalized algebraic immunity
Designs, Codes and Cryptography
Information Security and Cryptology --- ICISC 2008
IWCC '09 Proceedings of the 2nd International Workshop on Coding 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
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Algebraic cryptanalysis of the data encryption standard
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Constructions of cryptographically significant boolean functions using primitive polynomials
IEEE Transactions on Information Theory
Designs, Codes and Cryptography
Nonlinear equivalence of stream ciphers
FSE'10 Proceedings of the 17th international conference on Fast software encryption
Designs, Codes and Cryptography
A note on fast algebraic attacks and higher order nonlinearities
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
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
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In FSE 2010, Rønjom and Cid put forward a nonlinear equivalence for Boolean functions and demonstrated that many cryptographic properties are not invariant among functions within the same equivalence class by providing some special examples. Their paper presented the idea and many problems were left open. In this paper, we investigate equivalence of Boolean functions more deeply using a new method and discuss the number of Boolean functions in each equivalence class. We investigate further the cryptographic properties including algebraic immunity, algebraic degree and nonlinearity of equivalence classes, and deduce tight bounds on them. We find that there are many equivalence classes of Boolean functions with optimum algebraic immunity, optimum algebraic degree and a good nonlinearity. Moreover, we discuss how to construct equivalence classes with desired properties and show that it is possible to construct practical Boolean functions such that their equivalence classes have guaranteed cryptographic properties.