Handbook of Applied Cryptography
Handbook of Applied Cryptography
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Essential Algebraic Structure within the AES
CRYPTO '02 Proceedings of the 22nd 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
Sequences, DFT and Resistance against Fast Algebraic Attacks
SETA '08 Proceedings of the 5th international conference on Sequences and Their Applications
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
Algebraic cryptanalysis of the data encryption standard
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
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
Open problems related to algebraic attacks on stream ciphers
WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
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
Algebraic attacks on combiners with memory and several outputs
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
A New Attack on the Filter Generator
IEEE Transactions on Information Theory
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
Boolean functions optimizing most of the cryptographic criteria
Discrete Applied Mathematics
On the resistance of boolean functions against fast algebraic attacks
ICISC'11 Proceedings of the 14th 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
A new method to construct Boolean functions with good cryptographic properties
Information Processing Letters
Secondary constructions of Boolean functions with maximum algebraic immunity
Cryptography and Communications
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In this paper the possibilities of an iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The notion of $\mathcal{AAR}$ (Algebraic Attack Resistant) function is introduced as a unified measure of protection against classical algebraic attacks as well as fast algebraic attacks. Then, it is shown that functions that posses the highest resistance to fast algebraic attacks are necessarily of maximum $\mathcal{AI}$ (Algebraic Immunity ), the notion introduced in [20] defined as a minimum degree of functions that annihilate either f or 1 + f . More precisely, if for any non-annihilating function g of degree e an optimum degree relation e + d *** n is satisfied in the product fg = h (denoting deg (h ) = d ), then the function f in n variables must have maximum $\mathcal{AI}$, i.e. for nonzero function g the relation fg = 0 or (1 + f )g = 0 implies $deg(g)\geq \frac{n}{2}$. The presented theoretical framework allows us to iteratively construct functions with maximum $\mathcal{AI}$ satisfying e + d *** n *** 1, thus almost optimized resistance to fast algebraic cryptanalysis. This infinite class for the first time, apart from almost optimal resistance to algebraic cryptanalysis, in addition generates the functions that possess high nonlinearity (superior to previous constructions) and maximum algebraic degree, thus unifying most of the relevant cryptographic criteria.