Handbook of combinatorics (vol. 1)
Handbook of combinatorics (vol. 1)
Restriction, terms and nonlinearity of Boolean functions
Theoretical Computer Science - Special issue: cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Shift Register Sequences
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
Nonlinearity Bounds and Constructions of Resilient Boolean Functions
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
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
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Computing the algebraic immunity efficiently
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
Results on algebraic immunity for cryptographically significant boolean functions
INDOCRYPT'04 Proceedings of the 5th international conference on Cryptology in India
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
Mutually Clock-Controlled Feedback Shift Registers Provide Resistance to Algebraic Attacks
Information Security and Cryptology
On the security of the LILI family of stream ciphers against algebraic attacks
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
On extended algebraic immunity
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
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Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function fc called the algebraic complement of f. This motivates us to examine AI(fc). We define the extended algebraic immunity of f as AI*(f)= min {AI(f), AI(fc)}. We prove that 0≤AI(f)–AI*(f)≤1. Since AI(f)–AI*(f)= 1 holds for a large number of cases, the difference between AI(f) and AI*(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI*(f).