Handbook of Applied Cryptography
Handbook of Applied Cryptography
The Berlekamp-Massey Algorithm revisited
Applicable Algebra in Engineering, Communication and Computing
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Maximal values of generalized algebraic immunity
Designs, Codes and Cryptography
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
Using wiedemann's algorithm to compute the immunity against algebraic and fast algebraic attacks
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
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
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
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
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
Algebraic immunity for cryptographically significant Boolean functions: analysis and construction
IEEE Transactions on Information Theory
On the Construction of Boolean Functions With Optimal Algebraic Immunity
IEEE Transactions on Information Theory
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Constructions of 1-resilient Boolean functions on odd number of variables with a high nonlinearity
Security and Communication Networks
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
On the immunity of rotation symmetric Boolean functions against fast algebraic attacks
Discrete Applied Mathematics
| Hi-index | 754.84 |
In the past few years, algebraic attacks against stream ciphers with linear feedback function have been significantly improved. As a response to the new attacks, the notion of algebraic immunity of a Boolean function f was introduced, defined as the minimum degree of the annihilators of f and f + 1. An annihilator of f is a nonzero Boolean function g, such that f ċ g = 0. While several constructions of Boolean functions with optimal algebraic immunity have been proposed, there is no significant progress concerning the resistance against the so-called fast algebraic attacks. In this paper, we provide a framework to assess the resistance of Boolean functions against the new algebraic attacks, including fast algebraic attacks. The analysis is based on the univariate polynomial representation of Boolean functions and necessary and sufficient conditions are presented for a Boolean function to have optimal behavior against all the new algebraic attacks. Finally, we introduce a new infinite family of balanced Boolean functions described by their univariate polynomial representation. By applying the new framework, we prove that all the members of the family have optimal algebraic immunity and we efficiently evaluate their behavior against fast algebraic attacks.