Nonlinearity criteria for cryptographic functions
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Relations between roots and coefficients, interpolation and application to system solving
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
On Correlation-Immune Functions
CRYPTO '91 Proceedings of the 11th 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
Decrypting a Class of Stream Ciphers Using Ciphertext Only
IEEE Transactions on Computers
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Introducing a new variant of fast algebraic attacks and minimizing their successive data complexity
Mycrypt'05 Proceedings of the 1st international conference on Progress in Cryptology in Malaysia
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
Upper bounds on algebraic immunity of boolean power functions
FSE'06 Proceedings of the 13th international conference on Fast Software Encryption
On the (im)possibility of practical and secure nonlinear filters and combiners
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
ICISC'05 Proceedings of the 8th international conference on Information Security and Cryptology
IEEE Transactions on Information Theory
Mutually Clock-Controlled Feedback Shift Registers Provide Resistance to Algebraic Attacks
Information Security and Cryptology
On Cryptographically Significant Mappings over GF(2n)
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
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
On guess and determine cryptanalysis of LFSR-based stream ciphers
IEEE Transactions on Information Theory
Extensions of the Cube Attack Based on Low Degree Annihilators
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Efficient computation of algebraic immunity of symmetric boolean functions
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
On extended algebraic immunity
Designs, Codes and Cryptography
Designs, Codes and Cryptography
IEEE Transactions on Information Theory
Upper bound for algebraic immunity on a subclass of Maiorana McFarland class of bent functions
Information Processing Letters
Results on the immunity of Boolean functions against probabilistic algebraic attacks
ACISP'11 Proceedings of the 16th Australasian conference on Information security and privacy
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
ISPEC'10 Proceedings of the 6th international conference on Information Security Practice and Experience
Reducing the number of homogeneous linear equations in finding annihilators
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
On the higher order nonlinearities of algebraic immune functions
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
On algebraic immunity and annihilators
ICISC'06 Proceedings of the 9th international conference on Information Security and Cryptology
On the resistance of boolean functions against fast algebraic attacks
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
Gröbner-free normal forms for Boolean polynomials
Journal of Symbolic Computation
Algebraic immunity of S-boxes and augmented functions
FSE'07 Proceedings of the 14th international conference on Fast Software Encryption
Perfect algebraic immune functions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Secondary constructions of Boolean functions with maximum algebraic immunity
Cryptography and Communications
Algebraic attacks on a class of stream ciphers with unknown output function
Designs, Codes and Cryptography
On the immunity of rotation symmetric Boolean functions against fast algebraic attacks
Discrete Applied Mathematics
| Hi-index | 0.12 |
In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSR-based stream ciphers. An algorithm is described which permits to compute the algebraic immunity d of a Boolean function with n variables in $\mathcal{O}(D^2)$ operations, for $D \approx \binom{n}{d}$, rather than in $\mathcal{O}(D^3)$ operations necessary in all previous algorithms. Our algorithm is based on multivariate polynomial interpolation. For assessing the vulnerability of arbitrary Boolean functions with respect to fast algebraic attacks, an efficient generic algorithm is presented that is not based on interpolation. This algorithm is demonstrated to be particularly efficient for symmetric Boolean functions. As an application it is shown that large classes of symmetric functions are very vulnerable to fast algebraic attacks despite their proven resistance against conventional algebraic attacks.