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
Algebraic attacks on stream ciphers with linear feedback
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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
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
INDOCRYPT'04 Proceedings of the 5th 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
Evaluating the resistance of stream ciphers with linear feedback against fast algebraic attacks
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
On exact algebraic [non-]immunity of s-boxes based on power functions
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
Probabilistic algebraic attacks
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
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Given a Boolean function f on n-variables, we find a reduced set of homogeneous linear equations by solving which one can decide whether there exist annihilators at degree d or not. Using our method the size of the associated matrix becomes $\nu_f \times (\sum_{i=0}^{d} \binom{n}{i} -- \mu_f)$, where, νf = |{x | wt(x) d, f(x) = 1}| and μf = |{x | wt(x) ≤d, f(x) = 1}| and the time required to construct the matrix is same as the size of the matrix. This is a preprocessing step before the exact solution strategy (to decide on the existence of the annihilators) that requires to solve the set of homogeneous linear equations (basically to calculate the rank) and this can be improved when the number of variables and the number of equations are minimized. As the linear transformation on the input variables of the Boolean function keeps the degree of the annihilators invariant, our preprocessing step can be more efficiently applied if one can find an affine transformation over f(x) to get h(x) = f(Bx+b) such that μh = |{x | h(x) = 1, wt(x) ≤d}| is maximized (and in turn νh is minimized too). We present an efficient heuristic towards this. Our study also shows for what kind of Boolean functions the asymptotic reduction in the size of the matrix is possible and when the reduction is not asymptotic but constant.