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
Basic Theory in Construction of Boolean Functions with Maximum Possible Annihilator Immunity
Designs, Codes and Cryptography
Mutually Clock-Controlled Feedback Shift Registers Provide Resistance to Algebraic Attacks
Information Security and Cryptology
Information Security and Cryptology
Maximal values of generalized algebraic immunity
Designs, Codes and Cryptography
Constructing symmetric boolean functions with maximum algebraic immunity
IEEE Transactions on Information Theory
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
Enumeration of balanced symmetric functions over GF(p)
Information Processing Letters
On extended algebraic immunity
Designs, Codes and Cryptography
FSE'05 Proceedings of the 12th international conference on Fast Software Encryption
Reducing the number of homogeneous linear equations in finding annihilators
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Partially perfect nonlinear functions and a construction of cryptographic boolean functions
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
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Recent algebraic attacks on LFSR-based stream ciphers and S-boxes have generated much interest as they appear to be extremely powerful. Theoretical work has been developed focusing around the Boo- lean function case. In this paper, we generalize this theory to arbitrary finite fields and extend the theory of annihilators and ideals introduced at Eurocrypt 2004 by Meier, Pasalic and Carlet. In particular, we prove that for any function f in the multivariate polynomial ring over GF(q), f has a low degree multiple precisely when two low degree functions appear in the same coset of the annihilator of fq−−1 – 1. In this case, many such low degree multiples exist.