Bent Functions, Partial Difference Sets, and Quasi-FrobeniusLocal Rings
Designs, Codes and Cryptography
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
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Improved fast correlation attacks using parity-check equations of weight 4 and 5
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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
Enumeration of 9-variable rotation symmetric boolean functions having nonlinearity 240
INDOCRYPT'06 Proceedings of the 7th international conference on Cryptology in India
On bent and highly nonlinear balanced/resilient functions and their algebraic immunities
AAECC'06 Proceedings of the 16th international conference on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Large families of quaternary sequences with low correlation
IEEE Transactions on Information Theory
On the existence of (9,3,5,240) resilient functions
IEEE Transactions on Information Theory
p-Ary and q-ary versions of certain results about bent functions and resilient functions
Finite Fields and Their Applications
q-ary Bent Functions Constructed from Chain Rings
Finite Fields and Their Applications
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New results on quaternary (Z4 = {0, 1, 2, 3}-valued) cryptographic functions are presented. We define and characterize completely the Z4-balancedness and the Z4-nonlinearity according the Hamming metric and the LEE metric. In the particular case of quaternary Bent functions we show that the maximal nonlinearity of these functions is bounded for the HAMMING metric and we give the exact value of the maximal nonlinearity of these functions for the LEE metric. A general construction, based on Galois ring is detailed and applied to obtain a class of balanced and high nonlinearity quaternary cryptographic functions. We use Gray map to derive these constructed quaternary functions to obtain balanced boolean functions having high nonlinearity.