Introduction to finite fields and their applications
Introduction to finite fields and their applications
Nonlinearly balanced Boolean functions and their propagation characteristics
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Differentially uniform mappings for cryptography
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On almost perfect nonlinear permutations
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Linear cryptanalysis method for DES cipher
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Elliptic Curves and Resilient Functions
ICISC '00 Proceedings of the Third International Conference on Information Security and Cryptology
Maximum Correlation Analysis of Nonlinear S-boxes in Stream Ciphers
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Block ciphers sensitive to gröbner basis attacks
CT-RSA'06 Proceedings of the 2006 The Cryptographers' Track at the RSA conference on Topics in Cryptology
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In this paper, we give some relationship between the nonlinearity of rational functions over F2n and the number of points of associated hyperelliptic curve. Using this, we get a lower bound on nonlinearity of rational-typed vector Boolean functions over F2n. While the previous works give us a lower bound on nonlinearity only for special-typed monomials, our result gives us general bound applicable for all rational fuctions defined over F2n. As an application of our results, we get a lower bound on nonlinearity of n × kn S-boxes.