Citation: | LIU Jian and CHEN Lusheng, “On Nonlinearity of S-Boxes and Their Related Binary Codes,” Chinese Journal of Electronics, vol. 25, no. 1, pp. 167-173, 2016, doi: 10.1049/cje.2016.01.025 |
O.S. Rothaus, “On “bent” functions”, Journal of Combinatorial Theory, Series A, Vol.20, No.3, pp.300-305, 1976.
|
K. Nyberg, “Perfect nonlinear S-boxes”, Advances in Cryptology—EUROCRYPT'91, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Vol.547, pp.378-386, 1992.
|
F. Chabaud and S. Vaudenay, “Links between differential and linear cryptanalysis”, Advances in Cryptology— EUROCRYPT'94, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Vol.950, pp.356-365, 1995.
|
A.M. Kerdock, “A class of low-rate nonlinear codes”, Information and Control, Vol.20, No.2, pp.182-187, 1972.
|
P. Delsarte, “An algebraic approach to the association schemes of coding theory”, Ph.D.Thesis, Université Catholique de Louvain, Belgium, 1973.
|
F.J. MacWilliams and N.J.A. Sloane, The Theory of Error- Correcting Codes, North-Holland Publishing Company, Amsterdam, 1977.
|
C. Carlet, “Vectorial Boolean functions for cryptography”, Y. Crama, P. Hammer (eds.), Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, London, U.K., pp.398-469, 2010.
|
C. Carlet and C. Ding, “Nonlinearities of S-boxes”, Finite Fields and Their Applications, Vol.13, No.1, pp.121-135, 2007.
|
T. Wadayama, T. Hada, K. Wagasugi, et al., “Upper and lower bounds on the maximum nonlinearity of n-input m-output Boolean functions”, Designs, Codes and Cryptography, Vol.23, No.1, pp.23-34, 2001.
|
C. Carlet, “Recursive lower bounds on the nonlinearity profile of Boolean functions and their applications”,IEEE Transactions on Information Theory, Vol.54, No.3, pp.1262-1272, 2008.
|
C. Carlet and S. Mesnager, “Improving the upper bounds on the covering radii of binary Reed-Muller codes”, IEEE Transactions on Information Theory, Vol.53, No.1, pp.162-173, 2007.
|
C. Carlet, “Boolean functions for cryptography and error correcting codes”, Y. Crama and P. Hammer (eds.), Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, London, U.K., pp.257- 397, 2010.
|
K. Nyberg, “On the construction of highly nonlinear permutations”, Advances in Cryptology—EUROCRYPT'92, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Vol.658, pp.92-98, 1993.
|
C. Carlet, C. Ding and J. Yuan, “Linear codes from perfect nonlinear mappings and their secret sharing schemes”, IEEE Transactions on Information Theory, Vol.51, No.6, pp.2089- 2102, 2005.
|
Q. Dai and C. Li, “Weight distributions of two classes of linear codes from perfect nonlinear functions”, Chinese Journal of Electronics, Vol.18, No.3, pp.465-470, 2009.
|
R. Gold, “Maximal recursive sequences with 3-valued recursive cross-correlation functions”, IEEE Transactions on Information Theory, Vol.14, No.1, pp.154-156, 1968.
|
K. Nyberg, “Differentially uniform mappings for cryptography”, Advances in Cryptology—EUROCRYPT'93, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Vol.765, pp.55-64, 1994.
|
M. Grassl, “Bounds on the minimum distance of linear codes and quantum codes”, http://www.codetables.de., 2009-9-07.
|