Bijective S-boxes of different sizes obtained from quasi-cyclic codes
DOI:
https://doi.org/10.13069/jacodesmath.617232Keywords:
S-box, Simplex code, Quasi-cyclic codesAbstract
The aim of this paper is to construct S-boxes of different sizes with good cryptographic properties. An algebraic construction for bijective S-boxes is described. It uses quasi-cyclic representations of the binary simplex code. Good S-boxes of sizes 4, 6, 8, 9, 10, 11, 12, 14, 15, 16 and 18 are obtained.
Received: 4 July 2018 Accepted: 23 April 2019Downloads
References
D. Bikov and I. Bouyukliev, BoolSPLG: A library with parallel algorithms for Boolean functions and S-boxes for GPU.
D. Bikov and I. Bouyukliev, Parallel fast Walsh transform algorithm and its implementation with CUDA on GPUs, Cybernet. Inform. Tech. 18(5) (2018) 21–43.
I. Bouyukliev, D. Bikov, and S. Bouyuklieva, S-boxes from binary quasi-cyclic codes, Electron. Notes Discrete Math. 57 (2017) 67–72.
C. Carlet, Boolean Functions for Cryptography and Error Correcting Codes, In: Y. Crama and P. L. Hammer (Eds.), Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, 2010, pp. 257–397.
C. Carlet, Vectorial Boolean Functions for Cryptography, In: Y. Crama and P. L. Hammer (Eds.), Boolean Models and Methods in Mathematics, Computer Science, and Engineering, Cambridge University Press, 2010, pp. 398–469.
E. Z. Chen, New quasi-cyclic codes from simplex codes, IEEE Trans. Inform. Theory 53(3) (2007) 1193–1196.
CUDA Zone, https://developer.nvidia.com/cuda-zone.
J. Daemen and V. Rijmen, The Design of Rijndael: AES – The Advanced Encryption Standard, Information Security and Cryptography, Springer-Verlag, Berlin, Heidelberg, 2002.
I. Hussain, T. Shah, M. A. Gondal, and W. A. Khan, Construction of cryptographically strong $8 \times 8$ S-boxes, World Appl. Sci. J. 13(11) (2011) 2389–2395.
G. Ivanov, N. Nikolov, and S. Nikova, Reversed genetic algorithms for generation of bijective S-boxes with good cryptographic properties, Cryptogr. Commun. 8(2) (2016) 247–276.
K. Lally and P. Fitzpatrick, Algebraic structure of quasi-cyclic codes, Discrete Appl. Math. 111(1–2) (2001) 157–175.
G. Leander and A. Poschmann, On the classification of 4 bit S-boxes, In: C. Carlet and B. Sunar (Eds.), Arithmetic of Finite Fields, WAIFI 2007, Lecture Notes in Comput. Sci., vol. 4547, Springer, Berlin, Heidelberg, 2007, pp. 159–176.
S. Ling and P. Solé, On the algebraic structure of quasi-cyclic codes I: Finite fields, IEEE Trans. Inform. Theory 47(7) (2001) 2751–2760.
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.
NVIDIA Data Center, https://www.nvidia.com/en-us/data-center/.
M. J. O. Saarinen, Cryptographic analysis of all $4 \times 4$–bit S–boxes, In: Selected Areas in Cryptography, SAC 2011, Lecture Notes in Comput. Sci., vol. 7118, Springer, Berlin, Heidelberg, 2012, pp. 118–133.
W. Zhang, Z. Bao, V. Rijmen, and M. Liu, A new classification of 4-bit optimal S-boxes and its application to PRESENT, RECTANGLE and SPONGENT, In: G. Leander (Ed.), Fast Software Encryption, FSE 2015, Lecture Notes in Comput. Sci., vol. 9054, Springer, Berlin, Heidelberg, 2015, pp. 494–515.
