Designing chaotic S-boxes based on time-delay chaotic system

Nonlinear Dynamics

Volumn 74, Issue 3, 2013, Pages 551-557

  Özkaynak, Fatih ^a   Yavuz, Sirma ^b  

^a FIRAT UNIVERSITY   (Turkey)

^b YILDIZ TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Chaos; Cryptography; S Box; Time delay chaotic system

Indexed keywords

BLOCK ENCRYPTION; CRYPTOLOGY; EFFICIENT IMPLEMENTATION; ENCRYPTION SYSTEM; PERFORMANCE REQUIREMENTS; S-BOX; S-BOX DESIGN; TIME DELAY CHAOTIC SYSTEM;

ALGORITHMS; CHAOS THEORY; COMPUTER SIMULATION; DESIGN;

CRYPTOGRAPHY;

EID: 84886233591     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-0987-4     Document Type: Article

References (36)

1. Alvarez, G.; Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. Int. J. Bifurc. Chaos Appl. Sci. Eng. 16(8), 2129-2153 (2006) (Pubitemid 44671739)
2. Amigo, J.M.; Kocarev, L.; Szczapanski, J.: Theory and practice of chaotic cryptography. Phys. Lett. A 336, 211-216 (2007)
3. Jakimoski, G.; Kocarev, L.: Chaos and cryptography: block encryption ciphers. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 48(2), 163-169 (2001) (Pubitemid 32254607)
4. Tang, G.; Liao, X.; Chen, Y.: A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23, 413-419 (2005)
5. Tang, G.; Liao, X.: A method for designing dynamical S-boxes based on discretized chaotic map. Chaos Solitons Fractals 23(5), 1901-1909 (2005)
6. Chen, G.; Chen, Y.; Liao, X.: An extended method for obtaining S-boxes based on 3-dimensional chaotic baker maps. Chaos Solitons Fractals 31, 571-579 (2007) (Pubitemid 44247626)
7. Chen, G.: A novel heuristic method for obtaining S-boxes. Chaos Solitons Fractals 36, 1028-1036 (2008)
8. Özkaynak, F.; Özer, A.B.: A method for designing strong S-boxes based on chaotic Lorenz system. Phys. Lett. A 374, 3733-3738 (2010)
9. Khan, M.; Shah, T.; Mahmood, H.; Gondal, M.A.: An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn. 71(3), 489-492 (2013)
10. Khan, M.; Shah, T.; Mahmood, H.; Gondal, M.A.; Hussain, I.: A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dyn. 70, 2303-2311 (2012)
11. Hussain, I.; Shah, T.; Gondal, M.A.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70, 1791-1794 (2012)
12. Sprott, J.C.: A simple chaotic delay differential equation. Phys. Lett. A 366, 397-402 (2007)
13. Uçar, A.: A prototype model for chaos studies. Int. J. Eng. Sci. 40, 251-258 (2002) (Pubitemid 32997731)
14. Prokhorow, M.D.; Ponomarenko, V.I.: Encryption and decryption of information in chaotic communication systems governed by delay-differential equations. Chaos Solitons Fractals 35, 871-877 (2008) (Pubitemid 47562744)
15. Tang, Y.; Wang, Z.; Fang, J.: Image encryption using chaotic coupled map lattices with time-varying delays. Commun. Nonlinear Sci. Numer. Simul. 15, 2456-2468 (2010)
16. Sprott, J.C.: Elegant Chaos Algebraically Simple Chaotic Flow. World Scientific, Singapore (2010)
17. Wang, Y.; Xie, Q.; Wu, Y.; Du, B.: A software for S-box performance analysis and test. In: 2009 International Conference on Electronic Commerce and Business Intelligence, Beijing, China, pp. 125-128 (2009)
18. Webster, A.; Tavares, S.: On the design of S-boxes. In: Advances in Cryptology: Proc. of Crypto'85, Santa Barbara, USA. Lecture Notes in Computer Science, vol. 218, pp. 523-534 (1986)
19. Adams, C.; Tavares, S.: Good S-boxes are easy to find. In: Advances in Cryptology: Proc. of Crypto'89, Santa Barbara, USA. Lecture Notes in Computer Science, vol. 435, pp. 612-615 (1989)
20. Biham, E.; Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. J. Cryptol. 4(1), 3-72 (1991)
21. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, London (1993)
22. Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, London (2003)
23. Ikeda, K.: Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt. Commun. 30, 257{261 (1979) (Pubitemid 10437376)
24. Verhulst, P.F.: Notice sur la loi que la population poursuit dans son accroissement. Corresp. Math. Phys. 10, 113-121 (1838)
25. Cusick, T.W.; Stanica, P.: Cryptographic Boolean Functions and Applications. Elsevier, Amsterdam (2009)
26. Youssef, A.M.; Tavares, S.E.; Gong, G.: On some probabilistic approximations for AES-like S-boxes. Discrete Math. 306(16), 2016-2020 (2006) (Pubitemid 44163528)
27. Youssef, A.M.; Tavares, S.E.: Affine equivalence in the AES round function. Discrete Appl. Math. 148(2), 161-170 (2005) (Pubitemid 40537248)
28. Jing-mei, L.; Bao-dian, W.; Xiang-guo, C.; Xin-mei, W.: Cryptanalysis of Rijndael S-box and improvement. Appl. Math. Comput. 170(2), 958-975 (2005) (Pubitemid 41497807)
29. Bard, G.V.: Algebraic Cryptanalysis. Springer, Berlin (2009)
30. Hussain, I.; Shah, T.; Mahmood, H.; Gondal, M.A.: A projective general linear group based algorithm for the construction of substitution box for block ciphers. Neural Comput. Appl. doi: 10.1007/s00521-012-0870-0
31. Hussain, I.; Shah, T.; Gondal, M.A.; Mahmood, H.: Analysis of S-box in image encryption using root mean square error method. Z. Naturforsch. 67, 327-332 (2012)
32. Özkaynak, F.; Özer, A.B.: A novel algorithm for strengthening of chaos based S-box generators. In: 2010 National Conference on Electrical, Electronics and Computer Engineering (ELECO 2010), Bursa, pp. 553-557 (2010). Art. No. 5698211
33. Hussain, I.; Shah, T.; Gondal, M.A.: An efficient image encryption algorithm based on S8 S-box transformation and NCA map. Optics Communications 285(24), 4887-4890
34. Hussain, I.: A novel approach of audio watermarking based on S-box transformation. Math. Comput. Model. 57(3-4), 963-969 (2013)
35. Hussain, I.; Shah, T.; Gondal, M.A.; Mahmood, H.: An efficient approach for the construction of LFT S-boxes using chaotic logistic map. Nonlinear Dyn. 71, 133-140 (2013)
36. Hussain, I.; Shah, T.; Gondal, M.A.: A novel approach for designing substitution-boxes based on nonlinear chaotic algorithm. Nonlinear Dyn. 70, 1791-1794 (2012)