Skip to main content
SpringerLink
Log in

Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers

  • Chapter
Chaos-Based Cryptography

Part of the book series: Studies in Computational Intelligence ((SCI,volume 354))

Introduction

The idea of using chaotic transformations in cryptography is explicit in the foundational papers of Shannon on secrecy systems (e.g., [96]). Although the word “chaos” was not minted till the 1970s [71], Shannon clearly refers to this very concept when he proposes the construction of secure ciphers by means of measure-preserving, mixing maps which depend ‘sensitively’ on their parameters. The implementation of Shannon’s intuitions had to wait till the development of Chaos Theory in the 1980s. Indeed, it was around 1990 when the first chaos-based ciphers were proposed (e.g., [78], [46]). Moreover, in 1990 chaos synchronization [91] entered the scene and shortly thereafter, the first applications to secure communications followed [56, 37]. The idea is remarkably simple: mask the message with a chaotic signal and use synchronization at the receiver to filter out the chaotic signal. The realization though had to overcome the desynchronization induced by the message itself. After this initial stage, the number of proposals which exploited the properties of chaotic maps for cryptographical purposes, grew in a spectacular way.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Addabbo, T., Alioto, M., Fort, A., Pasini, A., Rocchi, S., Vignoli, V.: A class of maximum-period nonlinear congruential generators derived from the reńyi chaotic map. IEEE Transactions on Circuits and Systems–I: Regular Papers 54(4), 816–828 (2007)

    Article  MathSciNet  Google Scholar 

  2. Alvarez, G.: Security problems with a chaos-based deniable authentication scheme. Chaos, Solitons & Fractals 26(1), 7–11 (2005)

    Article  MATH  Google Scholar 

  3. Alvarez, G., Arroyo, D., Nunez, J.: Application of Gray code to the cryptanalysis of chaotic cryptosystems. In: 3rd International IEEE Scientific Conference on Physics and Control (PhysCon 2007), September 3-7, Potsdam, Germany (2007), http://lib.physcon.ru/?item=1358

  4. Alvarez, G., Li, S.: Estimating short-time period to break different types of chaoitc modulation based secure communications. arxiv:nlin.CD/0406039 (2004), http://arxiv.org/abs/nlin/0406039

  5. Alvarez, G., Li, S.: Breaking an encryption scheme based on chaotic baker map. Physics Letters A 352(1-2), 78–82 (2006)

    Article  MATH  Google Scholar 

  6. Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems. International Journal of Bifurcation and Chaos 16(8), 2129–2151 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Alvarez, G., Li, S., Hernandez, L.: Analysis of security problems in a medical image encryption system. Computers in Biology and Medicine 37(3), 424–427 (2007)

    Article  Google Scholar 

  8. Alvarez, G., Li, S., Montoya, F., Romera, M., Pastor, G.: Breaking projective chaos synchronization secure communication using filtering and generalized synchronization. Chaos, Solitons & Fractals 24(3), 775–783 (2005)

    Article  MATH  Google Scholar 

  9. Alvarez, G., Montoya, F., Pastor, G.: Cryptanalysis of a discrete chaotic cryptosystem using external key. Physics Letters A 319, 334–339 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of a chaotic encryption system. Physics Letters A 276, 191–196 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of an ergodic chaotic cipher. Physics Letters A 311, 172–179 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  12. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Breaking parameter modulated chaotic secure communication system. Chaos, Solitons & Fractals 21(4), 793–797 (2004)

    Article  Google Scholar 

  13. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of dynamic look-up table based chaotic cryptosystems. Physics Letters A 326, 211–218 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  14. Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Keystream cryptanalysis of a chaotic cryptographic method. Computer Physics Communications 156, 205–207 (2004)

    Article  Google Scholar 

  15. Amigó, J., Kocarev, L., Szczepanski, J.: Theory and practice of chaotic cryptography. Physics Letters A 366(3), 211–216 (2007)

    Google Scholar 

  16. Amigó, J.M., Szczepanski, J.: Approximations of dynamical systems and their applications to cryptography. International Journal of Bifurcation and Chaos 13, 1937–1948 (2003)

    Article  MATH  Google Scholar 

  17. Amigó, J.M.: Chaos-Based Cryptography. In: Kocarev, L., Galias, Z., Lian, S. (eds.) Intelligent Computing Based on Chaos. Studies in Computational Intelligence, vol. 184, pp. 291–313. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Amigó, J.M., Szczepanski, J., Kocarev, L.: A chaos-based approach to the design of cryptographically secure substitutions. Physics Letters A 343, 55–60 (2005)

    Article  MATH  Google Scholar 

  19. Argenti, F., Benzi, S., Re, E.D., Genesio, R.: Stream cipher system based on chaotic maps. In: Proceedings of SPIE Mathematics and Applications of Data/Image Coding, Compression, and Encryption III, vol. 4122, pp. 10–17. SPIE (2001)

    Google Scholar 

  20. Ariffin, M., Noorani, M.: Modified Baptista type chaotic cryptosystem via matrix secret key. Physics Letters A 372, 5427–5430 (2008)

    Google Scholar 

  21. Arroyo, D.: Framework for the analysis and design of encryption strategies based on discrete-time chaotic dynamical systems. Ph.D. thesis, ETSIA of the Polytechnic University of Madrid, Madrid, Spain (2009), http://digital.csic.es/handle/10261/15668

  22. Arroyo, D., Alvarez, G., Amigó, J.M.: Estimation of the control parameter from symbolic sequences: Unimodal maps with variable critical point. Chaos: An Interdisciplinary Journal of Nonlinear Science 19 (2009), Art. no. 023125

    Google Scholar 

  23. Arroyo, D., Alvarez, G., Amigó, J.M., Li, S.: Cryptanalysis of a family of self-synchronizing chaotic stream ciphers. Communications in Nonlinear Science and Numerical Simulation 16(2), 805–813 (2011)

    Article  MathSciNet  Google Scholar 

  24. Arroyo, D., Alvarez, G., Li, S.: Some hints for the design of digital chaos-basedcryptosystems: lessons learned from cryptanalysis. In: Second IFAC Conference on Analysis and Control of Chaotic Systems, Queen Mary, University of London (2009)

    Google Scholar 

  25. Arroyo, D., Alvarez, G., Li, S., Li, C., Fernandez, V.: Cryptanalysis of a new chaotic cryptosystem based on ergodicity. International Journal of Modern Physics B 23(5), 651–659 (2009)

    Article  MATH  Google Scholar 

  26. Arroyo, D., Alvarez, G., Li, S., Li, C., Nunez, J.: Cryptanalysis of a discrete-time synchronous chaotic encryption system. Physics Letter A 372(7), 1034–1039 (2008)

    Article  MathSciNet  Google Scholar 

  27. Arroyo, D., Li, C., Li, S., Alvarez, G.: Cryptanalysis of a computer cryptography scheme based on a filter bank. Chaos, Solitons & Fractals 41, 410–413 (2009)

    Article  MATH  Google Scholar 

  28. Arroyo, D., Li, C., Li, S., Alvarez, G., Halang, W.A.: Cryptanalysis of an image encryption scheme based on a new total shuffling algorithm. Chaos, Solitons & Fractals 41(5), 2613–2616 (2009)

    Article  MATH  Google Scholar 

  29. Arroyo, D., Rhouma, R., Alvarez, G., Li, S., Fernandez, V.: On the security of a new image encryption scheme based on chaotic map lattices. Chaos: An Interdisciplinary Journal of Nonlinear Science 18 (2008), Art. no. 033112

    Google Scholar 

  30. Banerjee, S., Yorke, J.A., Grebogi, C.: Robust chaos. Physical Review Letters 80, 14 (1998)

    Article  MathSciNet  Google Scholar 

  31. Baptista, M.S.: Cryptography with chaos. Physics Letters A 240(1-2), 50–54 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  32. Beth, T., Lazic, D.E., Mathias, A.: Cryptanalysis of cryptosystems based on remote chaos replication. In: EUROCRYPT 1994. LNCS, vol. 950, pp. 318–331. Springer, Heidelberg (1994)

    Google Scholar 

  33. Brumley, D., Boneh, D.: Remote timing attacks are practical. In: Proceedings of the 12th USENIX Security Symposium, pp. 1–14. USENIX Association (2003)

    Google Scholar 

  34. Chee, C.Y., Xu, D.: Chaotic encryption using dicrete-time synchronous chaos. Physics Letters A 348(3-6), 284–292 (2006)

    Article  MATH  Google Scholar 

  35. Chen, G., Ueta, T.: Yet another chaotic attactor. International Journal of Bifurcation and Chaos 9(7), 1465–1466 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  36. Cornfeld, I.P., Fomin, S.V., Sinai, Y.G.: Ergodic theory. Springer, New York (1982)

    MATH  Google Scholar 

  37. Cuomo, K., Oppenheim, A.V., Strogatz, S.: Synchronization of Lorenz-based chaotic circuits with applications to communications. IEEE Transactions on Circuits and Systems–II: Analog and Digital Signal Processing 40(10), 626–633 (1993)

    Google Scholar 

  38. Dedieu, H., Kennedy, M., Hasler, M.: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE Transactions on Circuits and Systems–II: Analog and Digital Signal Processing 40, 634–641 (1993)

    Google Scholar 

  39. Dedieu, H., Ogorzalek, M.J.: Identifiability and identification of chaotic systems based on adaptive synchronization. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 44(10), 948–962 (1997)

    Article  MathSciNet  Google Scholar 

  40. Feki, M.: An adaptive chaos synchronization scheme applied to secure communication. Chaos, Solitons & Fractals 18(1), 141–148 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  41. Feldmann, U., Hasler, M., Schwarz, W.: Communication by chaotic signals: the inverse system approach. International Journal of Circuit Theory and Applications 24, 551–579 (1996)

    Article  MATH  Google Scholar 

  42. Fradkov, A.L., Markov, A.Y.: Adaptive synchronization of chaotic systems based on speed gradient method and passification. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 44, 905–912 (1997)

    Article  MathSciNet  Google Scholar 

  43. Fridrich, J.: Symmetric ciphers based on two-dimensional chaotic maps. International Journal of Bifurcation and Chaos 8, 1259–1284 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  44. Gao, T., Chen, Z.: Image encryption based on a new total shuffling algorithm. Chaos, Solitons & Fractals 38(1), 213–220 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  45. González-Miranda, J.: Synchronization and control of chaos. Imperial College Press, London (2004)

    Google Scholar 

  46. Habutsu, T., Nishio, Y., Sasase, I., Mori, S.: A secret key cryptosystem by iterating a chaotic map. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 127–140. Springer, Heidelberg (1991)

    Google Scholar 

  47. Hasler, M.: Synchronization of chaotic systems and transmission of information. International Journal of Bifurcation and Chaos 8(4), 647–659 (1998)

    Article  MATH  Google Scholar 

  48. Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (1961)

    Google Scholar 

  49. Hirsch, M.W., Smale, S.: Differential equations, dynamical systems, and linear algebra. Academic Press, Inc., San Diego (1974)

    MATH  Google Scholar 

  50. Hu, G., Feng, Z., Meng, R.: Chosen ciphertext attack on chaos communication based on chaos synchronization. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 50(2), 275–279 (2003)

    Article  MathSciNet  Google Scholar 

  51. Huijberts, H., Nijmeijer, H., Willems, R.: System identification in communication with chaotic systems. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 47, 800–808 (2000)

    Google Scholar 

  52. Inoue, E., Ushio, T.: Chaos communication using unknown input observers. Electronics and Communications in Japan Part III: Fundamental Electronic Science 84(12), 21–27 (2001)

    Google Scholar 

  53. Jakimoski, G., Kocarev, L.: Chaos and cryptography: Block encryption ciphers based on chaotic maps. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 48(2), 163–169 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  54. Jiang, Z.P.: A note on chaotic secure communication systems. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 49(1), 92–96 (2002)

    Article  Google Scholar 

  55. Kocarev, L.: Chaos-based cryptography: A brief overview. IEEE Circuits and Systems Magazine 1(2), 6–21 (2001)

    Article  MathSciNet  Google Scholar 

  56. Kocarev, L., Halle, K.S., Eckert, K., Chua, L.O., Parlitz, U.: Transimission of digital signals by chaotic synchronization. International Journal of Bifurcation and Chaos 2(4), 973–977 (1992)

    Article  MATH  Google Scholar 

  57. Kocarev, L., Makraduli, J., Amato, P.: Public-key encryption based on Chebyshev polynomials. Circuits, Systems, and Signal Processing 24, 497–517 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  58. Kocarev, L., Sterjev, M., Fekete, A., Vattay, G.: Public-key encryption with chaos. Chaos: An Interdisciplinary Journal of Nonlinear Science 14(4), 1078–1082 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  59. Kocarev, L., Szczepanski, J., Amigo, J., Tomovski, I.: Discrete chaos–I: Theory. IEEE Transactions on Circuits and Systems–I: Regular Papers 53(6), 1300–1309 (2006)

    Google Scholar 

  60. Kocher, P.C.: Timing attacks on implementations of diffie-hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104–113. Springer, Heidelberg (1996)

    Google Scholar 

  61. Kolumban, G., Kennedy, M., Chua, L.O.: The role of synchronization in digital communications using chaos - Part II: Chaotic modulation and chaotic synchronization. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 45(11), 1129–1140 (1998)

    Google Scholar 

  62. Letellier, C., Gouesbet, G.: Topological characterization of reconstructed attractors modding out symmetries. Journal de Physique II 6(11), 1615–1638 (1996)

    Article  Google Scholar 

  63. Li, C., Li, S., Alvarez, G., Chen, G., Lo, K.-T.: Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations. Physics Letters A 369, 23–30 (2007)

    Article  MATH  Google Scholar 

  64. Li, S.: Analyses and new designs of digital chaotic ciphers. Ph.D. thesis, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China (2003), http://www.hooklee.com/pub.html

  65. Li, S., Alvarez, G., Chen, G.: Breaking a chaos-based secure communication scheme designed by an improved modulation method. Chaos, Solitons & Fractals 25(1), 109–120 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  66. Li, S., Alvarez, G., Chen, G.: Return-map cryptanalysis revisited. International Journal of Bifurcation and Chaos 16(5), 1557–1568 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  67. Li, S., Alvarez, G., Li, Z., Halang, W.: Analog chaos-based secure communications and cryptanalysis: a brief survey. In: Kurths, J., Fradkov, A., Chen, G. (eds.) 3rd Int. IEEE Scientific Conference on Physics and Control (PhysCon 2007), Potsdam, Germany, p. 92 (2007), Full edition available at http://www.hooklee.com/Papers/PhysCon2007.pdf

  68. Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. International Journal of Bifurcation and Chaos 15(10), 3119–3151 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  69. Li, S., Li, C., Chen, G., Bourbakis, N.G., Lo, K.T.: A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Processing: Image Communication 23(3), 212–223 (2008)

    Google Scholar 

  70. Li, S., Mou, X., Cai, Y.: Pseudo-random bit generator based on couple chaotic systems and its applications in stream-ciphers cryptography. In: Pandu Rangan, C., Ding, C. (eds.) INDOCRYPT 2001. LNCS, vol. 2247, pp. 316–329. Springer, Heidelberg (2001)

    Google Scholar 

  71. Li, T.Y., Yorke, J.A.: Period three implies chaos. The American Mathematical Monthly 82, 985–992 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  72. Lian, K.Y., Liu, P.: Synchronization with message embedded for generalized Lorenz chaotic circuits and its error analysis. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 47(9), 1418–1424 (2000)

    Google Scholar 

  73. Ling, B.W.-K., Ho, C.Y.-F., Tam, P.K.-S.: Chaotic filter bank for computer cryptography. Chaos, Solitons & Fractals 34, 817–824 (2007)

    Article  Google Scholar 

  74. Liu, L., Wu, X., Hu, H.: Estimating system parameters of Chua’s circuit from synchronizing signal. Physics Letters A 324(1), 36–41 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  75. Lorenz, E.: Deterministic nonperiodic flow. Journal of the Atmospheric Sciences 20, 130–141 (1963)

    Google Scholar 

  76. Manjunath, G., Fournier-Prunaret, D.: A qualitative analysis of deciphering errors in chaos shift keying. International Journal of Bifurcation and Chaos 19(6), 2085–2092 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  77. Masuda, N., Jakimoski, G., Aihara, K., Kocarev, L.: Chaotic block ciphers: from theory to practical algorithms. IEEE Transactions on Circuits and Systems–I: Regular Papers 53(6), 1341–1352 (2006)

    Article  MathSciNet  Google Scholar 

  78. Matthews, R.: On the derivation of a chaotic encryption algorithm. Cryptologia 13, 29–42 (1989)

    Article  MathSciNet  Google Scholar 

  79. Maze, G.: Algebraic methods for constructing one-way trapdoor functions. Ph.D. thesis, University of Notre Dame (2003)

    Google Scholar 

  80. Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)

    Google Scholar 

  81. Millérioux, G., Amigó, J.M., Daafouz, J.: A connection between chaotic and conventional cryptography. IEEE Transactions on Circuits and Systems–I: Regular Papers 55(6), 1695–1703 (2008)

    Article  MathSciNet  Google Scholar 

  82. Millerioux, G., Daafouz, J.: Unknown input observers for message-embedded chaos synchronization of discrete-time systems. International Journal of Bifurcation and Chaos 14(4), 1357–1368 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  83. Millerioux, G., Mira, C.: Coding scheme based on chaos synchronization from noninvertible maps. International Journal of Bifurcation and Chaos 8, 2019–2029 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  84. NIST: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22 Revision 1A (2010), http://csrc.nist.gov/rng/rng2.html

  85. Orúe, A., Alvarez, G., Pastor, G., Romera, M., Montoya, F., Li, S.: A new parameter determination method for some double-scroll chaotic systems and its applications to chaotic cryptanalysis. Communications in Nonlinear Science and Numerical Simulations 15(11), 3471–3483 (2010)

    Article  Google Scholar 

  86. Orúe, A., Fernandez, V., Alvarez, G., Pastor, G., Romera, M., Montoya, F.: Determination of the parameters for a Lorenz system and application to break the security of two-channel chaotic cryptosystems. Physics Letters A 372(34), 5588–5592 (2008)

    Article  Google Scholar 

  87. Pareek, N.K., Patidar, V., Sud, K.K.: Discrete chaotic cryptography using external key. Physics Letters A 309, 75–82 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  88. Parker, A., Short, K.M.: Reconstructing the keystream form a chaotic encrypiton scheme. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 48(5), 624–630 (2001)

    Google Scholar 

  89. Parlitz, U., Chua, L.O., Kocarev, L., Halle, K.S., Shang, A.: Transmission of digital signals by chaotic synchronization. International Journal of Bifurcation and Chaos 2(4), 973–977 (1992)

    Article  MATH  Google Scholar 

  90. Pastor, G., Romera, M., Montoya, F.: A revision of the Lyapunov exponent in 1D quadratic maps. Physica D 107, 17–22 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  91. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Physical Review Letters 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  92. Pérez, G., Cerdeira, H.A.: Extracting messages masked by chaos. Physical Review Letters 74(11), 1970–1973 (1995)

    Article  Google Scholar 

  93. Pisarchik, A.N., Flores-Carmona, N.J., Carpio-Valadez, M.: Encryption and decryption of images with chaotic map lattices. Chaos: An Interdisciplinary Journal of Nonlinear Science 16(3) (2006), Art. no. 033118

    Google Scholar 

  94. Rajendra, U., Bhat, S., Kumar, S., Min, L.: Transimission and storage of medical images with patient information. Comput. Biol. Med. 33, 303–310 (2003)

    Google Scholar 

  95. Rhouma, R., Solak, E., Arroyo, D., Li, S., Alvarez, G., Belghith, S.: Comment on ”modified Baptista type chaotic cryptosystem via matrix secret key”. Phys. Lett. A 372, 5427 (2008); Physics Letters A  373(37), 3398–3400 (2009)

    Article  MathSciNet  Google Scholar 

  96. Shannon, C.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1949)

    MathSciNet  MATH  Google Scholar 

  97. Skrobek, A.: Approximation of a chaotic orbit as a cryptanalytical method on Baptista’s cipher. Physics Letters A 372(6), 849–859 (2008)

    Article  Google Scholar 

  98. Solak, E., Çokal, C., Yildiz, O.T., Biyikoğlu, T.: Cryptanalysis of Fridrich’s chaotic image encryption. International Journal of Bifurcation and Chaos 20(5), 1405–1413 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  99. Stamp, M., Low, R.M.: Applied cryptanalysis: breaking ciphers in the real world. John Wiley & Sons, Inc., Hoboken (2007)

    Google Scholar 

  100. Stinson, D.R.: Cryptography: Theory and Practice. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  101. Storm, C., Freeman, W.J.: Detection and classification of nonlinear dynamic switching events. Physical Review E 58, 1159–1162 (2002)

    MathSciNet  Google Scholar 

  102. Szczepanski, J., Amigó, J., Michalek, T., Kocarev, L.: Cryptographically secure substitutions based on the approximation of mixing maps. IEEE Transactions on Circuits and Systems–I: Regular Papers 52, 443–453 (2005)

    Article  MathSciNet  Google Scholar 

  103. Tao, C., Du, G.: A new approach to breaking down chaotic secure communication. International Journal of Bifurcation and Chaos 13(9), 2689–2698 (2003)

    Article  MATH  Google Scholar 

  104. Tao, C., Du, G., Zhang, Y.: Decoding digital information from the cascaded heterogeneous chaotic systems. International Journal of Bifurcation and Chaos 13(6), 1599–1608 (2003)

    Article  MATH  Google Scholar 

  105. Vaidya, P.G., Angadi, S.: Decoding chaotic cryptography without access to the superkey. Chaos, Solitons & Fractals 17(2-3), 379–386 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  106. Wang, X., Duan, C., Gu, N.: A new chaotic cryptography based on ergodicity. International Journal of Modern Physics B 22(7), 901–908 (2008)

    Article  MathSciNet  Google Scholar 

  107. Wang, X., Zhan, M., Lai, C.H., Hu, G.: Error function attack of chaos synchronization based encrypiton schemes. Chaos: An Interdisciplinary Journal of Nonlinear Science 14(1), 128–137 (2004)

    Google Scholar 

  108. Wu, C.W.: Synchronization in coupled chaotic circuits and systems. World Scientific, New Jersey (2002)

    Book  MATH  Google Scholar 

  109. Wu, C.W., Chua, L.O.: A simple way to synchronize chaotic systems with applications to secure communications systems. International Journal of Bifurcation and Chaos 3(6), 1619–1627 (1993)

    Article  MATH  Google Scholar 

  110. Xiao, D., Liao, X., Wong, K.W.: An efficient entire chaos-based scheme for deniable authentication. Chaos, Solitons & Fractals 23(4), 1327–1331 (2005)

    MATH  Google Scholar 

  111. Yang, T.: Recovery of digital signals from chaotic switching. International Journal of Circuit Theory and Applications 23(6), 611–615 (1995)

    Article  MATH  Google Scholar 

  112. Yang, T.: A survey of chaotic secure communication systems. Intenational Journal of Computational Cognition 2(2), 81–130 (2004)

    Google Scholar 

  113. Yang, T., Wu, C.W., Chua, L.O.: Cryptography based on chaotic systems. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 44(5), 469–472 (1997)

    Article  MATH  Google Scholar 

  114. Yang, T., Yang, L.–B., Yang, C.-M.: Breaking chaotic secure communications using spectrogram. Physics Letters A 247(1-2), 105–111 (1998)

    Article  Google Scholar 

  115. Yang, T., Yang, L.-B., Yang, C.-M.: Breaking chaotic switching using generalized synchronization. IEEE Transactions on Circuits and Systems–I: Fundamental Theory and Applications 45(10), 1062–1067 (1998)

    Article  Google Scholar 

  116. Zhang, Y., Tao, C., Jiang, J.J.: Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. Chaos: An Interdisciplinary Journal of Nonlinear Science 16(4) (2006), Art. no. 043122

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Consejo Superior de Investigaciones Científicas, Instituto de Física Aplicada, Serrano 144, 28006, Madrid, Spain

    Gonzalo Alvarez

  2. Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n., 03202, Elche, Alicante, Spain

    José María Amigó

  3. Consejo Superior de Investigaciones Científicas, Instituto de Acústica, Serrano 144, 28006, Madrid, Spain

    David Arroyo

  4. Fachbereich Informatik und Informationswissenschaft, Universität Konstanz, Universitätsstrasse 10, 78457, Konstanz, Germany

    Shujun Li

Authors
  1. Gonzalo Alvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José María Amigó
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. David Arroyo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shujun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Macedonain Academy of Sciences and Arts, bul. Krste Misirkov 2, 428, 1000, Skopje, Republic of Macedonia

    Ljupco Kocarev

  2. France Telecom R&D Beijing, 2 Science Institute South Rd,Haidian District, 100080, Beijing, China

    Shiguo Lian

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Alvarez, G., Amigó, J.M., Arroyo, D., Li, S. (2011). Lessons Learnt from the Cryptanalysis of Chaos-Based Ciphers. In: Kocarev, L., Lian, S. (eds) Chaos-Based Cryptography. Studies in Computational Intelligence, vol 354. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20542-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-20542-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20541-5

  • Online ISBN: 978-3-642-20542-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation