{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T15:44:36Z","timestamp":1780587876811,"version":"3.54.1"},"publisher-location":"Berlin, Heidelberg","reference-count":46,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642205415","type":"print"},{"value":"9783642205422","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-20542-2_4","type":"book-chapter","created":{"date-parts":[[2011,7,20]],"date-time":"2011-07-20T13:34:30Z","timestamp":1311168870000},"page":"99-136","source":"Crossref","is-referenced-by-count":12,"title":["Formation of High-Dimensional Chaotic Maps and Their Uses in Cryptography"],"prefix":"10.1007","author":[{"given":"Wallace K. S.","family":"Tang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"4_CR1","volume-title":"Ergodic problems of classical mechanics","author":"V.I. Arnold","year":"1968","unstructured":"Arnold, V.I., Aver, A.: Ergodic problems of classical mechanics. W. A. Benjamin, New York (1968)"},{"issue":"4","key":"4_CR2","doi-asserted-by":"publisher","first-page":"144101","DOI":"10.1103\/PhysRevLett.92.144101","volume":"92","author":"F.M. Atay","year":"2004","unstructured":"Atay, F.M., Jost, J.: Delays, connection topology, and synchronization of coupled chaotic maps. Phys. Rev. Lett.\u00a092(4), 144101 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"4_CR3","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1016\/S0960-0779(99)00204-0","volume":"12","author":"L. Billings","year":"2001","unstructured":"Billings, L., Bollt, E.M.: Probability density functions of some skew tent maps. Chaos, Solitons and Fractals\u00a012, 365\u2013376 (2001)","journal-title":"Chaos, Solitons and Fractals"},{"key":"4_CR4","unstructured":"Bourke, P.: Recurrence Plots (1998), local.wasp.uwa.edu.au\/pbourke\/fractals\/recurrence\/"},{"key":"4_CR5","unstructured":"Brookes, M.: Matrix Reference Manual (2005), www.ee.ic.ac.uk\/hp\/staff\/dmb\/matrix\/intro.html"},{"key":"4_CR6","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/j.chaos.2003.12.022","volume":"21","author":"G. Chen","year":"2004","unstructured":"Chen, G., Mao, Y., Chui, C.K.: A symmetric image encryption scheme based on 3D chaotic cat maps. Chaos, Solitons and Fractals\u00a021, 749\u2013761 (2004)","journal-title":"Chaos, Solitons and Fractals"},{"key":"4_CR7","unstructured":"Crypto++ Library, http:\/\/www.cryptopp.com"},{"issue":"10","key":"4_CR8","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1109\/82.246162","volume":"40","author":"J.M. Cruz","year":"1993","unstructured":"Cruz, J.M., Chua, L.O.: An IC chip of Chua\u2019s circuit. IEEE Trans.Circuits and Systems II: Analog and Digital Processing\u00a040(10), 614\u2013625 (1993)","journal-title":"IEEE Trans.Circuits and Systems II: Analog and Digital Processing"},{"key":"4_CR9","doi-asserted-by":"crossref","unstructured":"Dai, S., Wu, Q., Pei, W., Yang, L., He, Z.: Lissajous chaotic map. In: Int. Conf. on Neural Networks and Signal Processing, vol.\u00a01, pp. 772\u2013775 (2003)","DOI":"10.1109\/ICNNSP.2003.1279389"},{"issue":"9","key":"4_CR10","doi-asserted-by":"publisher","first-page":"2959","DOI":"10.1142\/S0218127405013800","volume":"15","author":"K.O. Donoghue","year":"2005","unstructured":"Donoghue, K.O., Kennedy, M.P., Forbes, P., Wu, M., Jones, S.: A fast and simple implementation of Chua\u2019s oscillator with cubic-like nonlinearity. Int. J. Bifurcation and Chaos\u00a015(9), 2959\u20132971 (2005)","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"4_CR11","doi-asserted-by":"publisher","first-page":"16220","DOI":"10.1103\/PhysRevE.72.016220","volume":"72","author":"M. Falcioni","year":"2005","unstructured":"Falcioni, M., Palatella, L., Pigolotti, S., Vulpiani, A.: Properties making a chaotic system a good pseudo random number generator. Phys. Rev. E\u00a072, 16220 (2005)","journal-title":"Phys. Rev. E"},{"issue":"1","key":"4_CR12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S0218126602000240","volume":"11","author":"G. Grassi","year":"2002","unstructured":"Grassi, G., Mascolo, S.: A systematic procedure for synchronizing hyperchaos via observer design. J. of Circuits, Systems and Computers\u00a011(1), 1\u201316 (2002)","journal-title":"J. of Circuits, Systems and Computers"},{"key":"4_CR13","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF01608556","volume":"50","author":"M. H\u00e9non","year":"1976","unstructured":"H\u00e9non, M.: A two-dimensional mapping with a strange attractor. Communications Math. Phys.\u00a050, 69\u201377 (1976)","journal-title":"Communications Math. Phys."},{"key":"4_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8732-7","volume-title":"A first course in discrete dynamical systems","author":"R.A. Holmgren","year":"1996","unstructured":"Holmgren, R.A.: A first course in discrete dynamical systems. Springer, New York (1996)"},{"key":"4_CR15","unstructured":"Jun, B., Kocher, P.: The Intel random number generator. Cryptography Research, White Paper Prepared for Intel Corporation (April 1999), http:\/\/www.cryptography.com\/resources\/whitepapers\/IntelRNG.pdf"},{"key":"4_CR16","volume-title":"Theory and applications of coupled map lattices","author":"K. Kaneko","year":"1993","unstructured":"Kaneko, K.: Theory and applications of coupled map lattices. John Wiley & Sons, Chichester (1993)"},{"key":"4_CR17","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1109\/18.567654","volume":"43","author":"T. Kohda","year":"1997","unstructured":"Kohda, T., Tsuneda, A.: Statistics of chaotic binary sequences. IEEE Trans. Information Theory\u00a043, 104\u2013112 (1997)","journal-title":"IEEE Trans. Information Theory"},{"issue":"4","key":"4_CR18","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1142\/S0218127404009892","volume":"14","author":"H.S. Kwok","year":"2004","unstructured":"Kwok, H.S., Tang, K.S.: Chaotification of discrete-time systems using neurons. Int. J. of Bifurcation and Chaos\u00a014(4), 1405\u20131411 (2004)","journal-title":"Int. J. of Bifurcation and Chaos"},{"key":"4_CR19","unstructured":"Kwok, H.S., Tang, K.S.: Applications of high-dimensional cat map and its mixing nature. In: Int. Symp. Nonlinear Theory and its Applications, pp. 687\u2013690 (2006)"},{"issue":"4","key":"4_CR20","doi-asserted-by":"publisher","first-page":"1518","DOI":"10.1016\/j.chaos.2005.11.090","volume":"32","author":"H.S. Kwok","year":"2007","unstructured":"Kwok, H.S., Tang, K.S.: A fast image encryption scheme based on high-dimensional chaotic map. Chaos, Solitons and Fractals\u00a032(4), 1518\u20131529 (2007)","journal-title":"Chaos, Solitons and Fractals"},{"key":"4_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/3-540-45325-3_19","volume-title":"Cryptography and Coding","author":"S. Li","year":"2001","unstructured":"Li, S., Li, Q., Li, W., Mou, X., Cai, Y.: Statistical properties of digital piecewise linear chaotic maps and their roles in cryptography and pseudo-random coding. In: Honary, B. (ed.) Cryptography and Coding 2001. LNCS, vol.\u00a02260, pp. 205\u2013221. Springer, Heidelberg (2001)"},{"key":"4_CR22","unstructured":"Li, S., Zheng, X.: Cryptanalysis of a Chaotic Image Encryption Method. In: IEEE Int. Symp. Circuits and Systems, vol.\u00a02, pp. 708\u2013711 (2002)"},{"key":"4_CR23","doi-asserted-by":"crossref","unstructured":"Lian, S., Mao, Y., Wang, Z.: 3D extensions of some 2D chaotic maps and their usage in data encryption. In: The Fourth Int. Conf. on Control and Automation, pp. 819\u2013823 (2003)","DOI":"10.1109\/ICCA.2003.1595137"},{"key":"4_CR24","first-page":"37","volume":"1","author":"Y. Liu","year":"2005","unstructured":"Liu, Y., Sun, L., Zhu, Y., Beadle, P.: Novel method for measuring the complexity of schizophrenic EEG based on symbolic entropy analysis. IEEE-EMBS\u00a01, 37\u201340 (2005)","journal-title":"IEEE-EMBS"},{"key":"4_CR25","doi-asserted-by":"publisher","DOI":"10.4324\/9780203214589","volume-title":"The essence of chaos","author":"E.N. Lorenz","year":"1993","unstructured":"Lorenz, E.N.: The essence of chaos. University of Washington Press, Seattle (1993)"},{"issue":"17-19","key":"4_CR26","doi-asserted-by":"publisher","first-page":"2409","DOI":"10.1142\/S0217979204025440","volume":"18","author":"H. Lu","year":"2004","unstructured":"Lu, H., Wang, S., Wu, G.: Pseudo-random number generator based on coupled map lattices. Int. J. of Modern Phys. B\u00a018(17-19), 2409\u20132414 (2004)","journal-title":"Int. J. of Modern Phys. B"},{"issue":"10","key":"4_CR27","doi-asserted-by":"publisher","first-page":"3613","DOI":"10.1142\/S021812740401151X","volume":"14","author":"Y.B. Mao","year":"2004","unstructured":"Mao, Y.B., Chen, G., Lian, S.G.: A novel fast image encryption scheme based on the 3D chaotic baker map. Int. J. of Bifurcation and Chaos\u00a014(10), 3613\u20133624 (2004)","journal-title":"Int. J. of Bifurcation and Chaos"},{"key":"4_CR28","doi-asserted-by":"publisher","first-page":"348","DOI":"10.1111\/j.1749-6632.1980.tb29702.x","volume":"357","author":"M. Misiurewicz","year":"1980","unstructured":"Misiurewicz, M.: Strange attractors for the Lozi-mappings, nonlinear dynamic. New York Acad. of Sciences\u00a0357, 348\u2013358 (1980)","journal-title":"New York Acad. of Sciences"},{"issue":"5","key":"4_CR29","doi-asserted-by":"publisher","first-page":"258","DOI":"10.1016\/0375-9601(96)00012-6","volume":"211","author":"S. Morita","year":"1996","unstructured":"Morita, S.: Bifurcations in globally coupled chaotic maps. Phys. Lett. A\u00a0211(5), 258\u2013264 (1996)","journal-title":"Phys. Lett. A"},{"key":"4_CR30","unstructured":"Pareschi, F., Rovatti, R., Setti, G.: Simple and effective post-processing stage for random stream generated by a chaos-based RNG. In: Int. Symp. Nonlinear Theory and its Applications, pp. 383\u2013386 (2006)"},{"key":"4_CR31","first-page":"2039","volume":"278","author":"J.S. Richman","year":"2000","unstructured":"Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol.\u00a0278, 2039\u20132049 (2000)","journal-title":"Am. J. Physiol."},{"key":"4_CR32","doi-asserted-by":"publisher","DOI":"10.1002\/3527604804","volume-title":"Deterministic chaos: an introduction","author":"H.G. Schuster","year":"2005","unstructured":"Schuster, H.G., Just, W.: Deterministic chaos: an introduction. Wiley-VCH, Weinheim (2005)"},{"key":"4_CR33","unstructured":"Security Requirements for Cryptographic Modules, Federal Information Processing Standards 140-2 (2001)"},{"key":"4_CR34","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1090\/S0002-9904-1967-11798-1","volume":"73","author":"S. Smale","year":"1967","unstructured":"Smale, S.: Differentiable dynamical systems. Bulletin of the Amer. Math. Soc.\u00a073, 747\u2013817 (1967)","journal-title":"Bulletin of the Amer. Math. Soc."},{"key":"4_CR35","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198508397.001.0001","volume-title":"Chaos and time-series analysis","author":"J.C. Sprott","year":"2003","unstructured":"Sprott, J.C.: Chaos and time-series analysis. Oxford University Press, Oxford (2003)"},{"issue":"3","key":"4_CR36","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1142\/S0218127408020719","volume":"18","author":"K.W. Tang","year":"2008","unstructured":"Tang, K.W., Kwok, H.S., Tang, K.S., Man, K.F.: A chaos-based random number generator for 8-bit micro-controller system. Int. J. Bifurcation and Chaos\u00a018(3), 851\u2013867 (2008)","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"4_CR37","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.physa.2006.10.049","volume":"376","author":"C. Tian","year":"2007","unstructured":"Tian, C., Chen, G.: Chaos in the sense of Li-Yorke in coupled map lattices. Physica A\u00a0376, 246\u2013252 (2007)","journal-title":"Physica A"},{"key":"4_CR38","first-page":"1","volume":"18","author":"P.F. Verhulst","year":"1845","unstructured":"Verhulst, P.F.: Recherches math\u00e9matiques sur la loi d\u2019accroissement de la population. Nouv. m\u00e9m. de l\u2019Academie Royale des Sci. et Belles-Lettres de Bruxelles\u00a018, 1\u201341 (1845)","journal-title":"Nouv. m\u00e9m. de l\u2019Academie Royale des Sci. et Belles-Lettres de Bruxelles"},{"key":"4_CR39","first-page":"1","volume":"20","author":"P.F. Verhulst","year":"1847","unstructured":"Verhulst, P.F.: Deuxi\u00e8me m\u00e9moire sur la loi d\u2019accroissement de la population. M\u00e9m. de l\u2019Academie Royale des Sci., des Lettres et des Beaux-Arts de Belgique\u00a020, 1\u201332 (1847)","journal-title":"M\u00e9m. de l\u2019Academie Royale des Sci., des Lettres et des Beaux-Arts de Belgique"},{"key":"4_CR40","unstructured":"Visual Recurrence Analysis (2007), http:\/\/www.myjavaserver.com\/nonlinear\/vra\/download.html"},{"key":"4_CR41","unstructured":"Weisstein, E.W.: Baker\u2019s map, MathWorld- A Wolfram Web Resource, mathworld.wolfram.com\/BakersMap.html"},{"issue":"2","key":"4_CR42","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1063\/1.1568692","volume":"13","author":"F.H. Willeboordse","year":"2003","unstructured":"Willeboordse, F.H.: The spatial logistic map as a simple prototype for spatiotemporal chaos. Chaos\u00a013(2), 533\u2013540 (2003)","journal-title":"Chaos"},{"issue":"11","key":"4_CR43","doi-asserted-by":"publisher","first-page":"1808","DOI":"10.1103\/PhysRevLett.76.1808","volume":"76","author":"W. Yang","year":"1996","unstructured":"Yang, W., Ding, E., Ding, M.: Universal scaling law for the largest Lyapunov exponent in coupled map lattices. Phys. Rev. Lett.\u00a076(11), 1808\u20131811 (1996)","journal-title":"Phys. Rev. Lett."},{"key":"4_CR44","doi-asserted-by":"crossref","unstructured":"Yen, J., Guo, J.: A new chaotic key-based design for image encryption and decryption. In: IEEE Int. Conf. Circuits and Systems, vol.\u00a04, pp. 49\u201352 (2000)","DOI":"10.1109\/ISCAS.2000.858685"},{"issue":"9","key":"4_CR45","doi-asserted-by":"publisher","first-page":"3317","DOI":"10.1142\/S0218127404011223","volume":"14","author":"H. Zhang","year":"2004","unstructured":"Zhang, H., Chen, G.: Single-input multi-output state-feedback chaotification of general discrete systems. Int. J. of Bifurcation and Chaos\u00a014(9), 3317\u20133323 (2004)","journal-title":"Int. J. of Bifurcation and Chaos"},{"issue":"6","key":"4_CR46","doi-asserted-by":"publisher","first-page":"1375","DOI":"10.1109\/72.963774","volume":"12","author":"L. Zhao","year":"2001","unstructured":"Zhao, L., Elbert, E.N.: A network dynamically coupled chaotic maps for scene segmentation. IEEE Trans. on Neural Networks\u00a012(6), 1375\u20131385 (2001)","journal-title":"IEEE Trans. on Neural Networks"}],"container-title":["Studies in Computational Intelligence","Chaos-Based Cryptography"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-20542-2_4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,7]],"date-time":"2025-03-07T06:50:52Z","timestamp":1741330252000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-20542-2_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642205415","9783642205422"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-20542-2_4","relation":{},"ISSN":["1860-949X","1860-9503"],"issn-type":[{"value":"1860-949X","type":"print"},{"value":"1860-9503","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}