{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T01:51:59Z","timestamp":1780365119367,"version":"3.54.1"},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540430261","type":"print"},{"value":"9783540453253","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2001]]},"DOI":"10.1007\/3-540-45325-3_19","type":"book-chapter","created":{"date-parts":[[2007,10,27]],"date-time":"2007-10-27T07:51:25Z","timestamp":1193471485000},"page":"205-221","source":"Crossref","is-referenced-by-count":42,"title":["Statistical Properties of Digital Piecewise Linear Chaotic Maps and Their Roles in Cryptography and Pseudo-Random Coding"],"prefix":"10.1007","author":[{"given":"Shujun","family":"Li","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qi","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenmin","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuanqin","family":"Mou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanlong","family":"Cai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2001,12,4]]},"reference":[{"key":"19_CR1","volume-title":"Chaos, Fractals, and Noise-Stochastic Aspects of Dynamics","author":"A. Lasota","year":"1997","unstructured":"Andrzej Lasota and Michael C. Mackey. Chaos, Fractals, and Noise-Stochastic Aspects of Dynamics. Springer-Verlag, New York, second edition, 1997.","edition":"second edition"},{"key":"19_CR2","first-page":"514","volume":"4","author":"L. Kocarev","year":"1998","unstructured":"Ljup\u010do Kocarev, Goce Jakimoski, Toni Stojanovski, and Ulrich Parlitz. From chaotic maps to encryption schemes. In Proc. IEEE Int. Symposium Circuits and Systems 1998, volume 4, pages 514\u2013517. IEEE, 1998.","journal-title":"Proc. IEEE Int. Symposium Circuits and Systems 1998"},{"issue":"6","key":"19_CR3","doi-asserted-by":"publisher","first-page":"1259","DOI":"10.1142\/S021812749800098X","volume":"8","author":"J. Fridrich","year":"1998","unstructured":"Jiri Fridrich. Symmetric ciphers based on two-dimensional chaotic maps. Int. J. Bifurcation and Chaos, 8(6):1259\u20131284, 1998.","journal-title":"Int. J. Bifurcation and Chaos"},{"issue":"2","key":"19_CR4","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1142\/S0218127496000023","volume":"6","author":"R. Brown","year":"1996","unstructured":"R. Brown and L. O. Chua. Clarifying chaos: Examples and counterexamples. Int. J. Bifurcation and Chaos, 6(2):219\u2013249, 1996.","journal-title":"Int. J. Bifurcation and Chaos"},{"issue":"1","key":"19_CR5","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1080\/0161-118991863745","volume":"XIII","author":"R. Matthews","year":"1989","unstructured":"R. Matthews. On the derivation of a \u2018chaotic\u2019 encryption algorithm. Cryptologia, XIII(1):29\u201342, 1989.","journal-title":"Cryptologia"},{"issue":"1","key":"19_CR6","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1142\/S0218127497000145","volume":"7","author":"Z. Hong","year":"1997","unstructured":"Zhou Hong and Ling Xieting. Generating chaotic secure sequences with desired statistical properties and high security. Int. J. Bifurcation and Chaos, 7(1):205\u2013213, 1997.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"19_CR7","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/3-540-46416-6_11","volume-title":"Advances in Cryptology-EuroCrypt\u201991","author":"T. Habutsu","year":"1991","unstructured":"T. Habutsu, Y. Nishio, I. Sasase, and S. Mori. A secret key cryptosystem by iterating a chaotic map. In Advances in Cryptology-EuroCrypt\u201991, Lecture Notes in Computer Science 0547, pages 127\u2013140, Berlin, 1991. Spinger-Verlag."},{"issue":"3","key":"19_CR8","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1109\/81.557386","volume":"44","author":"H. Zhou","year":"1997","unstructured":"Hong Zhou and Xie-Ting Ling. Problems with the chaotic inverse system encryption approach. IEEE Trans. Circuits and Systems I, 44(3):268\u2013271, 1997.","journal-title":"IEEE Trans. Circuits and Systems I"},{"issue":"9","key":"19_CR9","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1049\/el:19980680","volume":"34","author":"S. Tao","year":"1998","unstructured":"Sang Tao, Wang Ruili, and Yan Yixun. Perturbance-based algorithm to expand cycle length of chaotic key stream. Electronics Letters, 34(9):873\u2013874, 1998.","journal-title":"Electronics Letters"},{"issue":"3","key":"19_CR10","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1080\/0161-118991863934","volume":"XIII","author":"D. D. Wheeler","year":"1989","unstructured":"D. D. Wheeler. Problems with chaotic cryptosystems. Cryptologia, XIII(3):243\u2013250, 1989.","journal-title":"Cryptologia"},{"issue":"2","key":"19_CR11","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1080\/0161-119191865821","volume":"XV","author":"D. D. Wheeler","year":"1991","unstructured":"D. D. Wheeler and R. Matthews. Supercomputer investigations of a chaotic encryption algorithm. Cryptologia, XV(2):140\u2013151, 1991.","journal-title":"Cryptologia"},{"key":"19_CR12","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1007\/3-540-46416-6_49","volume-title":"Advances in Cryptology-EuroCrypt\u201991","author":"E. Biham","year":"1991","unstructured":"E. Biham. Cryptoanalysis of the chaotic-map cryptosystem suggested at Euro-Crypt\u201991. In Advances in Cryptology-EuroCrypt\u201991, Lecture Notes in Computer Science 0547, pages 532\u2013534, Berlin, 1991. Spinger-Verlag."},{"issue":"2\/3\/4","key":"19_CR13","doi-asserted-by":"publisher","first-page":"1524","DOI":"10.1109\/TCOMM.1994.582834","volume":"42","author":"G. Heidari-Bateni","year":"1994","unstructured":"Ghobad Heidari-Bateni and Clare D. McGillem. A chaotic direct-sequence spreadspectrum communication system. IEEE Trans. Communications, 42(2\/3\/4):1524\u20131527, 1994.","journal-title":"IEEE Trans. Communications"},{"issue":"9","key":"19_CR14","first-page":"534","volume":"E 65","author":"S. Oishi","year":"1982","unstructured":"Shin\u2019ichi Oishi and Hajime Inoue. Pseudo-random number generators and chaos. Trans. IECE Japan, E 65(9):534\u2013541, 1982.","journal-title":"Trans. IECE Japan"},{"issue":"1","key":"19_CR15","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1109\/18.567654","volume":"43","author":"T. Kohda","year":"1997","unstructured":"Tohru Kohda and Akio Tsuneda. Statistics of chaotic binary sequences. IEEE Trans. Information Theory, 43(1):104\u2013112, 1997.","journal-title":"IEEE Trans. Information Theory"},{"key":"19_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0010-4655(99)00233-7","volume":"120","author":"J. A. Gonz\u00e1lez","year":"1999","unstructured":"Jorge A. Gonz\u00e1lez and Ramiro Pino. A random number generator based on unpredictable chaotic functions. Computer Physics Communications, 120:109\u2013114, 1999.","journal-title":"Computer Physics Communications"},{"issue":"6","key":"19_CR17","doi-asserted-by":"publisher","first-page":"1585","DOI":"10.1142\/S0218127495001198","volume":"5","author":"A. Baranovsky","year":"1995","unstructured":"A. Baranovsky and D. Daems. Design of one-dimensional chaotic maps with prescribed statistical properties. Int. J. Bifurcation and Chaos, 5(6):1585\u20131598, 1995.","journal-title":"Int. J. Bifurcation and Chaos"},{"key":"19_CR18","volume-title":"Applied Cryptography \u2014 Protocols, algorithms, and souce code in C","author":"B. Schneier","year":"1996","unstructured":"Bruce Schneier. Applied Cryptography \u2014 Protocols, algorithms, and souce code in C. John Wiley & Sons, Inc., New York, second edition, 1996.","edition":"second edition"},{"key":"19_CR19","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0167-2789(90)90069-2","volume":"D 42","author":"J. Palmore","year":"1990","unstructured":"Julian Palmore and Charles Herring. Computer arithmetic, chaos and fractals. Physica D, D 42:99\u2013110, 1990.","journal-title":"Physica D"},{"issue":"7","key":"19_CR20","first-page":"95","volume":"25","author":"Z. Hong","year":"1997","unstructured":"Zhou Hong and Ling Xieting. Realizing finite precision chaotic systems via perturbation of m-sequences. Acta Eletronica Sinica(In Chinese), 25(7):95\u201397, 1997.","journal-title":"Acta Eletronica Sinica"},{"key":"19_CR21","volume-title":"Applied Modern Algebra","author":"H. Guanhua","year":"1999","unstructured":"Hu Guanhua. Applied Modern Algebra. Tsinghua University Press, Beijing, China, second edition, 1999.","edition":"second edition"},{"key":"19_CR22","volume-title":"Concise Number Theory","author":"P. Chengdong","year":"1998","unstructured":"Pan Chengdong and Pan Chengbiao. Concise Number Theory. Beijing University Press, Beijing, China, 1998."},{"key":"19_CR23","volume-title":"Modern Applied Mathematics Handbook-vol. Probability Theory and Stochastic Process","author":"The Committee of Modern Applied Mathematics Handbook.","year":"2000","unstructured":"The Committee of Modern Applied Mathematics Handbook. Modern Applied Mathematics Handbook-vol. Probability Theory and Stochastic Process. Tsinghua University Press, Beijing, China, 2000."}],"container-title":["Lecture Notes in Computer Science","Cryptography and Coding"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-45325-3_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,24]],"date-time":"2019-02-24T16:17:01Z","timestamp":1551025021000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-45325-3_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001]]},"ISBN":["9783540430261","9783540453253"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/3-540-45325-3_19","relation":{},"ISSN":["0302-9743"],"issn-type":[{"value":"0302-9743","type":"print"}],"subject":[],"published":{"date-parts":[[2001]]}}}