{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:48:35Z","timestamp":1649040515337},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,8,7]],"date-time":"2015-08-07T00:00:00Z","timestamp":1438905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1007\/s12095-015-0151-8","type":"journal-article","created":{"date-parts":[[2015,8,6]],"date-time":"2015-08-06T02:57:30Z","timestamp":1438829850000},"page":"371-381","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the distinctness of primitive sequences over Z\/(p e q) modulo 2"],"prefix":"10.1007","volume":"8","author":[{"given":"Yuan","family":"Cheng","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Feng","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun-Xiong","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dong","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,8,7]]},"reference":[{"key":"151_CR1","unstructured":"ETSI\/SAGE Specification: Specification of the 3GPP confidentiality and integrity algorithms 128-EEA3 & 128-EIA3. Document 4: Design and evaluation report; version: 2.0; Date: 9th Sep. 2011, Tech. rep., ETSI 2011. Available at: http:\/\/www.gsmworld.com\/our-work\/programmes-and-initiatives\/fraud-and-security\/gsm_security_algorithms.htm"},{"key":"151_CR2","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1007\/s10623-012-9698-y","volume":"70","author":"QX Zheng","year":"2014","unstructured":"Zheng, Q.X., Qi, W.F., Tian, T.: On the distinctness of modular reduction of primitive sequences over Z\/(232\u22121). Des. Codes Crypt. 70, 359\u2013368 (2014)","journal-title":"Des. Codes Crypt."},{"key":"151_CR3","doi-asserted-by":"crossref","first-page":"1623","DOI":"10.1090\/S0025-5718-08-02075-9","volume":"77","author":"XY Zhu","year":"2008","unstructured":"Zhu, X.Y., Qi, W.F.: On the distinctness of modular reduction of maximal length modulo odd prime numbers. Math. Comput. 77, 1623\u20131637 (2008)","journal-title":"Math. Comput."},{"key":"151_CR4","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ffa.2008.07.005","volume":"15","author":"HJ Chen","year":"2009","unstructured":"Chen, H.J., Qi, W.F.: On the distinctness of maximal length sequences over Z\/(p q) modulo 2. Finite Fields Appl 15, 23\u201339 (2009)","journal-title":"Finite Fields Appl"},{"key":"151_CR5","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.ffa.2010.12.004","volume":"17","author":"QX Zheng","year":"2011","unstructured":"Zheng, Q.X., Qi, W.F.: A new result on the distinctness of primitive sequences over Z\/(p q) modulo 2. Finite Fields Appl 17, 254\u2013274 (2011)","journal-title":"Finite Fields Appl"},{"key":"151_CR6","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1109\/TIT.2012.2212694","volume":"59","author":"QX Zheng","year":"2013","unstructured":"Zheng, Q.X., Qi, W.F., Tian, T.: On the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers. IEEE Trans. Inf. Theory 59, 680\u2013690 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"151_CR7","doi-asserted-by":"crossref","first-page":"4013","DOI":"10.1109\/TIT.2013.2243817","volume":"59","author":"QX Zheng","year":"2013","unstructured":"Zheng, Q.X., Qi, W.F.: Further results on the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers. IEEE Trans. Inf. Theory 59, 4013\u20134019 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"151_CR8","doi-asserted-by":"crossref","unstructured":"Hu, Z., Wang, L.: Injectivity of compressing maps on the set of primitive sequences modulo square-free odd integers. Cryptogr. Commun. (2015)","DOI":"10.1007\/s12095-014-0121-6"},{"key":"151_CR9","doi-asserted-by":"crossref","first-page":"467","DOI":"10.1007\/s10623-013-9871-y","volume":"74","author":"D Yang","year":"2015","unstructured":"Yang, D., Qi, W.F., Zheng, Q.X.: Further results on the distinctness of modulo 2 reductions of primitive sequences over Z\/(232\u22121). Des. Codes Crypt. 74, 467\u2013480 (2015)","journal-title":"Des. Codes Crypt."},{"key":"151_CR10","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1090\/S0002-9947-1933-1501705-4","volume":"35","author":"M Ward","year":"1933","unstructured":"Ward, M.: The arithmetical theory of linear recurring series. Trans. Am. Math. Soc. 35, 600\u2013628 (1933)","journal-title":"Trans. Am. Math. Soc."},{"key":"151_CR11","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1134\/S0032946008020087","volume":"44","author":"DN Bylkov","year":"2008","unstructured":"Bylkov, D.N., Kamlovskii, O.V.: Occurrence indices of elements in linear recurrence sequences over primary residue rings. Probl. Inf. Transm. 44, 161\u2013168 (2008)","journal-title":"Probl. Inf. Transm."},{"key":"151_CR12","doi-asserted-by":"crossref","first-page":"31","DOI":"10.4213\/sm4528","volume":"200","author":"OV Kamlovskii","year":"2009","unstructured":"Kamlovskii, O.V.: Frequency characteristics of linear recurrences over Galois rings. Matematicheskii Sbornik 200, 31\u201352 (2009)","journal-title":"Matematicheskii Sbornik"},{"key":"151_CR13","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1007\/s00209-002-0449-z","volume":"243","author":"Y Bugeaud","year":"2003","unstructured":"Bugeaud, Y., Corvaja, P., Zannier, U.: An upper bound for the G.C.D. of a n \u22121 and b n \u22121. Math. Z. 243, 79\u201384 (2003)","journal-title":"Math. Z."},{"key":"151_CR14","doi-asserted-by":"crossref","unstructured":"Wan, Z.X.: Finite fields and Galois Rings. World Scientific Publisher, Singapore (2003)","DOI":"10.1142\/5350"},{"key":"151_CR15","first-page":"1047","volume":"37","author":"WF Qi","year":"1994","unstructured":"Qi, W.F., Zhou, J.J.: Polynomial splitting ring and root representation of linear recurring sequences over Z\/(p e ). Sci. China Ser 37, 1047\u20131052 (1994)","journal-title":"Sci. China Ser"},{"key":"151_CR16","doi-asserted-by":"crossref","unstructured":"Rueppel, R.A.: Analysis and Design of Stream Ciphers[M]. Springer Verlag, New York (1986)","DOI":"10.1007\/978-3-642-82865-2"},{"key":"151_CR17","first-page":"491","volume":"9","author":"WF Qi","year":"1996","unstructured":"Qi, W.F., Wang, J.L.: The Structure of Splitting Rings over Z\/(p e ). Mathematica applicata 9, 491\u2013494 (1996)","journal-title":"Mathematica applicata"},{"key":"151_CR18","doi-asserted-by":"crossref","first-page":"2793","DOI":"10.1007\/BF02362772","volume":"76","author":"VL Kurakin","year":"1995","unstructured":"Kurakin, V.L., Kuzmin, A.S., Mikhalev, A.V., Nechaev, A.A.: Linear recurring sequences over rings and modules. J. Math. Sci. 76, 2793\u20132915 (1995)","journal-title":"J. Math. Sci."}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-015-0151-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12095-015-0151-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-015-0151-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,29]],"date-time":"2019-08-29T03:08:46Z","timestamp":1567048126000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12095-015-0151-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,7]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["151"],"URL":"https:\/\/doi.org\/10.1007\/s12095-015-0151-8","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,7]]}}}