{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T21:32:56Z","timestamp":1775251976693,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2018,10,17]],"date-time":"2018-10-17T00:00:00Z","timestamp":1539734400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61502441"],"award-info":[{"award-number":["61502441"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61602526"],"award-info":[{"award-number":["61602526"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&D Program of China","award":["2017YFB0802004"],"award-info":[{"award-number":["2017YFB0802004"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s12095-018-0332-3","type":"journal-article","created":{"date-parts":[[2018,10,17]],"date-time":"2018-10-17T01:59:05Z","timestamp":1539741545000},"page":"951-963","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["New explicit injective compressing mappings on primitive sequences over \u2124 p e $\\mathbb {Z}_{p^e}$"],"prefix":"10.1007","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2578-4502","authenticated-orcid":false,"given":"Lin","family":"Wang","sequence":"first","affiliation":[]},{"given":"Zhi","family":"Hu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,10,17]]},"reference":[{"issue":"1","key":"332_CR1","doi-asserted-by":"publisher","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(1), 23\u201339 (2009)","journal-title":"Finite Fields Appl."},{"key":"332_CR2","unstructured":"Chakraborty, D., Mancillas-Lopez, C., Sarkar, P.: STES: A stream cipher based low cost scheme for securing stored data, IACR Cryptology ePrint Archive. 347. https:\/\/eprint.iacr.org\/2013\/347.pdf (2013)"},{"issue":"3","key":"332_CR3","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1007\/s12095-015-0151-8","volume":"8","author":"Y Cheng","year":"2016","unstructured":"Cheng, Y., Qi, W.-F., Zheng, Q.-X., Yang, D.: On the distinctness of primitive sequences over Z\/(p e q) modulo 2. Cryptogr. Commun. 8(3), 371\u2013381 (2016)","journal-title":"Cryptogr. Commun."},{"issue":"4","key":"332_CR4","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/s12095-014-0121-6","volume":"7","author":"Z Hu","year":"2015","unstructured":"Hu, Z., Wang, L.: Injectivity of compressing maps on the set of primitive sequences modulo square-free odd integers. Cryptogr. Commun. 7(4), 347\u2013361 (2015). https:\/\/doi.org\/10.1007\/s12095-014-0121-6","journal-title":"Cryptogr. Commun."},{"issue":"2","key":"332_CR5","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/00150517.1992.12429368","volume":"30","author":"M-Q Huang","year":"1992","unstructured":"Huang, M.-Q., Dai, Z.-D.: Projective maps of linear recurring sequences with maximal p-adic periods. Fibonacci Quart. 30(2), 139\u2013143 (1992)","journal-title":"Fibonacci Quart."},{"issue":"10","key":"332_CR6","doi-asserted-by":"publisher","first-page":"6602","DOI":"10.1109\/TIT.2014.2345769","volume":"60","author":"Y-P Jiang","year":"2014","unstructured":"Jiang, Y.-P., Lin, D.-D.: Distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers. IEEE Trans. Inf. Theory 60(10), 6602\u20136608 (2014)","journal-title":"IEEE Trans. Inf. Theory"},{"key":"332_CR7","doi-asserted-by":"publisher","first-page":"052102","DOI":"10.1007\/s11432-015-5472-x","volume":"60","author":"Y-P Jiang","year":"2017","unstructured":"Jiang, Y.-P., Zheng, Q.-X., Lin, D.-D.: On s-uniform property of compressing sequences derived from primitive sequences modulo odd prime powers. Sci. China Inf. Sci. 60, 052102 (2017). https:\/\/doi.org\/10.1007\/s11432-015-5472-x","journal-title":"Sci. China Inf. Sci."},{"issue":"3","key":"332_CR8","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1070\/RM1993v048n03ABEH001044","volume":"48","author":"AS Kuzmin","year":"1993","unstructured":"Kuzmin, A.S.: Lower estimates for the ranks of coordinate sequences of linear recurrent sequences over primary residue rings of integers. Russian Math. Surv. 48(3), 203\u2013204 (1993)","journal-title":"Russian Math. Surv."},{"issue":"1","key":"332_CR9","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1070\/RM1993v048n01ABEH000993","volume":"48","author":"AS Kuzmin","year":"1993","unstructured":"Kuzmin, A.S., Nechaev, A.A.: Linear recurring sequences over Galois ring. Russian Math. Surv. 48(1), 171\u2013172 (1993)","journal-title":"Russian Math. Surv."},{"issue":"4","key":"332_CR10","first-page":"107","volume":"3","author":"AA Nechaev","year":"1991","unstructured":"Nechaev, A.A.: Linear recurring sequences over commutative rings. Discrete Math. 3(4), 107\u2013121 (1991)","journal-title":"Discrete Math."},{"issue":"4","key":"332_CR11","first-page":"311","volume":"27","author":"WF Qi","year":"1997","unstructured":"Qi, W.F., Zhou, J.J.: The distribution of 0 and 1 in the highest level sequence of primitive sequences over Z\/(2e). Sci. China, Ser A 27(4), 311\u2013316 (1997). (in Chinese)","journal-title":"Sci. China, Ser A"},{"issue":"18","key":"332_CR12","doi-asserted-by":"crossref","first-page":"1938","DOI":"10.1360\/csb1997-42-18-1938","volume":"42","author":"WF Qi","year":"1997","unstructured":"Qi, W.F., Zhou, J.J.: The distribution of 0 and 1 in the highest level sequence of primitive sequences over Z\/(2e) (II). Chinese Sci. Bull. 42(18), 1938\u20131940 (1997). (in Chinese)","journal-title":"Chinese Sci. Bull."},{"key":"332_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3254-2","volume-title":"A Course in p-adic Analysis","author":"AM Robert","year":"2000","unstructured":"Robert, A.M.: A Course in p-adic Analysis. Springer, New York (2000)"},{"key":"332_CR14","unstructured":"Sarkar, P.: Tweakable enciphering schemes from stream ciphers with IV., IACR Cryptology ePrint Archive. 321. https:\/\/eprint.iacr.org\/2009\/321.pdf (2009)"},{"issue":"8","key":"332_CR15","doi-asserted-by":"publisher","first-page":"2960","DOI":"10.1109\/TIT.2007.901214","volume":"53","author":"T Tian","year":"2007","unstructured":"Tian, T., Qi, W.-F.: Injectivity of compressing maps on primitive sequences over \u2124 \/ ( p e ) $\\mathbb {Z}\/(p^{e})$ . IEEE Trans. Inform. Theory 53(8), 2960\u20132966 (2007)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"332_CR16","doi-asserted-by":"publisher","unstructured":"Wang, L., Hu, Z.: Injectivity on distribution of elements in the compressed sequences derived from primitive sequences over \u2124 p e $\\mathbb {Z}_{p^e}$ , Cryptogr. Commun. https:\/\/doi.org\/10.1007\/s12095-017-0278-x","DOI":"10.1007\/s12095-017-0278-x"},{"key":"332_CR17","doi-asserted-by":"publisher","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. Amer. Math. Soc. 35, 600\u2013628 (1933)","journal-title":"Trans. Amer. Math. Soc."},{"issue":"1","key":"332_CR18","doi-asserted-by":"publisher","first-page":"555","DOI":"10.1109\/TIT.2009.2034782","volume":"56","author":"Q-X Zheng","year":"2010","unstructured":"Zheng, Q.-X., Qi, W.-F.: Distribution properties of compressing sequences derived from primitive sequences over \u2124 \/ ( p e ) $\\mathbb {Z}\/(p^{e})$ . IEEE Trans. Inform. Theory 56(1), 555\u2013563 (2010)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"3","key":"332_CR19","doi-asserted-by":"publisher","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\/(q p) modulo 2. Finite Fields Appl. 17(3), 254\u2013274 (2011)","journal-title":"Finite Fields Appl."},{"issue":"1","key":"332_CR20","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1109\/TIT.2012.2212694","volume":"59","author":"Q-X 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(1), 680\u2013690 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"6","key":"332_CR21","doi-asserted-by":"publisher","first-page":"4013","DOI":"10.1109\/TIT.2013.2243817","volume":"59","author":"Q-X 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(6), 4013\u20134019 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"8","key":"332_CR22","doi-asserted-by":"publisher","first-page":"5016","DOI":"10.1109\/TIT.2013.2258712","volume":"59","author":"Q-X Zheng","year":"2013","unstructured":"Zheng, Q.-X., Qi, W.-F., Tian, T.: Further result on distribution properties of compressing sequences derived from primitive sequences over Z\/(p e). IEEE Trans. Inf. Theory 59(8), 5016\u20135022 (2013)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"10","key":"332_CR23","doi-asserted-by":"publisher","first-page":"2442","DOI":"10.1109\/TIT.2004.834791","volume":"50","author":"X-Y Zhu","year":"2004","unstructured":"Zhu, X.-Y., Qi, W.-F.: Compression mappings on primitive sequences over Z\/(p e). IEEE Trans. Inform. Theory 50(10), 2442\u20132448 (2004)","journal-title":"IEEE Trans. Inform. Theory"},{"key":"332_CR24","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.ffa.2004.04.001","volume":"11","author":"X-Y Zhu","year":"2005","unstructured":"Zhu, X.-Y., Qi, W.-F.: Uniqueness of the distribution of zeros of primitive level sequences over Z\/(p e). Finite Fields Appl. 11, 30\u201344 (2005)","journal-title":"Finite Fields Appl."},{"key":"332_CR25","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.ffa.2006.02.002","volume":"13","author":"X-Y Zhu","year":"2007","unstructured":"Zhu, X.-Y., Qi, W.-F.: Uniqueness of the distribution of zeros of primitive level sequences over \u2124 \/ ( p e ) $\\mathbb {Z}\/(p^{e})$ (II). Finite Fields Appl. 13, 230\u2013248 (2007)","journal-title":"Finite Fields Appl."},{"issue":"8","key":"332_CR26","doi-asserted-by":"publisher","first-page":"2985","DOI":"10.1109\/TIT.2007.901216","volume":"53","author":"X-Y Zhu","year":"2007","unstructured":"Zhu, X.-Y., Qi, W.-F.: Further result of compressing maps on primitive sequences modulo odd prime powers. IEEE Trans. Inform. Theory 53(8), 2985\u20132990 (2007)","journal-title":"IEEE Trans. Inform. Theory"},{"issue":"263","key":"332_CR27","doi-asserted-by":"publisher","first-page":"1623","DOI":"10.1090\/S0025-5718-08-02075-9","volume":"77","author":"X-Y Zhu","year":"2008","unstructured":"Zhu, X.-Y., Qi, W.-F.: On the distinctness of modular reductions of maximal length sequences modulo odd prime powers. Math. Comput. 77(263), 1623\u20131637 (2008)","journal-title":"Math. Comput."},{"key":"332_CR28","unstructured":"ETSI\/SAGE Specification. Specification of the 3GPP Confidentiality and Integrity Algorithms 128-EEA3 & 128-EIA3. Document 2: ZUC Specification; Version: 1.5. http:\/\/www.gsma.com\/technicalprojects\/fraud-security\/security-algorithms (2011)"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-018-0332-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s12095-018-0332-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-018-0332-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T20:21:39Z","timestamp":1775247699000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s12095-018-0332-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,17]]},"references-count":28,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["332"],"URL":"https:\/\/doi.org\/10.1007\/s12095-018-0332-3","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,17]]},"assertion":[{"value":"29 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}