{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T11:34:45Z","timestamp":1777548885531,"version":"3.51.4"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:00:00Z","timestamp":1629417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Cryptogr. Commun."],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s12095-021-00521-y","type":"journal-article","created":{"date-parts":[[2021,8,20]],"date-time":"2021-08-20T00:02:32Z","timestamp":1629417752000},"page":"117-134","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Linear complexity of some sequences derived from hyperelliptic curves of genus 2"],"prefix":"10.1007","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5404-790X","authenticated-orcid":false,"given":"Vishnupriya","family":"Anupindi","sequence":"first","affiliation":[]},{"given":"L\u00e1szl\u00f3","family":"M\u00e9rai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,8,20]]},"reference":[{"key":"521_CR1","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/978-3-642-59435-9_3","volume-title":"Pseudorandom sequences from elliptic curves, Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001)","author":"PHT Beelen","year":"2002","unstructured":"Beelen, P. H. T., Doumen, J. M.: Pseudorandom sequences from elliptic curves, Finite fields with applications to coding theory, cryptography and related areas (Oaxaca, 2001), pp 37\u201352. Springer, Berlin (2002)"},{"issue":"177","key":"521_CR2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1090\/S0025-5718-1987-0866101-0","volume":"48","author":"DG Cantor","year":"1987","unstructured":"Cantor, D.G.: Computing in the Jacobian of a hyperelliptic curve. Math. Comp. 48(177), 95\u2013101 (1987)","journal-title":"Math. Comp."},{"issue":"1","key":"521_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00605-008-0520-x","volume":"154","author":"Z Chen","year":"2008","unstructured":"Chen, Z.: Elliptic curve analogue of Legendre sequences. Monatsh Math. 154(1), 1\u201310 (2008)","journal-title":"Monatsh Math."},{"key":"521_CR4","volume-title":"Discrete Mathematics and its Applications","year":"2006","unstructured":"Cohen, H., Frey, G., Avanzi, R., Doche, C., Lange, T., Nguyen, K., Vercauteren, F. (eds.): Discrete Mathematics and its Applications. Chapman & Hall\/CRC, Boca Raton (2006)"},{"key":"521_CR5","doi-asserted-by":"crossref","unstructured":"El Mahassni, E., Shparlinski, I.: On the uniformity of distribution of congruential generators over elliptic curves, Discrete Math. Theor. Comput. Sci. (Lond.), pp. 257\u2013264. Springer, London (2002)","DOI":"10.1007\/978-1-4471-0673-9_19"},{"key":"521_CR6","doi-asserted-by":"crossref","unstructured":"Farashahi, R.R.: Extractors for Jacobian of hyperelliptic curves of genus 2 in odd characteristic, Cryptography and coding, Lecture Notes in Comput. Sci., vol. 4887, pp. 313\u2013335. Springer, Berlin (2007)","DOI":"10.1007\/978-3-540-77272-9_19"},{"key":"521_CR7","doi-asserted-by":"crossref","unstructured":"Farashahi, R.R., Pellikaan, R.: The quadratic extension extractor for (hyper)elliptic curves in odd characteristic, Arithmetic of finite fields, Lecture Notes in Comput. Sci., vol. 4547, pp. 219\u2013236. Springer, Berlin (2007)","DOI":"10.1007\/978-3-540-73074-3_17"},{"key":"521_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139012843","volume-title":"Mathematics of Public Key Cryptography","author":"SD Galbraith","year":"2012","unstructured":"Galbraith, S.D.: Mathematics of Public Key Cryptography. Cambridge University Press, Cambridge (2012)"},{"key":"521_CR9","doi-asserted-by":"crossref","unstructured":"Gong, G., Berson, T.A., Stinson, D.R.: Elliptic curve pseudorandom sequence generators, Selected areas in cryptography (Kingston, ON, 1999), Lecture Notes in Comput. Sci., vol. 1758, pp. 34\u201348. Springer, Berlin (2000)","DOI":"10.1007\/3-540-46513-8_3"},{"key":"521_CR10","doi-asserted-by":"crossref","unstructured":"Gong, G., Lam, C. C. Y.: Linear recursive sequences over elliptic curves, Discrete Math. Theor. Comput. Sci. (Lond.), pp. 182\u2013196. Springer, London (2002)","DOI":"10.1007\/978-1-4471-0673-9_13"},{"key":"521_CR11","first-page":"96","volume":"411","author":"D Grant","year":"1990","unstructured":"Grant, D.: Formal groups in genus two. J. Reine Angew. Math. 411, 96\u2013121 (1990)","journal-title":"J. Reine Angew. Math."},{"key":"521_CR12","unstructured":"Hallgren, S.: Linear congruential generators over elliptic curves, Tech. report, Dept. Of Comp. Sci. Cornegie Mellon Univ. (1994)"},{"key":"521_CR13","doi-asserted-by":"crossref","unstructured":"Hartshorne, R.: Algebraic geometry. Springer, New York. Graduate texts in mathematics No. 52 (1977)","DOI":"10.1007\/978-1-4757-3849-0"},{"issue":"1","key":"521_CR14","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s10623-003-6153-0","volume":"35","author":"F Hess","year":"2005","unstructured":"Hess, F., Shparlinski, I.E.: On the linear complexity and multidimensional distribution of congruential generators over elliptic curves. Des. Codes Cryptogr. 35(1), 111\u2013117 (2005)","journal-title":"Des. Codes Cryptogr."},{"key":"521_CR15","doi-asserted-by":"crossref","unstructured":"Hindry, M., Silverman, J.H.: Diophantine Geometry, Graduate Texts in Mathematics, vol. 201. Springer, New York. An introduction (2000)","DOI":"10.1007\/978-1-4612-1210-2"},{"key":"521_CR16","doi-asserted-by":"crossref","unstructured":"Koblitz, N.: Algebraic aspects of cryptography, Algorithms and Computation in Mathematics, vol. 3, Springer, Berlin. With an Appendix by Alfred J. Menezes, Yi-Hong Wu and Robert J. Zuccherato (1998)","DOI":"10.1007\/978-3-662-03642-6_1"},{"key":"521_CR17","doi-asserted-by":"crossref","unstructured":"Kohel, D.R., Shparlinski, I.E.: On exponential sums and group generators for elliptic curves over finite fields, Algorithmic number theory (Leiden, 2000), Lecture Notes in Comput. Sci., vol. 1838, pp. 395\u2013404. Springer, Berlin (2000)","DOI":"10.1007\/10722028_24"},{"issue":"5","key":"521_CR18","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/s00200-004-0154-8","volume":"15","author":"T Lange","year":"2005","unstructured":"Lange, T.: Formulae for arithmetic on genus 2 hyperelliptic curves. Appl. Algebra Engrg. Comm. Comput. 15(5), 295\u2013328 (2005)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"521_CR19","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s00200-004-0161-9","volume":"5","author":"T Lange","year":"2005","unstructured":"Lange, T., Shparlinski, I.: Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves. Appl. Algebra Engrg. Comm. Comput. 5, 329\u2013337 (2005)","journal-title":"Appl. Algebra Engrg. Comm. Comput."},{"key":"521_CR20","doi-asserted-by":"publisher","first-page":"338","DOI":"10.4153\/CJM-2005-015-8","volume":"2","author":"T Lange","year":"2005","unstructured":"Lange, T., Shparlinski, I.E.: Certain exponential sums and random walks on elliptic curves. Canad. J. Math. 2, 338\u2013350 (2005)","journal-title":"Canad. J. Math."},{"key":"521_CR21","volume-title":"Linear Complexity of Sequences and Multisequences, Handbook of Finite Fields","author":"W Meidl","year":"2013","unstructured":"Meidl, W., Winterhof, A.: Linear Complexity of Sequences and Multisequences, Handbook of Finite Fields. CRC Press, Boca Raton (2013)"},{"issue":"1-2","key":"521_CR22","doi-asserted-by":"publisher","first-page":"199","DOI":"10.5486\/PMD.2012.5057","volume":"80","author":"L M\u00e9rai","year":"2012","unstructured":"M\u00e9rai, L.: Construction of pseudorandom binary sequences over elliptic curves using multiplicative characters. Publ. Math. Debrecen 80(1-2), 199\u2013213 (2012)","journal-title":"Publ. Math. Debrecen"},{"key":"521_CR23","first-page":"301","volume":"3-4","author":"L M\u00e9rai","year":"2012","unstructured":"M\u00e9rai, L.: Remarks on pseudorandom binary sequences over elliptic curves. Fund. Inform. 3-4, 301\u2013308 (2012)","journal-title":"Fund. Inform."},{"issue":"2","key":"521_CR24","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/s10623-015-0140-0","volume":"81","author":"L M\u00e9rai","year":"2016","unstructured":"M\u00e9rai, L., Winterhof, A.: On the linear complexity profile of some sequences derived from elliptic curves. Des. Codes Cryptogr. 81(2), 259\u2013267 (2016)","journal-title":"Des. Codes Cryptogr."},{"key":"521_CR25","volume-title":"Modern Birkh\u00e4user Classics","author":"D Mumford","year":"2007","unstructured":"Mumford, D.: Modern Birkh\u00e4user Classics. Birkh\u00e4user Boston, Inc., Boston (2007). Jacobian theta functions and differential equations, With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura, Reprint of the 1984 original"},{"key":"521_CR26","doi-asserted-by":"crossref","unstructured":"Niederreiter, H.: Linear complexity and related complexity measures for sequences, Progress in cryptology\u2014INDOCRYPT, 2003, Lecture Notes in Comput. Sci., vol. 2904, pp. 1\u201317. Springer, Berlin (2003)","DOI":"10.1007\/978-3-540-24582-7_1"},{"issue":"2","key":"521_CR27","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF02567819","volume":"88","author":"J Schmid","year":"1995","unstructured":"Schmid, J.: On the affine Bezout inequality. Manuscripta Math. 88 (2), 225\u2013232 (1995)","journal-title":"Manuscripta Math."},{"key":"521_CR28","doi-asserted-by":"crossref","unstructured":"Shparlinski, I.E.: Pseudorandom number generators from elliptic curves, Recent trends in cryptography, Contemp, Math., vol. 477, pp. 121\u2013141. Amer. Math. Soc., Providence (2009)","DOI":"10.1090\/conm\/477\/09305"},{"key":"521_CR29","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-540-76878-4","volume-title":"Algebraic function felds and codes, 2nd edn., vol. 254","author":"H Stichtenoth","year":"2009","unstructured":"Stichtenoth, H.: Algebraic function felds and codes, 2nd edn., vol. 254. Graduate Texts in Mathematics. Springer, Berlin (2009)"},{"key":"521_CR30","doi-asserted-by":"crossref","unstructured":"Topuzo\u011flu, A., Winterhof, A.: Pseudorandom sequences, Topics in geometry, coding theory and cryptography, Algebr. Appl., vol. 6, p. 135\u2013166. Springer, Dordrecht (2007)","DOI":"10.1007\/1-4020-5334-4_4"},{"key":"521_CR31","doi-asserted-by":"crossref","unstructured":"Winterhof, A.: Linear complexity and related complexity measures, Selected topics in information and coding theory. Ser. Coding Theory Cryptol., vol. 7, pp. 3\u201340. World Sci. Publ., Hackensack (2010)","DOI":"10.1142\/9789812837172_0001"}],"container-title":["Cryptography and Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-021-00521-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12095-021-00521-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12095-021-00521-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,7]],"date-time":"2023-01-07T17:43:30Z","timestamp":1673113410000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12095-021-00521-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,20]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["521"],"URL":"https:\/\/doi.org\/10.1007\/s12095-021-00521-y","relation":{},"ISSN":["1936-2447","1936-2455"],"issn-type":[{"value":"1936-2447","type":"print"},{"value":"1936-2455","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,20]]},"assertion":[{"value":"9 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 July 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}