{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:58:11Z","timestamp":1772283491016,"version":"3.50.1"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,9,1]],"date-time":"2012-09-01T00:00:00Z","timestamp":1346457600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>From power series expansions of functions on curves over finite fields, one can obtain sequences with perfect or almost perfect linear complexity profile. It has been suggested by various authors to use such sequences as key streams for stream ciphers. In this work, we show how long parts of such sequences can be computed efficiently from short ones. Such sequences should therefore be considered to be cryptographically weak. Our attack leads in a natural way to a new measure of the complexity of sequences which we call expansion complexity.<\/jats:p>","DOI":"10.1112\/s146115701200109x","type":"journal-article","created":{"date-parts":[[2012,9,24]],"date-time":"2012-09-24T09:32:49Z","timestamp":1348479169000},"page":"326-340","source":"Crossref","is-referenced-by-count":18,"title":["On the use of expansion series for stream ciphers"],"prefix":"10.1112","volume":"15","author":[{"given":"Claus","family":"Diem","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,9,1]]},"reference":[{"key":"S146115701200109X_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3849-0"},{"key":"S146115701200109X_ref19","doi-asserted-by":"publisher","DOI":"10.3336\/gm.44.1.05"},{"key":"S146115701200109X_ref11","first-page":"191","volume-title":"Advances in cryptology \u2014 Eurocrypt\u201988","author":"Niederreiter","year":"1988"},{"key":"S146115701200109X_ref13","first-page":"523","volume-title":"Advances in cryptology \u2013 Eurocrypt \u201989","author":"Niederreiter","year":"1989"},{"key":"S146115701200109X_ref6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2010-02281-1"},{"key":"S146115701200109X_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107325951"},{"key":"S146115701200109X_ref12","first-page":"37","volume-title":"Advances in cryptology \u2013 Eurocrypt\u201987","author":"Niederreiter","year":"1988"},{"key":"S146115701200109X_ref18","first-page":"800","article-title":"A statistical test suite for random and pseudorandom number generators for cryptographic applications","author":"Rukhin","year":"2010","journal-title":"NIST special publication"},{"key":"S146115701200109X_ref3","volume-title":"A course in computational algebraic number theory","author":"Cohen","year":"1996"},{"key":"S146115701200109X_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82865-2"},{"key":"S146115701200109X_ref9","volume-title":"Sequences and their applications \u2014 proceedings of SETA\u201998","author":"Kohel","year":"1999"},{"key":"S146115701200109X_ref16","first-page":"564","article-title":"Stream ciphers","volume":"104","author":"Piper","year":"1987","journal-title":"Elektrotechnik und Maschinenbau"},{"key":"S146115701200109X_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0853-2"},{"key":"S146115701200109X_ref1","doi-asserted-by":"publisher","DOI":"10.1353\/ajm.2005.0037"},{"key":"S146115701200109X_ref8","article-title":"Computing Riemann\u2013Roch spaces in algebraic function fields and related topics","volume":"11","author":"He\u00df","year":"2001","journal-title":"J. Symbolic Comput."},{"key":"S146115701200109X_ref4","volume-title":"Number theory \u2013 vol. 1: Tools and diophantine equations","author":"Cohen","year":"2007"},{"key":"S146115701200109X_ref5","unstructured":"[5] Diem C. , \u2018On arithmetic and the discrete logarithm problem in class groups of curves\u2019, Habilitation Thesis, 2008."},{"key":"S146115701200109X_ref14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/BF00204450","article-title":"A combinatorial approach to probabilistic results on the linear complexity profile of random sequences","author":"Niederreiter","year":"1990","journal-title":"J. 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