{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T05:57:53Z","timestamp":1648533473226},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2014,7,14]],"date-time":"2014-07-14T00:00:00Z","timestamp":1405296000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2014,11]]},"abstract":"<jats:p>We consider redundant binary joint digital expansions of integer vectors. The redundancy is used to minimize the Hamming weight,<jats:italic>i.e.<\/jats:italic>, the number of non-zero digit vectors. This leads to efficient linear combination algorithms in abelian groups, which are used in elliptic curve cryptography, for instance.<\/jats:p><jats:p>If the digit set is a set of contiguous integers containing zero, a special syntactical condition is known to minimize the weight. We analyse the optimal weight of all non-negative integer vectors with maximum entry less than<jats:italic>N<\/jats:italic>. The expectation and the variance are given with a main term and a periodic fluctuation in the second-order term. Finally, we prove asymptotic normality.<\/jats:p>","DOI":"10.1017\/s0963548314000352","type":"journal-article","created":{"date-parts":[[2014,7,14]],"date-time":"2014-07-14T10:33:21Z","timestamp":1405334001000},"page":"1087-1113","source":"Crossref","is-referenced-by-count":1,"title":["Analysis of the Binary Asymmetric Joint Sparse Form"],"prefix":"10.1017","volume":"23","author":[{"given":"CLEMENS","family":"HEUBERGER","sequence":"first","affiliation":[]},{"given":"SARA","family":"KROPF","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,7,14]]},"reference":[{"key":"S0963548314000352_ref2","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610701002630"},{"key":"S0963548314000352_ref8","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-05-01769-2"},{"key":"S0963548314000352_ref6","doi-asserted-by":"crossref","unstructured":"Heuberger C. and Muir J. A. (2006) Minimal weight and colexicographically minimal integer representations: Online resources. http:\/\/www.math.tugraz.at\/~cheub\/publications\/colexi\/.","DOI":"10.1515\/jmc.2007.015"},{"key":"S0963548314000352_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.02.012"},{"key":"S0963548314000352_ref1","first-page":"130","volume-title":"Selected Areas in Cryptography","author":"Avanzi","year":"2005"},{"key":"S0963548314000352_ref4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009831204394"},{"key":"S0963548314000352_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(92)00065-Y"},{"key":"S0963548314000352_ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-60408-9_10"},{"key":"S0963548314000352_ref11","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1985-15349-2"},{"key":"S0963548314000352_ref7","doi-asserted-by":"publisher","DOI":"10.1515\/jmc.2007.015"},{"key":"S0963548314000352_ref9","first-page":"806","article-title":"Addition chains of vectors (problem 5125).","volume":"71","author":"Straus","year":"1964","journal-title":"Amer. Math. Monthly"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548314000352","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,12]],"date-time":"2019-08-12T19:30:48Z","timestamp":1565638248000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548314000352\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,14]]},"references-count":11,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2014,11]]}},"alternative-id":["S0963548314000352"],"URL":"https:\/\/doi.org\/10.1017\/s0963548314000352","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7,14]]}}}