{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T03:51:38Z","timestamp":1648785098886},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2010,10,7]],"date-time":"2010-10-07T00:00:00Z","timestamp":1286409600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2011,10]]},"DOI":"10.1007\/s10623-010-9439-z","type":"journal-article","created":{"date-parts":[[2010,10,6]],"date-time":"2010-10-06T12:52:48Z","timestamp":1286369568000},"page":"71-89","source":"Crossref","is-referenced-by-count":0,"title":["On the distribution of the coefficients of normal forms for Frobenius expansions"],"prefix":"10.1007","volume":"61","author":[{"given":"Roberto","family":"Avanzi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"suffix":"Jr","given":"Waldyr Dias","family":"Benits","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steven D.","family":"Galbraith","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"McKee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,10,7]]},"reference":[{"key":"9439_CR1","volume-title":"Handbook of elliptic and hyperelliptic cryptography","author":"R. Avanzi","year":"2006","unstructured":"Avanzi R., Cohen H., Doche C., Frey G., Lange T., Nguyen K., Vercauteren F.: Handbook of elliptic and hyperelliptic cryptography. Chapman and Hall\/CRC, Boca Raton (2006)"},{"key":"9439_CR2","doi-asserted-by":"crossref","unstructured":"Avanzi R., Heuberger C., Prodinger H.: Minimality of the Hamming weight of the \u03c4-NAF for Koblitz curves and improved combination with point halving. In: Preneel B., Tavares S.E. (eds.) SAC 2005, LNCS, vol. 3897, pp. 332\u2013344. Springer, Heidelberg (2006)","DOI":"10.1007\/11693383_23"},{"key":"9439_CR3","doi-asserted-by":"crossref","unstructured":"Avanzi R., Heuberger C., Prodinger H.: On Redundant \u03c4-adic Expansions and Non-Adjacent Digit Sets. In: Biham E., Youssef A.M. (eds.) SAC 2006, LNCS, vol. 4356, pp. 285\u2013301. Springer, Heidelberg (2007)","DOI":"10.1007\/978-3-540-74462-7_20"},{"key":"9439_CR4","unstructured":"Benits Jr. W.D.: Applications of Frobenius expansions in elliptic curve cryptography, PhD thesis, Royal Holloway University of London, London (2008)."},{"key":"9439_CR5","unstructured":"Brumley B.B., J\u00e4rvinen K.: Koblitz curves and integer equivalents of Frobenius expansions. In: Adams C., Miri A., Wiener M. (eds.), SAC 2007, LNCS, vol. 4876, pp. 126\u2013137, Springer, Heidelberg (2007)."},{"issue":"3","key":"9439_CR6","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/s10623-007-9101-6","volume":"45","author":"N. Ebeid","year":"2007","unstructured":"Ebeid N., Hasan M.: On \u03c4-adic representations of integers. Des. Codes Cryptogr. 45(3), 271\u2013296 (2007)","journal-title":"Des. Codes Cryptogr."},{"key":"9439_CR7","unstructured":"Galbraith S.D., Ruprai R.S.: An improvement to the Gaudry\u2013Schost algorithm for multidimensional discrete logarithm problems. In: Parker M. (ed.) Cryptography and Coding, LNCS, vol. 5921, pp. 368\u2013382, Springer, Heidelberg (2009)."},{"key":"9439_CR8","unstructured":"Gaudry P., Schost E.: A low-memory parallel version of Matsuo, Chao and Tsujii\u2019s algorithm. In: Buell D.A. (ed.) ANTS VI, LNCS, vol. 3076, pp. 208\u2013222, Springer, Heidelberg (2004)."},{"key":"9439_CR9","unstructured":"G\u00fcnther C., Lange T., Stein A.: Speeding up the arithmetic on Koblitz curves of genus two. In: Stinson D.R., Tavares S.E. (eds.), SAC 2000, LNCS, vol. 2012, pp. 106\u2013117, Springer, Heidelberg (2000)."},{"issue":"2","key":"9439_CR10","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s11786-009-0014-9","volume":"3","author":"C. Heuberger","year":"2010","unstructured":"Heuberger C.: Redundant \u03c4-adic expansions II: non-optimality and chaotic behaviour. Math. Comput. Sci. 3(2), 141\u2013157 (2010)","journal-title":"Math. Comput. Sci."},{"issue":"2","key":"9439_CR11","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/j.ffa.2004.07.001","volume":"11","author":"T. Lange","year":"2005","unstructured":"Lange T.: Koblitz curve cryptosystems. Finite Field. Appl. 11(2), 200\u2013229 (2005)","journal-title":"Finite Field. Appl."},{"issue":"5","key":"9439_CR12","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s00200-004-0161-9","volume":"15","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 Eng. Commun. Comput. 15(5), 329\u2013337 (2005)","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"1","key":"9439_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1515\/JMC.2007.001","volume":"1","author":"T. Lange","year":"2007","unstructured":"Lange T., Shparlinski I.: Distribution of some sequences of points on elliptic curves. J. Math. Cryptol. 1(1), 1\u201311 (2007)","journal-title":"J. Math. Cryptol."},{"issue":"177","key":"9439_CR14","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1090\/S0025-5718-1987-0866109-5","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"Koblitz N.: Elliptic curve cryptosystems. Math. Comp. 48(177), 203\u2013209 (1987)","journal-title":"Math. Comp."},{"key":"9439_CR15","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF02252872","volume":"1","author":"N. Koblitz","year":"1989","unstructured":"Koblitz N.: Hyperelliptic cryptosystems. J. Cryptol. 1, 139\u2013150 (1989)","journal-title":"J. Cryptol."},{"key":"9439_CR16","unstructured":"Koblitz N.: CM curves with good cryptographic properties. In: Feigenbaum J. (ed.) CRYPTO \u201991, LNCS, vol. 576, pp. 279\u2013287, Springer, Heidelberg (1992)."},{"key":"9439_CR17","unstructured":"Meier W., Staffelbach O.: Efficient multiplication on certain nonsupersingular elliptic curves. In: Brickell E.F. (ed.) CRYPTO \u201992, LNCS, vol. 740, pp. 333\u2013344, Springer, Heidelberg (1993)."},{"issue":"4","key":"9439_CR18","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s001459900045","volume":"11","author":"V. M\u00fcller","year":"1998","unstructured":"M\u00fcller V.: Fast Multiplication on Elliptic Curves over Small Fields of Characteristic Two. J. Cryptol. 11(4), 219\u2013234 (1998)","journal-title":"J. Cryptol."},{"key":"9439_CR19","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The arithmetic of elliptic curves. Graduate texts in mathematics, vol. 106","author":"J.H. Silverman","year":"1986","unstructured":"Silverman J.H.: The arithmetic of elliptic curves. Graduate texts in mathematics, vol. 106. Springer-Verlag, New York (1986)"},{"issue":"2","key":"9439_CR20","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/PL00003820","volume":"12","author":"N.P. Smart","year":"1999","unstructured":"Smart N.P.: Elliptic curve cryptosystems over small fields of odd characteristic. J. Cryptol. 12(2), 141\u2013151 (1999)","journal-title":"J. Cryptol."},{"key":"9439_CR21","unstructured":"Solinas J.: An improved algorithm for arithmetic on a family of elliptic curves. In: Kaliski Jr. B.S. (ed.), CRYPTO \u201997, LNCS, vol. 1294, pp. 357\u2013371, Springer, Heidelberg (1997)."},{"issue":"2\u20133","key":"9439_CR22","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1023\/A:1008306223194","volume":"19","author":"J. Solinas","year":"2000","unstructured":"Solinas J.: Efficient arithmetic on Koblitz curves. Des. Codes Cryptogr. 19(2\u20133), 195\u2013249 (2000)","journal-title":"Des. Codes Cryptogr."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-010-9439-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-010-9439-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-010-9439-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-010-9439-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T17:00:41Z","timestamp":1581958841000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-010-9439-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,10,7]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["9439"],"URL":"https:\/\/doi.org\/10.1007\/s10623-010-9439-z","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,10,7]]}}}