{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:33:51Z","timestamp":1776846831249,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540331087","type":"print"},{"value":"9783540331094","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11693383_23","type":"book-chapter","created":{"date-parts":[[2006,2,25]],"date-time":"2006-02-25T05:55:05Z","timestamp":1140846905000},"page":"332-344","source":"Crossref","is-referenced-by-count":17,"title":["Minimality of the Hamming Weight of the \u03c4-NAF for Koblitz Curves and Improved Combination with Point Halving"],"prefix":"10.1007","author":[{"given":"Roberto Maria","family":"Avanzi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemens","family":"Heuberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Helmut","family":"Prodinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"23_CR1","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/0166-218X(89)90001-2","volume":"25","author":"D.W. Ash","year":"1989","unstructured":"Ash, D.W., Blake, I.F., Vanstone, S.: Low complexity normal bases. Discrete Applied Math.\u00a025, 191\u2013210 (1989)","journal-title":"Discrete Applied Math."},{"key":"23_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1007\/978-3-540-24632-9_3","volume-title":"Public Key Cryptography \u2013 PKC 2004","author":"R.M. Avanzi","year":"2004","unstructured":"Avanzi, R.M., Ciet, M., Sica, F.: Faster Scalar Multiplication on Koblitz Curves combining Point Halving with the Frobenius Endomorphism. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol.\u00a02947, pp. 28\u201340. Springer, Heidelberg (2004)"},{"issue":"8","key":"23_CR3","doi-asserted-by":"publisher","first-page":"1047","DOI":"10.1109\/TC.2004.43","volume":"53","author":"K. Fong","year":"2004","unstructured":"Fong, K., Hankerson, D., Lopez, J., Menezes, A.: Field inversion and point halving revisited. IEEE Trans. on Computers\u00a053(8), 1047\u20131059 (2004)","journal-title":"IEEE Trans. on Computers"},{"key":"23_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-44499-8_1","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2000","author":"D. Hankerson","year":"2000","unstructured":"Hankerson, D., Lopez-Hernandez, J., Menezes, A.: Software Implementation of Elliptic Curve Cryptography over Binary Fields. In: Paar, C., Ko\u00e7, \u00c7.K. (eds.) CHES 2000. LNCS, vol.\u00a01965, pp. 1\u201324. Springer, Heidelberg (2000)"},{"key":"23_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/978-3-540-48000-6_12","volume-title":"Advances in Cryptology - ASIACRYPT\u201999","author":"E.W. Knudsen","year":"1999","unstructured":"Knudsen, E.W.: Elliptic Scalar Multiplication Using Point Halving. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol.\u00a01716, pp. 135\u2013149. Springer, Heidelberg (1999)"},{"key":"23_CR6","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. Mathematics of computation\u00a048, 203\u2013209 (1987)","journal-title":"Mathematics of computation"},{"key":"23_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/3-540-46766-1_22","volume-title":"Advances in Cryptology - CRYPTO \u201991","author":"N. Koblitz","year":"1992","unstructured":"Koblitz, N.: CM-curves with good cryptographic properties. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol.\u00a0576, pp. 279\u2013287. Springer, Heidelberg (1992)"},{"key":"23_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume-title":"Advances in Cryptology","author":"V.S. Miller","year":"1986","unstructured":"Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol.\u00a0218, pp. 417\u2013426. Springer, Heidelberg (1986)"},{"key":"23_CR9","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1016\/S0065-2458(08)60610-5","volume":"1","author":"G.W. Reitwiesner","year":"1960","unstructured":"Reitwiesner, G.W.: Binary arithmetic. Advances in Computers\u00a01, 231\u2013308 (1960)","journal-title":"Advances in Computers"},{"key":"#cr-split#-23_CR10.1","unstructured":"Schroeppel, R.: Point halving wins big. In: Talks at (i) Midwest Arithmetical Geometry in Cryptography Workshop, November 17-19 (2000);"},{"key":"#cr-split#-23_CR10.2","unstructured":"University of Illinois at Urbana-Champaign; and (ii) ECC 2001Workshop, University of Waterloo, Ontario, Canada, October 29-31 (2001)"},{"key":"23_CR11","unstructured":"Schroeppel, R.: Elliptic curve point ambiguity resolution apparatus and method. International Application Number PCT\/US00\/31014, filed 9 (November 2000)"},{"key":"23_CR12","volume-title":"An Introduction to the Analysis of Algorithms","author":"R. Sedgewick","year":"1996","unstructured":"Sedgewick, R., Flajolet, P.: An Introduction to the Analysis of Algorithms. Addison-Wesley, Reading (1996)"},{"key":"23_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/BFb0052248","volume-title":"Advances in Cryptology - CRYPTO \u201997","author":"J.A. Solinas","year":"1997","unstructured":"Solinas, J.A.: An improved algorithm for arithmetic on a family of elliptic curves. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol.\u00a01294, pp. 357\u2013371. Springer, Heidelberg (1997)"},{"issue":"2\/3","key":"23_CR14","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1023\/A:1008306223194","volume":"19","author":"J.A. Solinas","year":"2000","unstructured":"Solinas, J.A.: Efficient Arithmetic on Koblitz Curves. Designs, Codes and Cryptography\u00a019(2\/3), 125\u2013179 (2000)","journal-title":"Designs, Codes and Cryptography"},{"key":"23_CR15","unstructured":"IEEE Std 1363-2000. IEEE Standard Specifications for Public-Key Cryptography. IEEE Computer Society (August 29, 2000)"},{"key":"23_CR16","unstructured":"National Institute of Standards and Technology. Digital Signature Standard. FIPS Publication 186-2 (February 2000)"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11693383_23.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,27]],"date-time":"2021-04-27T06:50:57Z","timestamp":1619506257000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11693383_23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540331087","9783540331094"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/11693383_23","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}