{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:00:06Z","timestamp":1776844806358,"version":"3.51.2"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540338512","type":"print"},{"value":"9783540338529","type":"electronic"}],"license":[{"start":{"date-parts":[[2006,1,1]],"date-time":"2006-01-01T00:00:00Z","timestamp":1136073600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/11745853_13","type":"book-chapter","created":{"date-parts":[[2006,4,13]],"date-time":"2006-04-13T05:18:58Z","timestamp":1144905538000},"page":"191-206","source":"Crossref","is-referenced-by-count":32,"title":["Efficient Scalar Multiplication by Isogeny Decompositions"],"prefix":"10.1007","author":[{"given":"Christophe","family":"Doche","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Icart","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David R.","family":"Kohel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"13_CR1","volume-title":"Handbook of Elliptic and Hyperelliptic Curve Cryptography","author":"R.M. Avanzi","year":"2005","unstructured":"[ACD+05] Avanzi, R.M., Cohen, H., Doche, C., Frey, G., Lange, T., Nguyen, K., Vercauteren, F.: Handbook of Elliptic and Hyperelliptic Curve Cryptography. CRC Press, Inc., Boca Raton (2005)"},{"key":"13_CR2","unstructured":"[Ber01] Bernstein, D.J.: A software implementation of NIST P-224, slides of a talk given at ECC 2001 (2001)"},{"key":"13_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/3-540-44828-4_6","volume-title":"Applied Algebra, Algebraic Algorithms and Error-Correcting Codes","author":"\u00c9. Brier","year":"2003","unstructured":"Brier, \u00c9., Joye, M.: Fast point multiplication on elliptic curves through isogenies. In: Fossorier, M.P.C., H\u00f8holdt, T., Poli, A. (eds.) AAECC 2003. LNCS, vol.\u00a02643, pp. 43\u201350. Springer, Heidelberg (2003)"},{"key":"13_CR4","doi-asserted-by":"crossref","unstructured":"[CJLM05] Ciet, M., Joye, M., Lauter, K., Montgomery, P.L.: Trading inversions for multiplications in elliptic curve cryptography. Des. Codes Cryptogr. (to appear, 2005); Also available from Cryptology ePrint Archive","DOI":"10.1007\/s10623-005-3299-y"},{"key":"13_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1007\/3-540-39200-9_24","volume-title":"Advances in Cryptology \u2013 EUROCRPYT 2003","author":"M. Ciet","year":"2003","unstructured":"[CLSQ03] Ciet, M., Lange, T., Sica, F., Quisquater, J.-J.: Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol.\u00a02656, pp. 388\u2013400. Springer, Heidelberg (2003)"},{"key":"13_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"282","DOI":"10.1007\/BFb0028484","volume-title":"Information and Communications Security","author":"H. Cohen","year":"1997","unstructured":"[CMO97] Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation. In: Han, Y., Quing, S. (eds.) ICICS 1997. LNCS, vol.\u00a01334, pp. 282\u2013290. Springer, Heidelberg (1997)"},{"key":"13_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/3-540-49649-1_6","volume-title":"Advances in Cryptology - ASIACRYPT 1998","author":"H. Cohen","year":"1998","unstructured":"[CMO98] Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 51\u201365. Springer, Heidelberg (1998)"},{"key":"13_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/11554868_12","volume-title":"Progress in Cryptology \u2013 Mycrypt 2005","author":"M. Ciet","year":"2005","unstructured":"[CS05] Ciet, M., Sica, F.: An Analysis of Double Base Number Systems and a sublinear scalar multiplication algorithm. In: Dawson, E., Vaudenay, S. (eds.) Mycrypt 2005. LNCS, vol.\u00a03715, pp. 171\u2013182. Springer, Heidelberg (2005)"},{"key":"13_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/11593447_4","volume-title":"Advances in Cryptology - ASIACRYPT 2005","author":"V.S. Dimitrov","year":"2005","unstructured":"[DIM05] Dimitrov, V.S., Imbert, L., Mishra, P.K.: Efficient and secure elliptic curve point multiplication using double-base chains. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol.\u00a03788, pp. 59\u201378. Springer, Heidelberg (2005)"},{"issue":"10","key":"13_CR10","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1109\/12.805158","volume":"48","author":"V.S. Dimitrov","year":"1999","unstructured":"[DJM99] Dimitrov, V.S., Jullien, G.A., Miller, W.C.: Theory and applications of the double-base number system. IEEE Trans. on Computers\u00a048(10), 1098\u20131106 (1999)","journal-title":"IEEE Trans. on Computers"},{"key":"13_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/3-540-44647-8_11","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"R.P. Gallant","year":"2001","unstructured":"[GLV01] Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 190\u2013200. Springer, Heidelberg (2001)"},{"key":"13_CR12","volume-title":"Guide to elliptic curve cryptography","author":"D. Hankerson","year":"2003","unstructured":"[HMV03] Hankerson, D., Menezes, A.J., Vanstone, S.A.: Guide to elliptic curve cryptography. Springer, Heidelberg (2003)"},{"key":"13_CR13","doi-asserted-by":"crossref","unstructured":"[HT05] Han, D.-G., Takagi, T.: Some analysis of radix-r representations (preprint, 2005), \n                    \n                      http:\/\/eprint.iacr.org\/2005\/402\/","DOI":"10.1016\/j.laa.2004.12.015"},{"key":"13_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/11593447_2","volume-title":"Advances in Cryptology - ASIACRYPT 2005","author":"D. Jao","year":"2005","unstructured":"[JMV05] Jao, D., Miller, S.D., Venkatesan, R.: Do all elliptic curves of the same order have the same difficulty of discrete log? In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol.\u00a03788, pp. 21\u201340. Springer, Heidelberg (2005)"},{"key":"13_CR15","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 1991","author":"N. Koblitz","year":"1992","unstructured":"[Kob92] Koblitz, N.: CM-curves with good cryptographic properties. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol.\u00a0576, pp. 279\u2013287. Springer, Heidelberg (1992)"},{"issue":"2","key":"13_CR16","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.ffa.2004.07.001","volume":"11","author":"T. Lange","year":"2005","unstructured":"[Lan05] Lange, T.: Koblitz curve cryptosystems. Finite Fields Appl.\u00a011(2), 220\u2013229 (2005)","journal-title":"Finite Fields Appl."},{"key":"13_CR17","doi-asserted-by":"crossref","unstructured":"[LD98] L\u00f3pez, J., Dahab, R.: Improved algorithms for elliptic curve arithmetic in GF(2n), Tech. Report IC-98-39, Relat\u00f3rio T\u00e9cnico (October 1998)","DOI":"10.1007\/3-540-48892-8_16"},{"key":"13_CR18","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1051\/ita\/1990240605311","volume":"24","author":"F. Morain","year":"1990","unstructured":"[MO90] Morain, F., Olivos, J.: Speeding up the computations on an elliptic curve using addition-subtraction chains. Inform. Theory Appl.\u00a024, 531\u2013543 (1990)","journal-title":"Inform. Theory Appl."},{"key":"13_CR19","series-title":"Lecture Notes in Computer Science","first-page":"2","volume-title":"Advances in Cryptology - AUSCRYPT 1990","author":"A.J. Menezes","year":"1990","unstructured":"[MV90] Menezes, A.J., Vanstone, S.A.: The implementation of elliptic curve cryptosystems. In: Seberry, J., Pieprzyk, J.P. (eds.) AUSCRYPT 1990. LNCS, vol.\u00a0453, pp. 2\u201313. Springer, Heidelberg (1990)"},{"key":"13_CR20","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1023\/A:1008306223194","volume":"19","author":"J.A. Solinas","year":"2000","unstructured":"[Sol00] Solinas, J.A.: Efficient arithmetic on Koblitz curves. Des. Codes Cryptogr.\u00a019, 195\u2013249 (2000)","journal-title":"Des. Codes Cryptogr."},{"key":"13_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1007\/978-3-540-30144-8_9","volume-title":"Information Security","author":"T. Takagi","year":"2004","unstructured":"[TYW04] Takagi, T., Yen, S.-M., Wu, B.-C.: Radix-r non-adjacent form. In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol.\u00a03225, pp. 99\u2013110. Springer, Heidelberg (2004)"}],"container-title":["Lecture Notes in Computer Science","Public Key Cryptography - PKC 2006"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/11745853_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T13:26:12Z","timestamp":1558272372000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/11745853_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540338512","9783540338529"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/11745853_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006]]}}}