{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T23:13:23Z","timestamp":1751411603765},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642420009"},{"type":"electronic","value":"9783642420016"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-42001-6_5","type":"book-chapter","created":{"date-parts":[[2013,11,21]],"date-time":"2013-11-21T04:25:02Z","timestamp":1385007902000},"page":"50-72","source":"Crossref","is-referenced-by-count":2,"title":["Shorter Compact Representations in Real Quadratic Fields"],"prefix":"10.1007","author":[{"given":"Alan K.","family":"Silvester","sequence":"first","affiliation":[]},{"given":"Michael J.","family":"Jacobson","sequence":"additional","affiliation":[]},{"given":"Hugh C.","family":"Williams","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"5_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1007\/11935230_9","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2006","author":"R. Avanzi","year":"2006","unstructured":"Avanzi, R., Dimitrov, V., Doche, C., Sica, F.: Extending scalar multiplication using double bases. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol.\u00a04284, pp. 130\u2013144. Springer, Heidelberg (2006)"},{"key":"5_CR2","first-page":"159","volume-title":"Short representation of quadratic integers, Mathematics and its Applications","author":"J. Buchmann","year":"1995","unstructured":"Buchmann, J., Thiel, C., Williams, H.C.: Short representation of quadratic integers, Mathematics and its Applications, vol.\u00a0325, pp. 159\u2013185. Kluwer Academic Publishers, Amsterdam (1995)"},{"key":"5_CR3","unstructured":"Buchmann, J., Vollmer, U.: Binary Quadratic Forms, Algorithms and Computation in Mathematics, vol.\u00a020. Springer (2007)"},{"key":"5_CR4","volume-title":"A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics","author":"H. Cohen","year":"2000","unstructured":"Cohen, H.: A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics, 4th edn., vol.\u00a0138. Springer, New York (2000)","edition":"4"},{"key":"5_CR5","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. Dimitrov","year":"2005","unstructured":"Dimitrov, V., 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)"},{"key":"5_CR6","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/S0020-0190(98)00044-1","volume":"66","author":"V.S. Dimitrov","year":"1998","unstructured":"Dimitrov, V.S., Jullien, G.A., Miller, W.C.: An algorithm for modular exponentiation. Information Processing Letters\u00a066, 155\u2013159 (1998)","journal-title":"Information Processing Letters"},{"key":"5_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1007\/978-3-642-33481-8_12","volume-title":"Progress in Cryptology \u2013 LATINCRYPT 2012","author":"V. Dixon","year":"2012","unstructured":"Dixon, V., Jacobson Jr., M.J., Scheidler, R.: Improved exponentiation and key agreement in the infrastructure of a real quadratic field. In: Hevia, A., Neven, G. (eds.) LatinCrypt 2012. LNCS, vol.\u00a07533, pp. 214\u2013233. Springer, Heidelberg (2012)"},{"key":"5_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1007\/11941378_24","volume-title":"Progress in Cryptology - INDOCRYPT 2006","author":"C. Doche","year":"2006","unstructured":"Doche, C., Imbert, L.: Extended double-base number system with applications to elliptic curve cryptography. In: Barua, R., Lange, T. (eds.) INDOCRYPT 2006. LNCS, vol.\u00a04329, pp. 335\u2013348. Springer, Heidelberg (2006)"},{"key":"5_CR9","unstructured":"Fung, G.W., Williams, H.C.: Compact representation of the fundamental unit in a complex cubic field (1991) (unpublished manuscript)"},{"key":"5_CR10","unstructured":"de Haan, R.: A fast, rigorous technique for verifying the regulator of a real quadratic field. Master\u2019s thesis, University of Amsterdam (2004)"},{"key":"5_CR11","volume-title":"Guide to Elliptic Curve Cryptography","author":"D. Hankerson","year":"2004","unstructured":"Hankerson, D., Menezes, A., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, New York (2004)"},{"key":"5_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1007\/3-540-44983-3_21","volume-title":"Selected Areas in Cryptography","author":"D. H\u00fchnlein","year":"2001","unstructured":"H\u00fchnlein, D., Paulus, S.: On the implementation of cryptosystems based on real quadratic number fields (extended abstract). In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol.\u00a02012, pp. 288\u2013302. Springer, Heidelberg (2001)"},{"issue":"2","key":"5_CR13","doi-asserted-by":"publisher","first-page":"237","DOI":"10.3934\/amc.2010.4.237","volume":"4","author":"L. Imbert","year":"2010","unstructured":"Imbert, L., Jacobson Jr., M.J., Schmidt, A.: Fast ideal cubing in imaginary quadratic number and function fields. Advances in Mathematics of Communications\u00a04(2), 237\u2013260 (2010)","journal-title":"Advances in Mathematics of Communications"},{"key":"#cr-split#-5_CR14.1","unstructured":"Jacobson Jr., M.J., Scheidler, R., Williams, H.C.: The efficiency and security of a real quadratic field based key exchange protocol. In: Alster, K., Urbanowicz, J., Williams, H.C. (eds.) Public-Key Cryptography and Computational Number Theory, September 11-15 (2000); Walter de Gruyter GmbH & Co., Warsaw (2001)"},{"key":"#cr-split#-5_CR14.2","unstructured":"Walter de Gruyter GmbH & Co., Warsaw (2001)"},{"key":"5_CR15","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1007\/s00145-005-0357-6","volume":"19","author":"M.J. Jacobson Jr.","year":"2006","unstructured":"Jacobson Jr., M.J., Scheidler, R., Williams, H.C.: An improved real quadratic field based key exchange procedure. J. Cryptology\u00a019, 211\u2013239 (2006)","journal-title":"J. Cryptology"},{"key":"5_CR16","doi-asserted-by":"crossref","unstructured":"Jacobson Jr., M.J., Williams, H.C.: Solving the Pell Equation. CMS Books in Mathematics. Springer (2009)","DOI":"10.1007\/978-0-387-84923-2"},{"key":"5_CR17","doi-asserted-by":"crossref","unstructured":"Lagarias, J.C.: Succinct certificates for the solvability of binary quadratic diophantine equations (extended abstract). In: Proc. 20th IEEE Symp. on Foundations of Computer Science, pp. 47\u201354 (1979)","DOI":"10.1109\/SFCS.1979.40"},{"key":"5_CR18","unstructured":"Lagarias, J.C.: Succinct certificates for the solvability of binary quadratic diophantine equations. Tech. Rep. Technical Memorandum 81-11216-54, Bell Labs, 28 (1981)"},{"key":"5_CR19","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":"5_CR20","unstructured":"Shanks, D.: The infrastructure of a real quadratic field and its applications. In: Proc. 1972 Number Theory Conference, University of Colorado, Boulder, pp. 217\u2013224 (1972)"},{"key":"5_CR21","unstructured":"Silvester, A.K.: Improving regulator verification and compact representations in real quadratic fields. Ph.D. thesis, University of Calgary, Calgary, Alberta (2012)"}],"container-title":["Lecture Notes in Computer Science","\u2018"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-42001-6_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T08:35:34Z","timestamp":1597048534000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-42001-6_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642420009","9783642420016"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-42001-6_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2013]]}}}