{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,20]],"date-time":"2026-01-20T16:24:52Z","timestamp":1768926292238,"version":"3.49.0"},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540681595","type":"print"},{"value":"9783540681649","type":"electronic"}],"license":[{"start":{"date-parts":[[2008,1,1]],"date-time":"2008-01-01T00:00:00Z","timestamp":1199145600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"DOI":"10.1007\/978-3-540-68164-9_13","type":"book-chapter","created":{"date-parts":[[2008,5,30]],"date-time":"2008-05-30T10:48:34Z","timestamp":1212144514000},"page":"191-208","source":"Crossref","is-referenced-by-count":5,"title":["An Adaptation of the NICE Cryptosystem to Real Quadratic Orders"],"prefix":"10.1007","author":[{"suffix":"Jr.","given":"Michael J.","family":"Jacobson","sequence":"first","affiliation":[]},{"given":"Renate","family":"Scheidler","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"Weimer","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"13_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/3-540-45861-1_6","volume-title":"Information Security and Cryptology - ICISC 2001","author":"J. Buchmann","year":"2002","unstructured":"Buchmann, J., Sakurai, K., Takagi, T.: An IND-CCA2 public-key cryptosystem with fast decryption. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol.\u00a02288, pp. 51\u201371. Springer, Heidelberg (2002)"},{"key":"13_CR2","series-title":"Math. Appl.","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/978-94-017-1108-1_12","volume-title":"Computational Algebra and Number Theory (Sydney, 1992)","author":"J. Buchmann","year":"1995","unstructured":"Buchmann, J., Thiel, C., Williams, H.: Short representation of quadratic integers. In: Computational Algebra and Number Theory (Sydney, 1992). Math. Appl., vol.\u00a0325, pp. 159\u2013185. Kluwer, Dordrecht (1995)"},{"key":"13_CR3","doi-asserted-by":"publisher","first-page":"247","DOI":"10.4064\/aa117-3-3","volume":"117","author":"K.H.F. Cheng","year":"2005","unstructured":"Cheng, K.H.F., Williams, H.C.: Some results concerning certain periodic continued fractions. Acta Arith.\u00a0117, 247\u2013264 (2005)","journal-title":"Acta Arith."},{"key":"13_CR4","volume-title":"Primes of the Form x 2\u2009+\u2009ny 2","author":"D.A. Cox","year":"1989","unstructured":"Cox, D.A.: Primes of the Form x\n                           2\u2009+\u2009ny\n                           2. John Wiley & Sons, Inc, New York (1989)"},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02403921","volume":"44","author":"G.H. Hardy","year":"1923","unstructured":"Hardy, G.H., Littlewood, J.E.: Partitio numerorum III: On the expression of a number as a sum of primes. Acta Math.\u00a044, 1\u201370 (1923)","journal-title":"Acta Math."},{"key":"13_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1007\/BFb0054134","volume-title":"Advances in Cryptology - EUROCRYPT \u201998","author":"D. H\u00fchnlein","year":"1998","unstructured":"H\u00fchnlein, D., Jacobson Jr., M.J., Paulus, S., Takagi, T.: A cryptosystem based on non-maximal imaginary quadratic orders with fast decryption. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol.\u00a01403, pp. 294\u2013307. Springer, Heidelberg (1998)"},{"key":"13_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1007\/3-540-45539-6_26","volume-title":"Advances in Cryptology - EUROCRYPT 2000","author":"E. Jaulmes","year":"2000","unstructured":"Jaulmes, E., Joux, A.: A NICE Cryptanalysis. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol.\u00a01807, pp. 382\u2013391. Springer, Heidelberg (2000)"},{"key":"13_CR8","doi-asserted-by":"crossref","first-page":"197","DOI":"10.3934\/amc.2007.1.197","volume":"1","author":"M.J. Jacobson Jr.","year":"2007","unstructured":"Jacobson Jr., M.J., Scheidler, R., Stein, A.: Cryptographic protocols on real hyperelliptic curves. Adv. Math. Commun.\u00a01, 197\u2013221 (2007)","journal-title":"Adv. Math. Commun."},{"key":"13_CR9","first-page":"83","volume":"1","author":"M.J. Jacobson Jr.","year":"2006","unstructured":"Jacobson Jr., M.J., Sawilla, R.E., Williams, H.C.: Efficient Ideal Reduction in Quadratic Fields. Internat. J. Math. Comput. Sci.\u00a01, 83\u2013116 (2006)","journal-title":"Internat. J. Math. Comput. Sci."},{"key":"13_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/3-540-45682-1_5","volume-title":"Advances in Cryptology - ASIACRYPT 2001","author":"A.K. Lenstra","year":"2001","unstructured":"Lenstra, A.K.: Unbelievable Security. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol.\u00a02248, pp. 67\u201386. Springer, Heidelberg (2001)"},{"key":"13_CR11","first-page":"259","volume":"41","author":"R.A. Mollin","year":"1992","unstructured":"Mollin, R.A., Williams, H.C.: Computation of the class number of a real quadratic field. Util. Math.\u00a041, 259\u2013308 (1992)","journal-title":"Util. Math."},{"key":"13_CR12","unstructured":"National Institute of Standards and Technology (NIST), Recommendation for key management - part 1: General (revised). NIST Special Publication 800-57 (March 2007), \n                    \n                      http:\/\/csrc.nist.gov\/groups\/ST\/toolkit\/documents\/SP800-57Part1_3-8-07.pdf"},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/s001459910010","volume":"13","author":"S. Paulus","year":"2000","unstructured":"Paulus, S., Takagi, T.: A new public key cryptosystem over quadratic orders with quadratic decryption time. J. Cryptology\u00a013, 263\u2013272 (2000)","journal-title":"J. Cryptology"},{"key":"13_CR14","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1090\/S0025-5718-00-01234-5","volume":"70","author":"A.J. Poorten van der","year":"2001","unstructured":"van der Poorten, A.J., te Riele, H.J.J., Williams, H.C.: Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000. Math. Comp.\u00a070, 1311\u20131328 (2001)","journal-title":"Math. Comp."},{"key":"13_CR15","doi-asserted-by":"crossref","first-page":"393","DOI":"10.4064\/aa-6-4-393-413","volume":"6","author":"A. Schinzel","year":"1961","unstructured":"Schinzel, A.: On some problems of the arithmetical theory of continued fractions. Acta Arith.\u00a06, 393\u2013413 (1961)","journal-title":"Acta Arith."},{"key":"13_CR16","unstructured":"Shoup, V.: NTL: A Library for Doing Number Theory. Software (2001), Available at \n                    \n                      http:\/\/www.shoup.net\/ntl"},{"key":"13_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1007\/BFb0055738","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"T. Takagi","year":"1998","unstructured":"Takagi, T.: Fast RSA-type cryptosystem modulo p\n                           \n                    k\n                  \n                           q. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 318\u2013326. Springer, Heidelberg (1998)"},{"key":"13_CR18","unstructured":"Takagi, T.: A New Public-Key Cryptosystems with Fast Decryption. PhD Thesis, Technische Universit\u00e4t Darmstadt (Germany) (2001)"},{"key":"13_CR19","unstructured":"Weimer, D.: An Adaptation of the NICE Cryptosystem to Real Quadratic Orders. Master\u2019s Thesis, Technische Universit\u00e4t Darmstadt (Germany) (2004), \n                    \n                      http:\/\/www.cdc.informatik.tu-darmstadt.de\/reports\/reports\/DanielWeimer.diplom.pdf"},{"key":"13_CR20","volume-title":"\u00c9douard Lucas and Primality Testing","author":"H.C. Williams","year":"1998","unstructured":"Williams, H.C.: \u00c9douard Lucas and Primality Testing. John Wiley & Sons, New York (1998)"},{"key":"13_CR21","doi-asserted-by":"publisher","first-page":"405","DOI":"10.2307\/2007899","volume":"48","author":"H.C. Williams","year":"1987","unstructured":"Williams, H.C., Wunderlich, M.C.: On the parallel generation of the residues for the continued fraction factoring algorithm. Math. Comp.\u00a048, 405\u2013423 (1987)","journal-title":"Math. Comp."}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 AFRICACRYPT 2008"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-68164-9_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T10:00:33Z","timestamp":1580378433000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-68164-9_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"ISBN":["9783540681595","9783540681649"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-68164-9_13","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008]]}}}