{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,5]],"date-time":"2024-09-05T19:26:30Z","timestamp":1725564390371},"publisher-location":"Berlin, Heidelberg","reference-count":15,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540205920"},{"type":"electronic","value":"9783540400615"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/978-3-540-40061-5_19","type":"book-chapter","created":{"date-parts":[[2010,9,5]],"date-time":"2010-09-05T23:06:00Z","timestamp":1283727960000},"page":"311-325","source":"Crossref","is-referenced-by-count":2,"title":["On Class Group Computations Using the Number Field Sieve"],"prefix":"10.1007","author":[{"given":"Mark L.","family":"Bauer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Safuat","family":"Hamdy","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"1\u20132","key":"19_CR1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0304-3975(99)00061-4","volume":"226","author":"L.M. Adleman","year":"1999","unstructured":"Adleman, L.M., DeMarrais, J., Huang, M.-D.: A subexponential algorithm for discrete logarithms over hyperelliptic curves of large genus over GF(q). Theoretical Computer Science\u00a0226, 1\u20132, 7\u201318 (1999)","journal-title":"Theoretical Computer Science"},{"key":"19_CR2","series-title":"LNM","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/BFb0091539","volume-title":"The development of the number field sieve","author":"J.P. Buhler","year":"1993","unstructured":"Buhler, J.P., Lenstra Jr., H.W., Pomerance, C.: Factoring integers with the number field sieve. In: Lenstra, A.K., Lenstra, H.W. (eds.) The development of the number field sieve. LNM, vol.\u00a01554, pp. 50\u201394. Springer, Heidelberg (1993)"},{"key":"19_CR3","series-title":"GTM","volume-title":"A Course in Computational Algebraic Number Theory","author":"H. Cohen","year":"1995","unstructured":"Cohen, H.: A Course in Computational Algebraic Number Theory. GTM, vol.\u00a0138. Springer, Heidelberg (1995)"},{"key":"19_CR4","volume-title":"Prime Numbers: A Computational Perspective","author":"R. Crandall","year":"2000","unstructured":"Crandall, R., Pomerance, C.: Prime Numbers: A Computational Perspective. Springer, Heidelberg (2000)"},{"key":"19_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/3-540-36178-2_8","volume-title":"Advances in Cryptology - ASIACRYPT 2002","author":"I.B. Damg\u00e5rd","year":"2002","unstructured":"Damg\u00e5rd, I.B., Fujisaki, E.: A statistically-hiding integer commitment scheme based on groups with hidden order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol.\u00a02501, pp. 125\u2013142. Springer, Heidelberg (2002)"},{"issue":"1","key":"19_CR6","doi-asserted-by":"publisher","first-page":"83","DOI":"10.4064\/aa102-1-6","volume":"102","author":"A. Enge","year":"2002","unstructured":"Enge, A., Gaudry, P.A.: A general framework for subexponential discrete logarithm algorithms. Acta Arithmetica\u00a0102(1), 83\u2013103 (2002)","journal-title":"Acta Arithmetica"},{"issue":"1","key":"19_CR7","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1137\/0406010","volume":"6","author":"D.M. Gordon","year":"1993","unstructured":"Gordon, D.M.: Discrete logarithms in gf(p) using the number field sieve. SIAM Journal of Discrete Mathematics\u00a06(1), 124\u2013138 (1993)","journal-title":"SIAM Journal of Discrete Mathematics"},{"key":"19_CR8","unstructured":"Hamdy, S.: IQ cryptography: A secure and efficient alternative. Journal of Cryptology (2003) (submitted)"},{"issue":"226","key":"19_CR9","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1090\/S0025-5718-99-01003-0","volume":"68","author":"M.J. Jacobson Jr.","year":"1999","unstructured":"Jacobson Jr., M.J.: Applying sieving to the computation of quadratic class groups. Mathematics of Computation\u00a068(226), 859\u2013867 (1999)","journal-title":"Mathematics of Computation"},{"key":"19_CR10","unstructured":"Jacobson, Jr., M.J.: Subexponential Class Group Computation in Quadratic Orders. PhD thesis, Technische Universit\u00e4t Darmstadt, Fachbereich Informatik, Darmstadt, Germany (1999)"},{"key":"19_CR11","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03642-6","volume-title":"Algebraic Aspects of Cryptography","author":"N. Koblitz","year":"1998","unstructured":"Koblitz, N.: Algebraic Aspects of Cryptography. Algorithms and Computation in Mathematics, vol.\u00a03. Springer, Heidelberg (1998)"},{"issue":"1676","key":"19_CR12","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1098\/rsta.1993.0139","volume":"345","author":"O. Schirokauer","year":"1993","unstructured":"Schirokauer, O.: Discrete logarithms and local units. Philosophical Transactions of the Royal Society of London, Series A\u00a0345(1676), 409\u2013423 (1993)","journal-title":"Philosophical Transactions of the Royal Society of London, Series A"},{"issue":"231","key":"19_CR13","doi-asserted-by":"publisher","first-page":"1267","DOI":"10.1090\/S0025-5718-99-01137-0","volume":"69","author":"O. Schirokauer","year":"2000","unstructured":"Schirokauer, O.: Using number fields to compute logarithms in finite fields. Mathematics of Computation\u00a069(231), 1267\u20131283 (2000)","journal-title":"Mathematics of Computation"},{"key":"19_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/3-540-61581-4_66","volume-title":"Algorithmic Number Theory","author":"O. Schirokauer","year":"1996","unstructured":"Schirokauer, O., Weber, D., Denny, T.: Discrete logarithms: The effectiveness of the index calculus method. In: Cohen, H. (ed.) ANTS 1996. LNCS, vol.\u00a01122, pp. 337\u2013361. Springer, Heidelberg (1996)"},{"key":"19_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1007\/3-540-61581-4_70","volume-title":"Algorithmic Number Theory","author":"D. Weber","year":"1996","unstructured":"Weber, D.: Computing discrete logarithms with the general number field sieve. In: Cohen, H. (ed.) ANTS 1996. LNCS, vol.\u00a01122, pp. 391\u2013403. Springer, Heidelberg (1996)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - ASIACRYPT 2003"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-40061-5_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,20]],"date-time":"2019-03-20T01:43:26Z","timestamp":1553046206000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-40061-5_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540205920","9783540400615"],"references-count":15,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-40061-5_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2003]]}}}