{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T20:32:37Z","timestamp":1770841957816,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,2,5]],"date-time":"2016-02-05T00:00:00Z","timestamp":1454630400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10623-016-0184-9","type":"journal-article","created":{"date-parts":[[2016,2,5]],"date-time":"2016-02-05T02:10:28Z","timestamp":1454638228000},"page":"601-616","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A new method for decomposition in the Jacobian of small genus hyperelliptic curves"],"prefix":"10.1007","volume":"82","author":[{"given":"Palash","family":"Sarkar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4374-3125","authenticated-orcid":false,"given":"Shashank","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,2,5]]},"reference":[{"key":"184_CR1","doi-asserted-by":"crossref","unstructured":"Adleman L.M., DeMarrais J., Huang M.-D. A.: A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields. In: Adleman L.M., Huang M.-D.A. (eds.) Proceedings of the First International Symposium: Algorithmic Number Theory, ANTS-I, Ithaca, 6\u20139 May, 1994. Lecture Notes in Computer Science, vol. 877, pp. 28\u201340. Springer, Berlin (1994).","DOI":"10.1007\/3-540-58691-1_39"},{"key":"184_CR2","doi-asserted-by":"crossref","unstructured":"Bosma W., Cannon J., Playoust C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24(3\u20134), 235\u2013265 (1997). Computational algebra and number theory (London, 1993).","DOI":"10.1006\/jsco.1996.0125"},{"key":"184_CR3","unstructured":"Diem C.: The GHS attack in odd characteristic. J. Ramanujan Math. Soc. 18(1), 1\u201332 (2003)."},{"key":"184_CR4","doi-asserted-by":"crossref","unstructured":"Diem C., Thom\u00e9 E.: Index calculus in class groups of non-hyperelliptic curves of genus three. J. Cryptol. 21(4), 593\u2013611 (2008).","DOI":"10.1007\/s00145-007-9014-6"},{"key":"184_CR5","doi-asserted-by":"crossref","unstructured":"Enge A.: Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time. Math. Comput. 71(238), 729\u2013742 (2002).","DOI":"10.1090\/S0025-5718-01-01363-1"},{"key":"184_CR6","doi-asserted-by":"crossref","unstructured":"Enge A., Gaudry P.: A general framework for subexponential discrete logarithm algorithms. Acta Arith. 102, 83\u2013103 (2002).","DOI":"10.4064\/aa102-1-6"},{"key":"184_CR7","doi-asserted-by":"crossref","unstructured":"Flassenberg R., Paulus S.: Sieving in function fields. Exp. Math. 8(4), 339\u2013349 (1999).","DOI":"10.1080\/10586458.1999.10504623"},{"key":"184_CR8","unstructured":"Frey G.: How to disguise an elliptic curve (Weil descent). Talk at the 2nd Elliptic Curve Cryptography (ECC) Workshop (1998)."},{"key":"184_CR9","doi-asserted-by":"crossref","unstructured":"Gaudry P.: An algorithm for solving the discrete log problem on hyperelliptic curves. In: Preneel B. (ed.) Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology\u2014EUROCRYPT, Bruges, 14\u201318 May, 2000. Lecture Notes in Computer Science, vol. 1807, pp. 19\u201334. Springer, Berlin (2000).","DOI":"10.1007\/3-540-45539-6_2"},{"key":"184_CR10","doi-asserted-by":"crossref","unstructured":"Gaudry P., Hess F., Smart N.P.: Constructive and destructive facets of weil descent on elliptic curves. J. Cryptol. 15(1), 19\u201346 (2002).","DOI":"10.1007\/s00145-001-0011-x"},{"key":"184_CR11","doi-asserted-by":"crossref","unstructured":"Gaudry P., Thom\u00e9 E., Th\u00e9riault N., Diem C.: A double large prime variation for small genus hyperelliptic index calculus. Math. Comput. 76(257), 475\u2013492 (2007).","DOI":"10.1090\/S0025-5718-06-01900-4"},{"key":"184_CR12","unstructured":"Joux A., Vitse V.: Cover and decomposition index calculus on elliptic curves made practical: application to a previously unreachable curve over $$\\mathbb{F}_{p^6}$$ F p 6 . In: Pointcheval D., Johansson T. (eds.) Proceedings of the 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology, EUROCRYPT, Cambridge, 15\u201319 April, 2012. Lecture Notes in Computer Science, vol. 7237, pp. 9\u201326. Springer, Berlin (2012)."},{"key":"184_CR13","doi-asserted-by":"crossref","unstructured":"Koblitz N.: Elliptic curve cryptosystems. Math. Comp. 48(177), 203\u2013209 (1987).","DOI":"10.1090\/S0025-5718-1987-0866109-5"},{"key":"184_CR14","doi-asserted-by":"crossref","unstructured":"Koblitz N.: Hyperelliptic cryptosystems. J. Cryptol. 1(3), 139\u2013150 (1989).","DOI":"10.1007\/BF02252872"},{"key":"184_CR15","unstructured":"Menezes A., Wu Y.-H., Zuccherato R.: An elementary introduction to hyperelliptic curves. Appendix in \u2018Algebraic Aspects of Cryptography\u2019 by Neal Koblitz (1998)."},{"key":"184_CR16","unstructured":"Miller V.S.: Use of elliptic curves in cryptography. In: Williams H.C. (ed.) Proceedings of the CRYPTO \u201985: Advances in Cryptology, Santa Barbara, 18\u201322 August, 1985. Lecture Notes in Computer Science, vol. 218, pp. 417\u2013426. Springer, Berlin (1985)."},{"key":"184_CR17","doi-asserted-by":"crossref","unstructured":"Nagao K.-I.: Decomposition attack for the Jacobian of a hyperelliptic curve over an extension field. In: Algorithmic Number Theory. Lecture Notes in Computer Science. vol. 6197, pp. 285\u2013300. Springer, Berlin (2010).","DOI":"10.1007\/978-3-642-14518-6_23"},{"key":"184_CR18","doi-asserted-by":"crossref","unstructured":"Smith B.A.: Isogenies and the discrete logarithm problem in Jacobians of genus 3 hyperelliptic curves. J. Cryptol. 22(4), 505\u2013529 (2009).","DOI":"10.1007\/s00145-009-9038-1"},{"key":"184_CR19","doi-asserted-by":"crossref","unstructured":"Swan R.G.: Factorization of polynomials over finite fields. Pac. J. Math. 12(3), 1099\u20131106 (1962).","DOI":"10.2140\/pjm.1962.12.1099"},{"key":"184_CR20","doi-asserted-by":"crossref","unstructured":"Th\u00e9riault N.: Index calculus attack for hyperelliptic curves of small genus. In: Laih C.-S. (ed.) ASIACRYPT. Lecture Notes in Computer Science, vol. 2894, pp. 75\u201392. Springer, Berlin (2003)","DOI":"10.1007\/978-3-540-40061-5_5"},{"key":"184_CR21","doi-asserted-by":"crossref","unstructured":"Velichka M.D., Jacobson M.J. Jr., Stein A.: Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields. Math. Comput., 83(286) (2014).","DOI":"10.1090\/S0025-5718-2013-02748-2"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0184-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-016-0184-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0184-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-016-0184-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,4]],"date-time":"2019-09-04T04:48:12Z","timestamp":1567572492000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-016-0184-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,5]]},"references-count":21,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["184"],"URL":"https:\/\/doi.org\/10.1007\/s10623-016-0184-9","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,2,5]]}}}