{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:19:04Z","timestamp":1776827944710,"version":"3.51.2"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","issue":"238","license":[{"start":{"date-parts":[[2002,10,4]],"date-time":"2002-10-04T00:00:00Z","timestamp":1033689600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We show how to use the parallelized kangaroo method for computing invariants in real quadratic function fields. Specifically, we show how to apply the kangaroo method to the infrastructure in these fields. We also show how to speed up the computation by using heuristics on the distribution of the divisor class number, and by using the relatively inexpensive baby steps in the real quadratic model of a hyperelliptic function field. Furthermore, we provide examples for regulators and class numbers of hyperelliptic function fields of genus\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"3\">\n                        <mml:semantics>\n                          <mml:mn>3<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">3<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    that are larger than those ever reported before.\n                  <\/p>","DOI":"10.1090\/s0025-5718-01-01343-6","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:28Z","timestamp":1027707268000},"page":"793-814","source":"Crossref","is-referenced-by-count":9,"title":["The parallelized Pollard kangaroo method in real quadratic function fields"],"prefix":"10.1090","volume":"71","author":[{"given":"Andreas","family":"Stein","sequence":"first","affiliation":[]},{"given":"Edlyn","family":"Teske","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2001,10,4]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[Art24] E. Artin. Quadratische K\u00f6rper im Gebiete der h\u00f6heren Kongruenzen I, II. Math. Zeitschr., 19:153\u2013206, 1924.","DOI":"10.1007\/BF01181074"},{"issue":"177","key":"2","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2307\/2007876","article-title":"Computing in the Jacobian of a hyperelliptic curve","volume":"48","author":"Cantor, David G.","year":"1987","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"3","doi-asserted-by":"crossref","unstructured":"[GH] P. Gaudry and R. Harley. Counting points on hyperelliptic curves over finite fields. In Algorithmic Number Theory Seminar ANTS-IV, volume 1838 of Lecture Notes in Computer Science, pages 313\u2013332. Springer, 2000.","DOI":"10.1007\/10722028_18"},{"key":"4","unstructured":"[LiD97] LiDIA Group, Technische Universit\u00e4t Darmstadt, Darmstadt, Germany. LiDIA - A library for computational number theory, Version 1.3, 1997."},{"key":"5","doi-asserted-by":"crossref","unstructured":"[Pol] J. M. Pollard. Kangaroos, Monopoly and discrete logarithms. J. Cryptology 13:437\u2013447, 2000.","DOI":"10.1007\/s001450010010"},{"issue":"143","key":"6","doi-asserted-by":"publisher","first-page":"918","DOI":"10.2307\/2006496","article-title":"Monte Carlo methods for index computation (\ud835\udc5a\ud835\udc5c\ud835\udc51\ud835\udc5d)","volume":"32","author":"Pollard, J. M.","year":"1978","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"227","key":"7","doi-asserted-by":"publisher","first-page":"1233","DOI":"10.1090\/S0025-5718-99-01066-2","article-title":"Real and imaginary quadratic representations of hyperelliptic function fields","volume":"68","author":"Paulus, Sachar","year":"1999","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"8","first-page":"415","article-title":"Class number, a theory of factorization, and genera","author":"Shanks, Daniel","year":"1971"},{"key":"9","first-page":"217","article-title":"The infrastructure of a real quadratic field and its applications","author":"Shanks, Daniel","year":"1972"},{"issue":"1-2","key":"10","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1007\/BF00125081","article-title":"Key-exchange in real quadratic congruence function fields","volume":"7","author":"Scheidler, R.","year":"1996","journal-title":"Des. Codes Cryptogr.","ISSN":"https:\/\/id.crossref.org\/issn\/0925-1022","issn-type":"print"},{"key":"11","unstructured":"[ST99a] A. Stein and E. Teske. Catching kangaroos in function fields. Technical Report CORR 99-09, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, 1999. 19 pages."},{"key":"12","unstructured":"[ST99b] A. Stein and E. Teske. Explicit bounds and heuristics on class numbers in hyperelliptic function fields. Math. Comp., posted on October 4, 2001, PII S0025-5718(01)01385-0 (to appear in print)."},{"key":"13","unstructured":"[Ste99] A. Stein. Sharp upper bounds for arithmetics in hyperelliptic function fields. J. Ramanujan Math. Soc., 9\u201316 (2):1\u201386, 2001."},{"key":"14","series-title":"Universitext","isbn-type":"print","volume-title":"Algebraic function fields and codes","author":"Stichtenoth, Henning","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540564896"},{"key":"15","isbn-type":"print","doi-asserted-by":"publisher","first-page":"607","DOI":"10.1007\/BFb0054896","article-title":"An improved method of computing the regulator of a real quadratic function field","author":"Stein, Andreas","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/3540646574"},{"key":"16","doi-asserted-by":"crossref","unstructured":"[SZ91] A. Stein and H. G. Zimmer. An algorithm for determining the regulator and the fundamental unit of a hyperelliptic congruence function field. In Proc. 1991 Int. Symp. on Symbolic and Algebraic Computation, ISAAC, Bonn, July 15-17, pages 183\u2013184. ACM Press, 1991.","DOI":"10.1145\/120694.120719"},{"key":"17","isbn-type":"print","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1007\/BFb0054891","article-title":"Speeding up Pollard\u2019s rho method for computing discrete logarithms","author":"Teske, Edlyn","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/3540646574"},{"issue":"234","key":"18","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1090\/S0025-5718-00-01213-8","article-title":"On random walks for Pollard\u2019s rho method","volume":"70","author":"Teske, Edlyn","year":"2001","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/PL00003816","article-title":"Parallel collision search with cryptanalytic applications","volume":"12","author":"van Oorschot, Paul C.","year":"1999","journal-title":"J. Cryptology","ISSN":"https:\/\/id.crossref.org\/issn\/0933-2790","issn-type":"print"},{"key":"20","unstructured":"[{Zim}97] H. G. Zimmer et al. Simath manual, 1997. Universit\u00e4t des Saarlandes, Saarbr\u00fccken, Germany."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01343-6\/S0025-5718-01-01343-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01343-6\/S0025-5718-01-01343-6.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:56:52Z","timestamp":1776725812000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2002-71-238\/S0025-5718-01-01343-6\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,10,4]]},"references-count":20,"journal-issue":{"issue":"238","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["S0025-5718-01-01343-6"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-01-01343-6","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2001,10,4]]}}}