Landquist, Eric; Scheidler, Renate; Stein, Andreas Class number and regulator computation in cubic function fields. arXiv:1601.03309 Preprint, arXiv:1601.03309 [math.NT] (2016). MSC: 11R16 11R58 11R29 11Y16 11Y40 14H05 14Q05 BibTeX Cite \textit{E. Landquist} et al., ``Class number and regulator computation in cubic function fields'', Preprint, arXiv:1601.03309 [math.NT] (2016) Full Text: arXiv OA License
Velichka, M. D.; Jacobson, M. J. jun.; Stein, A. Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields. (English) Zbl 1285.14031 Math. Comput. 83, No. 286, 935-963 (2014). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 14G50 11G20 11Y16 11Y40 PDFBibTeX XMLCite \textit{M. D. Velichka} et al., Math. Comput. 83, No. 286, 935--963 (2014; Zbl 1285.14031) Full Text: DOI
Heß, Florian; Stein, Andreas; Stein, Sandra; Lochter, Manfred The magic of elliptic curves and public-key cryptography. (English) Zbl 1273.94349 Jahresber. Dtsch. Math.-Ver. 114, No. 2, 59-88 (2012). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 94A60 11T71 11Y16 14G50 14H52 94-03 PDFBibTeX XMLCite \textit{F. Heß} et al., Jahresber. Dtsch. Math.-Ver. 114, No. 2, 59--88 (2012; Zbl 1273.94349) Full Text: DOI
Jacobson, Michael J. jun.; Scheidler, Renate; Stein, Andreas Cryptographic aspects of real hyperelliptic curves. (English) Zbl 1287.94075 Tatra Mt. Math. Publ. 47, 31-65 (2010). MSC: 94A60 11Y16 11Y40 14G50 PDFBibTeX XMLCite \textit{M. J. Jacobson jun.} et al., Tatra Mt. Math. Publ. 47, 31--65 (2010; Zbl 1287.94075) Full Text: DOI Link
Scheidler, Renate; Stein, Andreas Approximating Euler products and class number computation in algebraic function fields. (English) Zbl 1222.11139 Rocky Mt. J. Math. 40, No. 5, 1689-1727 (2010). Reviewer: Michael J. Jacobson jun. (Calgary) MSC: 11R58 11Y35 11R65 11M38 PDFBibTeX XMLCite \textit{R. Scheidler} and \textit{A. Stein}, Rocky Mt. J. Math. 40, No. 5, 1689--1727 (2010; Zbl 1222.11139) Full Text: DOI
Stein, Andreas Explicit infrastructure for real quadratic function fields and real hyperelliptic curves. (English) Zbl 1243.11109 Glas. Mat., III. Ser. 44, No. 1, 89-126 (2009). MSC: 11R58 11Y16 11Y65 11T71 11M38 PDFBibTeX XMLCite \textit{A. Stein}, Glas. Mat., III. Ser. 44, No. 1, 89--126 (2009; Zbl 1243.11109) Full Text: DOI Link
van der Poorten, Alfred J. (ed.); Stein, Andreas (ed.) Algorithmic number theory. 8th international symposium, ANTS-VIII Banff, Canada, May 17–22, 2008 Proceedings. (English) Zbl 1136.11003 Lecture Notes in Computer Science 5011. Berlin: Springer (ISBN 978-3-540-79455-4/pbk). ix, 455 p. (2008). MSC: 11-06 11Yxx 00B25 PDFBibTeX XMLCite \textit{A. J. van der Poorten} (ed.) and \textit{A. Stein} (ed.), Algorithmic number theory. 8th international symposium, ANTS-VIII Banff, Canada, May 17--22, 2008 Proceedings. Berlin: Springer (2008; Zbl 1136.11003) Full Text: DOI
Jacobson, M. J. jun.; Scheidler, R.; Stein, A. Fast arithmetic on hyperelliptic curves via continued fraction expansions. (English) Zbl 1132.14306 Shaska, T. (ed.) et al., Advances in coding theory and cryptography. Selected papers based on the presentations at the Vlora conference in coding theory and cryptography, Vlora, Albania, May 26–27, 2007 and a special session on coding theory as part of the applications of computer algebra conference, Rochester, MI, USA, July 19–22, 2007. Hackensack, NJ: World Scientific (ISBN 978-981-270-701-7/hbk). Series on Coding Theory and Cryptology 3, 200-243 (2007). MSC: 14G50 11Y16 94A60 14Q05 11T71 14H45 94A62 PDFBibTeX XMLCite \textit{M. J. Jacobson jun.} et al., Ser. Coding Theory Cryptol. 3, 200--243 (2007; Zbl 1132.14306)
Erickson, Stefan; Jacobson, Michael J. jun.; Shang, Ning; Shen, Shuo; Stein, Andreas Explicit formulas for real hyperelliptic curves of genus 2 in affine representation. (English) Zbl 1222.14050 Carlet, Claude (ed.) et al., Arithmetic of finite fields. First international workshop, WAIFI 2007, Madrid, Spain, June 21–22, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73073-6/pbk). Lecture Notes in Computer Science 4547, 202-218 (2007). MSC: 14G50 94A60 11Y16 PDFBibTeX XMLCite \textit{S. Erickson} et al., Lect. Notes Comput. Sci. 4547, 202--218 (2007; Zbl 1222.14050) Full Text: DOI
Stein, Andreas; Teske, Edlyn Optimized baby step-giant step methods. (English) Zbl 1122.11086 J. Ramanujan Math. Soc. 20, No. 1, 27-58 (2005). Reviewer: Harvey Cohn (Laguna Woods) MSC: 11Y16 11R58 PDFBibTeX XMLCite \textit{A. Stein} and \textit{E. Teske}, J. Ramanujan Math. Soc. 20, No. 1, 27--58 (2005; Zbl 1122.11086)
Jacobson, Michael jun.; Menezes, Alfred; Stein, Andreas Hyperelliptic curves and cryptography. (English) Zbl 1098.94023 van der Poorten, Alf (ed.) et al., High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams. Selected papers from the international conference on number theory, Banff, AB, Canada, May 24–30, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3353-7/hbk). Fields Institute Communications 41, 255-282 (2004). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 94A60 11R58 11Y16 11Y65 14G50 PDFBibTeX XMLCite \textit{M. Jacobson jun.} et al., Fields Inst. Commun. 41, 255--282 (2004; Zbl 1098.94023)
Stein, Andreas; Teske, Edlyn Explicit bounds and heuristics on class numbers in hyperelliptic function fields. (English) Zbl 0992.11068 Math. Comput. 71, No. 238, 837-861 (2002). Reviewer: Bjorn Poonen (Berkeley) MSC: 11Y16 11Y40 11R29 11R58 11M38 11R65 PDFBibTeX XMLCite \textit{A. Stein} and \textit{E. Teske}, Math. Comput. 71, No. 238, 837--861 (2002; Zbl 0992.11068) Full Text: DOI
Stein, Andreas; Teske, Edlyn The parallelized Pollard kangaroo method in real quadratic function fields. (English) Zbl 0992.11069 Math. Comput. 71, No. 238, 793-814 (2002). Reviewer: Bjorn Poonen (Berkeley) MSC: 11Y16 11Y40 11R29 11R58 14H05 PDFBibTeX XMLCite \textit{A. Stein} and \textit{E. Teske}, Math. Comput. 71, No. 238, 793--814 (2002; Zbl 0992.11069) Full Text: DOI
Jacobson, Michael; Menezes, Alfred; Stein, Andreas Solving elliptic curve discrete logarithm problems using Weil descent. (English) Zbl 1017.11030 J. Ramanujan Math. Soc. 16, No. 3, 231-260 (2001). Reviewer: Juan Tena Ayuso (Valladolid) MSC: 11G20 14G50 11Y16 PDFBibTeX XMLCite \textit{M. Jacobson} et al., J. Ramanujan Math. Soc. 16, No. 3, 231--260 (2001; Zbl 1017.11030)
Stein, Andreas; Williams, H. C. Explicit primality criteria for \((p-1) p^n-1\). (English) Zbl 1018.11062 Math. Comput. 69, No. 232, 1721-1734 (2000). MSC: 11Y11 11Y16 PDFBibTeX XMLCite \textit{A. Stein} and \textit{H. C. Williams}, Math. Comput. 69, No. 232, 1721--1734 (2000; Zbl 1018.11062) Full Text: DOI
Jacobson, Michael J.; Koblitz, Neal; Silverman, Joseph H.; Stein, Andreas; Teske, Edlyn Analysis of the Xedni calculus attack. (English) Zbl 0948.11048 Des. Codes Cryptography 20, No. 1, 41-64 (2000). Reviewer: Franck Leprévost (Berlin) MSC: 11Y16 94A60 14Q05 11G05 PDFBibTeX XMLCite \textit{M. J. Jacobson} et al., Des. Codes Cryptography 20, No. 1, 41--64 (2000; Zbl 0948.11048) Full Text: DOI
Stein, Andreas; Williams, Hugh C. Some methods for evaluating the regulator of a real quadratic function field. (English) Zbl 0987.11071 Exp. Math. 8, No. 2, 119-133 (1999). Reviewer: Horst G.Zimmer (Saarbrücken) MSC: 11R58 11Y40 11Y65 12E30 PDFBibTeX XMLCite \textit{A. Stein} and \textit{H. C. Williams}, Exp. Math. 8, No. 2, 119--133 (1999; Zbl 0987.11071) Full Text: DOI Euclid EuDML
Müller, Volker; Stein, Andreas; Thiel, Christoph Computing discrete logarithms in real quadratic congruence function fields of large genus. (English) Zbl 1036.11064 Math. Comput. 68, No. 226, 807-822 (1999). MSC: 11Y16 11R60 11T71 68P25 94A60 PDFBibTeX XMLCite \textit{V. Müller} et al., Math. Comput. 68, No. 226, 807--822 (1999; Zbl 1036.11064) Full Text: DOI
Stein, Andreas; Williams, Hugh C. An improved method of computing the regulator of a real quadratic function field. (English) Zbl 0935.11048 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21-25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 607-620 (1998). Reviewer: Claus Fieker (Berlin) MSC: 11Y40 11R27 11R58 11R11 PDFBibTeX XMLCite \textit{A. Stein} and \textit{H. C. Williams}, Lect. Notes Comput. Sci. 1423, 607--620 (1998; Zbl 0935.11048)
Scheidler, Renate; Stein, Andreas Unit computation in purely cubic function fields of unit rank 1. (English) Zbl 0935.11051 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21-25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 592-606 (1998). Reviewer: Claus Fieker (Berlin) MSC: 11Y40 11R27 11R16 11R58 PDFBibTeX XMLCite \textit{R. Scheidler} and \textit{A. Stein}, Lect. Notes Comput. Sci. 1423, 592--606 (1998; Zbl 0935.11051)
Paulus, Sachar; Stein, Andreas Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves. (English) Zbl 0935.11052 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21-25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 576-591 (1998). Reviewer: Claus Fieker (Berlin) MSC: 11Y40 14Q05 11R58 11R29 14G50 PDFBibTeX XMLCite \textit{S. Paulus} and \textit{A. Stein}, Lect. Notes Comput. Sci. 1423, 576--591 (1998; Zbl 0935.11052)
Stein, Andreas Equivalences between elliptic curves and real quadratic congruence function fields. (English) Zbl 0899.11054 J. Théor. Nombres Bordx. 9, No. 1, 75-95 (1997). Reviewer: Ian F.Blake (Palo Alto) MSC: 11R58 11T71 94A60 11Y16 11G05 14H52 PDFBibTeX XMLCite \textit{A. Stein}, J. Théor. Nombres Bordx. 9, No. 1, 75--95 (1997; Zbl 0899.11054) Full Text: DOI Numdam EuDML EMIS
Stein, Andreas Algorithms in real-quadratic congruence function fields. (Algorithmen in reell-quadratischen Kongruenzfunktionenkörpern.) (German) Zbl 0997.11511 Saarbrücken: Univ. des Saarlandes, Mathematisch-Naturwissenschaftliche Fakultät, 216 S. (1996). MSC: 11Y40 11Y16 11R58 94A60 PDFBibTeX XMLCite \textit{A. Stein}, Algorithmen in reell-quadratischen Kongruenzfunktionenkörpern. Saarbrücken: Univ. des Saarlandes, Mathematisch-Naturwissenschaftliche Fakultät (1996; Zbl 0997.11511)
Stein, Andreas Elliptic congruence function fields. (English) Zbl 0899.11055 Cohen, Henri (ed.), Algorithmic number theory. Second international symposium, ANTS-II, Talence, France, May 18-23, 1996. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1122, 375-384 (1996). Reviewer: Ian F.Blake (Palo Alto) MSC: 11R58 11T71 94A60 11Y16 11G05 14H52 PDFBibTeX XMLCite \textit{A. Stein}, Lect. Notes Comput. Sci. 1122, 375--384 (1996; Zbl 0899.11055)
Stein, Andreas; Zimmer, Horst Günter An algorithm for determining the regulator and the fundamental unit of a hyperelliptic congruence function field. (English) Zbl 0925.11054 Watt, Stephen M. (ed.), ISSAC ’91. Proceedings of the 1991 international symposium on Symbolic and algebraic computation. Bonn, Germany, July 15–17, 1991. New York, NY: ACM Press, 183-184 (1991). MSC: 11Y40 11R27 11R58 PDFBibTeX XMLCite \textit{A. Stein} and \textit{H. G. Zimmer}, in: ISSAC '91. Proceedings of the 1991 international symposium on Symbolic and algebraic computation. Bonn, Germany, July 15--17, 1991. New York, NY: ACM Press. 183--184 (1991; Zbl 0925.11054)