Relevant bibliographies by topics / Curves and Jacobians over finite fields

Academic literature on the topic 'Curves and Jacobians over finite fields'

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Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Curves and Jacobians over finite fields"

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Voloch, José Felipe. "Jacobians of Curves over Finite Fields." Rocky Mountain Journal of Mathematics 30, no. 2 (June 2000): 755–59. http://dx.doi.org/10.1216/rmjm/1022009294.

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FORD, KEVIN, and IGOR SHPARLINSKI. "ON CURVES OVER FINITE FIELDS WITH JACOBIANS OF SMALL EXPONENT." International Journal of Number Theory 04, no. 05 (October 2008): 819–26. http://dx.doi.org/10.1142/s1793042108001687.

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We show that finite fields over which there is a curve of a given genus g ≥ 1 with its Jacobian having a small exponent, are very rare. This extends a recent result of Duke in the case of g = 1. We also show that when g = 1 or g = 2, our lower bounds on the exponent, valid for almost all finite fields 𝔽q and all curves over 𝔽q, are best possible.
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Xiong, Maosheng, and Alexandru Zaharescu. "Statistics of the Jacobians of hyperelliptic curves over finite fields." Mathematical Research Letters 19, no. 2 (2012): 255–72. http://dx.doi.org/10.4310/mrl.2012.v19.n2.a1.

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Shparlinski, Igor. "On the size of the Jacobians of curves over finite fields." Bulletin of the Brazilian Mathematical Society, New Series 39, no. 4 (December 2008): 587–95. http://dx.doi.org/10.1007/s00574-008-0006-4.

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Overkamp, Otto. "Jumps and Motivic Invariants of Semiabelian Jacobians." International Mathematics Research Notices 2019, no. 20 (January 29, 2018): 6437–79. http://dx.doi.org/10.1093/imrn/rnx303.

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Abstract We investigate Néron models of Jacobians of singular curves over strictly Henselian discretely valued fields and their behavior under tame base change. For a semiabelian variety, this behavior is governed by a finite sequence of (a priori) real numbers between 0 and 1, called jumps. The jumps are conjectured to be rational, which is known in some cases. The purpose of this paper is to prove this conjecture in the case where the semiabelian variety is the Jacobian of a geometrically integral curve with a push-out singularity. Along the way, we prove the conjecture for algebraic tori which are induced along finite separable extensions and generalize Raynaud’s description of the identity component of the Néron model of the Jacobian of a smooth curve (in terms of the Picard functor of a proper, flat, and regular model) to our situation. The main technical result of this paper is that the exact sequence that decomposes the Jacobian of one of our singular curves into its toric and Abelian parts extends to an exact sequence of Néron models. Previously, only split semiabelian varieties were known to have this property.
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Ahmadi, Omran, Gary McGuire, and Antonio Rojas-León. "Decomposing Jacobians of curves over finite fields in the absence of algebraic structure." Journal of Number Theory 156 (November 2015): 414–31. http://dx.doi.org/10.1016/j.jnt.2015.04.014.

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Lauder, Alan G. B., and Daqing Wan. "Computing Zeta Functions of Artin–schreier Curves over Finite Fields." LMS Journal of Computation and Mathematics 5 (2002): 34–55. http://dx.doi.org/10.1112/s1461157000000681.

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AbstractThe authors present a practical polynomial-time algorithm for computing the zeta function of certain Artin–Schreier curves over finite fields. This yields a method for computing the order of the Jacobian of an elliptic curve in characteristic 2, and more generally, any hyperelliptic curve in characteristic 2 whose affine equation is of a particular form. The algorithm is based upon an efficient reduction method for the Dwork cohomology of one-variable exponential sums.
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Bruin, Peter, and Filip Najman. "Hyperelliptic modular curves and isogenies of elliptic curves over quadratic fields." LMS Journal of Computation and Mathematics 18, no. 1 (2015): 578–602. http://dx.doi.org/10.1112/s1461157015000157.

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We study elliptic curves over quadratic fields with isogenies of certain degrees. Let $n$ be a positive integer such that the modular curve $X_{0}(n)$ is hyperelliptic of genus ${\geqslant}2$ and such that its Jacobian has rank $0$ over $\mathbb{Q}$. We determine all points of $X_{0}(n)$ defined over quadratic fields, and we give a moduli interpretation of these points. We show that, with a finite number of exceptions up to $\overline{\mathbb{Q}}$-isomorphism, every elliptic curve over a quadratic field $K$ admitting an $n$-isogeny is $d$-isogenous, for some $d\mid n$, to the twist of its Galois conjugate by a quadratic extension $L$ of $K$. We determine $d$ and $L$ explicitly, and we list all exceptions. As a consequence, again with a finite number of exceptions up to $\overline{\mathbb{Q}}$-isomorphism, all elliptic curves with $n$-isogenies over quadratic fields are in fact $\mathbb{Q}$-curves.
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Cornelissen, G. "Two-torsion in the Jacobian of hyperelliptic curves over finite fields." Archiv der Mathematik 77, no. 3 (September 2001): 241–46. http://dx.doi.org/10.1007/pl00000487.

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Garra, Ricard, Josep M. Miret, Jordi Pujolàs, and Nicolas Thériault. "The 2-adic valuation of the cardinality of Jacobians of genus 2 curves over quadratic towers of finite fields." Journal of Algebra and Its Applications 18, no. 07 (July 2019): 1950135. http://dx.doi.org/10.1142/s0219498819501354.

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Given a genus 2 curve [Formula: see text] defined over a finite field [Formula: see text] of odd characteristic such that [Formula: see text], we study the growth of the 2-adic valuation of the cardinality of the Jacobian over a tower of quadratic extensions of [Formula: see text]. In the cases of simpler regularity, we determine the exponents of the 2-Sylow subgroup of [Formula: see text].
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Dissertations / Theses on the topic "Curves and Jacobians over finite fields"

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Smith, Benjamin Andrew. "Explicit endomorphisms and correspondences." University of Sydney, 2006. http://hdl.handle.net/2123/1066.

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Doctor of Philosophy (PhD)
In this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.
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Smith, Benjamin Andrew. "Explicit endomorphisms and correspondences." Thesis, The University of Sydney, 2005. http://hdl.handle.net/2123/1066.

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In this work, we investigate methods for computing explicitly with homomorphisms (and particularly endomorphisms) of Jacobian varieties of algebraic curves. Our principal tool is the theory of correspondences, in which homomorphisms of Jacobians are represented by divisors on products of curves. We give families of hyperelliptic curves of genus three, five, six, seven, ten and fifteen whose Jacobians have explicit isogenies (given in terms of correspondences) to other hyperelliptic Jacobians. We describe several families of hyperelliptic curves whose Jacobians have complex or real multiplication; we use correspondences to make the complex and real multiplication explicit, in the form of efficiently computable maps on ideal class representatives. These explicit endomorphisms may be used for efficient integer multiplication on hyperelliptic Jacobians, extending Gallant--Lambert--Vanstone fast multiplication techniques from elliptic curves to higher dimensional Jacobians. We then describe Richelot isogenies for curves of genus two; in contrast to classical treatments of these isogenies, we consider all the Richelot isogenies from a given Jacobian simultaneously. The inter-relationship of Richelot isogenies may be used to deduce information about the endomorphism ring structure of Jacobian surfaces; we conclude with a brief exploration of these techniques.
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Keller, Timo [Verfasser], Uwe [Akademischer Betreuer] Jannsen, and Walter [Akademischer Betreuer] Gubler. "The conjecture of Birch and Swinnerton-Dyer for Jacobians of constant curves over higher dimensional bases over finite fields / Timo Keller. Betreuer: Uwe Jannsen ; Walter Gubler." Regensburg : Universitätsbibliothek Regensburg, 2013. http://d-nb.info/1059569612/34.

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Voloch, J. F. "Curves over finite fields." Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355283.

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Rovi, Carmen. "Algebraic Curves over Finite Fields." Thesis, Linköping University, Department of Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-56761.

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This thesis surveys the issue of finding rational points on algebraic curves over finite fields. Since Goppa's construction of algebraic geometric codes, there has been great interest in finding curves with many rational points. Here we explain the main tools for finding rational points on a curve over a nite eld and provide the necessary background on ring and field theory. Four different articles are analyzed, the first of these articles gives a complete set of table showing the numbers of rational points for curves with genus up to 50. The other articles provide interesting constructions of covering curves: covers by the Hemitian curve, Kummer extensions and Artin-Schreier extensions. With these articles the great difficulty of finding explicit equations for curves with many rational points is overcome. With the method given by Arnaldo García in [6] we have been able to nd examples that can be used to define the lower bounds for the corresponding entries in the tables given in http: //wins.uva.nl/~geer, which to the time of writing this Thesis appear as "no information available". In fact, as the curves found are maximal, these entries no longer need a bound, they can be given by a unique entry, since the exact value of Nq(g) is now known.

At the end of the thesis an outline of the construction of Goppa codes is given and the NXL and XNL codes are presented.

 

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Thuen, Øystein Øvreås. "Constructing elliptic curves over finite fields using complex multiplication." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2006. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9434.

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We study and improve the CM-method for the creation of elliptic curves with specified group order over finite fields. We include a thorough review of the mathematical theory needed to understand this method. The ability to construct elliptic curves with very special group order is important in pairing-based cryptography.

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Cam, Vural. "Drinfeld Modular Curves With Many Rational Points Over Finite Fields." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613118/index.pdf.

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In our study Fq denotes the finite field with q elements. It is interesting to construct curves of given genus over Fq with many Fq -rational points. Drinfeld modular curves can be used to construct that kind of curves over Fq . In this study we will use reductions of the Drinfeld modular curves X_{0} (n) to obtain curves over finite fields with many rational points. The main idea is to divide the Drinfeld modular curves by an Atkin-Lehner involution which has many fixed points to obtain a quotient with a better #{rational points} /genus ratio. If we divide the Drinfeld modular curve X_{0} (n) by an involution W, then the number of rational points of the quotient curve WX_{0} (n) is not less than half of the original number. On the other hand, if this involution has many fixed points, then by the Hurwitz-Genus formula the genus of the curve WX_{0} (n) is much less than half of the g (X_{0}(n)).
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Kirlar, Baris Bulent. "Isomorphism Classes Of Elliptic Curves Over Finite Fields Of Characteristic Two." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12606489/index.pdf.

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In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphism classes of elliptic curves recommended by National Institute of Standards and Technology are listed and their properties are discussed.
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Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g<=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la recherche de bonnes courbes, dont l'implémentation fournit de nouveaux records de nombre de points sur les corps finis d'ordres 2 et 3. Nous étudions dans la seconde partie une formule de trace d'opérateurs de Hecke sur des formes modulaires quaternioniques, et montrons que les courbes de Shimura associées forment naturellement des suites récursives de courbes asymptotiquement optimales sur une extension quadratique du corps de base. Nous prouvons également qu'alors la contribution essentielle en points rationnels est fournie par les points supersinguliers
The study of the number of rational points of a curve defined over a finite field naturally falls into two cases: when the genus is small (typically g<=50), and when it tends to infinity. We devote one part of this thesis to each of these cases. In the first part of our study, we explain how to compute the equation of any abelian covering of a curve defined over a finite field. For this we use explicit class field theory provided by Kummer and Artin-Schreier-Witt extensions. We also detail an algorithm for the search of good curves, whose implementation provides new records of number of points over the finite fields of order 2 and 3. In the second part, we study a trace formula of Hecke operators on quaternionic modular forms, and we show that the associated Shimura curves of the form naturally form recursive sequences of asymptotically optimal curves over a quadratic extension of the base field. Moreover, we then prove that the essential contribution to the rational points is provided by supersingular points
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Vrioni, Brikena. "A census for curves and surfaces with diophantine stability over finite fields." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/673261.

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An algebraic variety defined over a field is said to have Diophantine stability for an extension of this field if the variety does not acquire new points in the extension. Diophantine stability has a growing interest due to recent conjectures of Mazur and Rubin linked to the well-known Lang conjectures, generalizing the celebrated Faltings theorem on rational points on curves of genus grater or equal than 2. Their framework is characteristic zero, and we shall focus on the analogous and related questions in positive characteristic. More precisely, the aim of the thesis is to initiate the study of Diophantine stability for curves and surfaces defined over finite fields. First we prove the finiteness of the finite field extensions where an algebraic variety can exhibit Diophantine stability (DS) in terms of its Betti numbers (the genus in the case of curves, the Hodge diamond in the case of surfaces, etc.) Then, we analyze the existence of curves with Diophantine stability. More precisely, for curves of genus g<=3 we give the complete list of (isomorphism classes of) DS-curves, and we also provide data on the candidate Weil polynomials for DS-curves of genus g=4 and 5. For curves of large genus, we exhibit certain families of DS-curves: Deligne-Lusztig curves, Carlitz curves, .... Finally, we also aim to make a contribution on surfaces defined over finite fields with Diophantine stability. From the classification of surfaces of Enriques-Munford-Bombieri we derive partial results and a census of DS-surfaces.
Es diu que una varietat algebraica definida sobre un cos té estabilitat diofantina per a una extensió d'aquest cos si la varietat no adquireix punts nous a l'extensió. L'estabilitat diofantina té un interès creixent a causa de les recents conjectures de Mazur i Rubin vinculades a les conegudes conjectures de Lang, generalitzant el famós teorema de Faltings sobre punts racionals de corbes de gènere major o igual a 2. El seu marc de treball és en característica zero, i en aquesta tesi ens centrem en les qüestions anàlogues i d'altres relacionades en característica positiva. Més precisament, l'objectiu de la tesi és iniciar l'estudi de l'estabilitat diofantina per a corbes i superfícies definides sobre cossos finits. Primer, demostrem la finitud de les extensions de cossos finits on una varietat algebraica pot presentar estabilitat diofantina (DS) en funció dels seus nombres de Betti (el gènere en el cas de les corbes, el diamant de Hodge en el cas de les superfícies, etc.) Després, analitzem l'existència de corbes amb estabilitat diofantina. Més precisament, per a les corbes de gènere g <= 3 donem la llista completa (de classes d'isomorfisme) de corbes DS i també proporcionem dades sobre els polinomis de Weil candidats per a les corbes DS de gèneres g = 4 i 5. Per a les corbes de gènere gran, exposem algunes famílies de corbes DS: corbes de Deligne-Lusztig, corbes de Carlitz, .... A continuació, també fem una contribució sobre superfícies definides sobre cossos finits amb estabilitat diofantina. De la classificació de superfícies d'Enriques-Munford-Bombieri obtenim resultats parcials i un cens de superfícies DS
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Books on the topic "Curves and Jacobians over finite fields"

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Moreno, Carlos J. Algebraic curves over finite fields. Cambridge [England]: Cambridge University Press, 1991.

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Fried, Michael D., ed. Applications of Curves over Finite Fields. Providence, Rhode Island: American Mathematical Society, 1999. http://dx.doi.org/10.1090/conm/245.

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Alam, Shajahan. Zeta-functions of curves over finite fields. Manchester: UMIST, 1996.

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Hansen, Søren Have. Rational points on curves over finite fields. [Aarhus, Denmark: Aarhus Universitet, Matematisk Institut, 1995.

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AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields (1997 University of Washington). Applications of curves over finite fields: 1997 AMS-IMS-SIAM Joint Summer Research Conference on Applications of Curves over Finite Fields, July 27-31, 1997, University of Washington, Seattle. Edited by Fried Michael D. 1942-. Providence, R.I: American Mathematical Society, 1999.

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Algebraic curves and cryptography. Providence, R.I: American Mathematical Society, 2010.

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Shparlinski, Igor E., and David R. Kohel. Frobenius distributions: Lang-Trotter and Sato-Tate conjectures : Winter School on Frobenius Distributions on Curves, February 17-21, 2014 [and] Workshop on Frobenius Distributions on Curves, February 24-28, 2014, Centre International de Rencontres Mathematiques, Marseille, France. Providence, Rhode Island: American Mathematical Society, 2016.

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1965-, Aubry Yves, Ritzenthaler Christophe 1976-, Zykin Alexey 1984-, and Geocrypt Conference (2011 : Bastia, France), eds. Arithmetic, geometry, cryptography and coding theory: 13th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, March 14-18, 2011, CIRM, Marseille, France : Geocrypt 2011, June 19-24, 2011, Bastia, France. Providence, R.I: American Mathematical Society, 2012.

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International Conference Arithmetic, Geometry, Cryptography and Coding Theory (14th 2013 Marseille, France). Algorithmic arithmetic, geometry, and coding theory: 14th International Conference, Arithmetic, Geometry, Cryptography, and Coding Theory, June 3-7 2013, CIRM, Marseille, France. Edited by Ballet Stéphane 1971 editor, Perret, M. (Marc), 1963- editor, and Zaytsev, Alexey (Alexey I.), 1976- editor. Providence, Rhode Island: American Mathematical Society, 2015.

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Alta.) WIN (Conference) (2nd 2011 Banff. Women in Numbers 2: Research directions in number theory : BIRS Workshop, WIN2 - Women in Numbers 2, November 6-11, 2011, Banff International Research Station, Banff, Alberta, Canada. Edited by David Chantal 1964-, Lalín Matilde 1977-, and Manes Michelle 1970-. Providence, Rhode Island: American Mathematical Society, 2013.

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Book chapters on the topic "Curves and Jacobians over finite fields"

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Adleman, Leonard M., Jonathan DeMarrais, and Ming-Deh Huang. "A subexponential algorithm for discrete logarithms over the rational subgroup of the Jacobians of large genus hyperelliptic curves over finite fields." In Lecture Notes in Computer Science, 28–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58691-1_39.

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Ulmer, Douglas. "Curves and Jacobians over Function Fields." In Advanced Courses in Mathematics - CRM Barcelona, 281–337. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0853-8_5.

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Tsfasman, Michael, Serge Vlǎduţ, and Dmitry Nogin. "Curves over finite fields." In Mathematical Surveys and Monographs, 133–89. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/139/03.

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Husemöller, Dale. "Elliptic Curves over Finite Fields." In Elliptic Curves, 242–61. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4757-5119-2_14.

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Blake, Ian F., XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, and Tomik Yaghoobian. "Elliptic Curves over Finite Fields." In Applications of Finite Fields, 139–50. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4757-2226-0_7.

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Silverman, Joseph H. "Elliptic Curves over Finite Fields." In The Arithmetic of Elliptic Curves, 137–56. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-09494-6_5.

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Sury, B. "Elliptic Curves over Finite Fields." In Elliptic Curves, Modular Forms and Cryptography, 33–47. Gurgaon: Hindustan Book Agency, 2003. http://dx.doi.org/10.1007/978-93-86279-15-6_3.

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Enge, Andreas. "Elliptic Curves Over Finite Fields." In Elliptic Curves and Their Applications to Cryptography, 45–107. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4615-5207-9_3.

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Silverman, Joseph H., and John Tate. "Cubic Curves over Finite Fields." In Rational Points on Elliptic Curves, 107–44. New York, NY: Springer New York, 1992. http://dx.doi.org/10.1007/978-1-4757-4252-7_5.

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Silverman, Joseph H. "Elliptic Curves over Finite Fields." In The Arithmetic of Elliptic Curves, 130–45. New York, NY: Springer New York, 1986. http://dx.doi.org/10.1007/978-1-4757-1920-8_6.

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Conference papers on the topic "Curves and Jacobians over finite fields"

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Freeman, David, and Kristin Lauter. "Computing endomorphism rings of Jacobians of genus 2 curves over finite fields." In Proceedings of the First SAGA Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793430_0002.

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Cohen, Ran. "Group Law Algorithms for Jacobian Varieties of Curves over Finite Fields." In Proceedings of the First SAGA Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793430_0011.

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Shparlinski, Igor E. "Pseudorandom Points on Elliptic Curves over Finite Fields." In Proceedings of the First SAGA Conference. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812793430_0006.

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Voight, John. "Curves over finite fields with many points: an introduction." In Computational Aspects of Algebraic Curves. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812701640_0010.

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Shankar, B. R., and Kamath K. Karuna. "(2,1)-Lagged Fibonacci Generators Using Elliptic Curves over Finite Fields." In 2009 International Conference on Computer Engineering and Technology (ICCET). IEEE, 2009. http://dx.doi.org/10.1109/iccet.2009.103.

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Buchmann, Johannes, and Volker Müller. "Computing the number of points of elliptic curves over finite fields." In the 1991 international symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/120694.120718.

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Daikpor, Michael Naseimo, and Oluwole Adegbenro. "Arithmetic Operations on Elliptic Curves Defined over Un-conventional Element Finite Fields." In 2012 International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery (CyberC). IEEE, 2012. http://dx.doi.org/10.1109/cyberc.2012.29.

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Zhang, Yuhong, Meng Zhang, and Maozhi Xu. "Finding vulnerable curves over finite fields of characteristic 2 by pairing reduction." In 2017 IEEE/ACIS 16th International Conference on Computer and Information Science (ICIS). IEEE, 2017. http://dx.doi.org/10.1109/icis.2017.7960080.

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McEliece, Robert J., and M. C. Rodriguez-palanquex. "AG Goppa Codes from Maximal Curves over determined Finite Fields of characteristic 2." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.261891.

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10

HENNINGSEN, M. "COMPUTING THE ENDOMORPHISM TYPE OF ORDINARY ELLIPTIC CURVES OVER FINITE FIELDS WITH KANT V4." In Proceedings of the First International Congress of Mathematical Software. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777171_0026.

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