Equivalences between elliptic curves and real quadratic congruence function fields
Journal de théorie des nombres de Bordeaux (1997)
- Volume: 9, Issue: 1, page 75-95
- ISSN: 1246-7405
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] C.S. AbelEin Algorithmus zur Berechnung der Klassenzahl und des Regulators reellquadratischer Ordnungen. Dissertation, Universität des Saarlandes, Saarbrücken (Germany) 1994.
- [2] W.W. Adams & M.J. Razar, Multiples of points on elliptic curves and continued fractions. Proc. London Math. Soc.41, 1980, 481-498. Zbl0403.14002MR591651
- [3] E. Artin, Quadratische Körper im Gebiete der höheren Kongruenzen I, II. Math. Zeitschr.19 (1924), 153-206. Zbl50.0107.01MR1544651JFM50.0107.01
- [4] H. Cohen, A Course in Computation AlgebraicNumber Theory.Springer, Berlin1994. Zbl0786.11071MR1228206
- [5] M. Deuring, Lectures on the Theory of Algebraic Functions of One Variable. LNM314, Berlin1973. Zbl0249.14008MR344231
- [6] W. Diffie & M.E. Hellman, New directions in cryptography. IEEE Trans. Inform. Theory22, 6, 644-654, 1976. Zbl0435.94018MR437208
- [7] E. Friedman & L.C. Washington, On the distribution of divisor class groups of curves over finite fields. Theorie des Nombres, Proc. Int. Number Theory Conf. Laval, 1987, Walter de Gruyter, Berlin and New York, 227-239, 1989. Zbl0693.12013MR1024565
- [8] A. Stein, V. Müller, & C. ThielComputing discrete logarithms in real quadratic congruence function fields of large genus. Submitted. Zbl1036.11064
- [9] R. Scheidler, J.A. Buchmann & H.C. Williams, A key exchange protocol using real quadratic fields. J. Cryptology7, 171-199, 1994. Zbl0816.94018MR1286662
- [10] R. Scheidler, A. Stein, & H.C. Williams, Key-exchange in real quadratic congruence function fields. Designs, Codes and Cryptography7, (1996), no. 1/2, 153-174. Zbl0851.94021MR1377761
- [11] F.K. Schmidt, Analytische Zahlentheorie in Körpern der Charakteristik p. Math. Zeitschr.33 (1931), 1-32. Zbl0001.05401MR1545199JFM57.0229.02
- [12] R.J. SchoofQuadratic fields and factorization. Computational Methods in Number Theory (H. W. Lenstra and R. Tijdemans, eds.,). Math. Centrum Tracts155, 235-286, Part II, Amsterdam1983. Zbl0527.12003MR702519
- [13] D. Shanks, The Infrastructure of a Real Quadratic Field and its Applications. Proc. 1972 Number Theory Conf., Boulder, Colorado, (1972), 217-224. Zbl0334.12005MR389842
- [14] D. Shanks, On Gauss's Class Number Problems. Math. Comp.23 (1969), 151-163. Zbl0177.07103MR262204
- [15] J.H. Silverman, The Arithmetic of Elliptic Curves. Springer, New York, 1986. Zbl0585.14026MR817210
- [16] A. Stein & H.G. Zimmer, An Algorithm for Determining the Regulator and the Fundamental Unit of a Hyperelliptic Congruence Function Field. Proc. 1991 Int. Symp. on Symbolic and Algebraic Computation, Bonn (Germany), July 15-17, ACM Press, 183-184. Zbl0925.11054
- [17] A. Stein, Baby step-Giant step-Verfahren in reell-quadratischen Kongruenzfunktionenkörpern mit Charakteristik ungleich 2. Diplomarbeit, Universität des Saarlandes, Saarbrücken (Germany) 1992.
- [18] A. Stein, Elliptic Congruence Function Fields. Proc. of ANTS II, Bordeaux, 1996, Lecture Notes in Computer Science1122, Springer (1996), 375-384. Zbl0899.11055MR1446525
- [19] A. Stein & H.C. Williams, Baby step Giant step in Real Quadratic Function Fields. Unpublished Manuscript.
- [20] H. Stichtenoth, Algebraic Function Fields and Codes. Springer Verlag, Berlin (1993). Zbl0816.14011MR1251961
- [21] B. Weis & H.G. Zimmer, Artin's Theorie der quadratischen Kongruenzfunktionenkörper und ihre Anwendung auf die Berechnung der Einheiten- und Klassengruppen. Mitt. Math. Ges. Hamburg, Sond.XII (1991), no. 2. Zbl0757.11046MR1144788
- [22] H.C. Williams & M.C. Wunderlich, On the Parallel Generation of the Residues for the Continued Fraction Algorithm. Math. Comp.48 (1987), 405-423. Zbl0617.10005MR866124