Constructing elliptic curves with given group order over large finite fields
作者： Georg-Johann Lay , Horst G. Zimmer
关键词: Elliptic curve 、 Counting points on elliptic curves 、 Supersingular elliptic curve 、 Edwards curve 、 Hessian form of an elliptic curve 、 Complex multiplication 、 Algebra 、 Schoof's algorithm 、 Twists of curves 、 Pure mathematics 、 Mathematics
摘要: A procedure is developed for constructing elliptic curves with given group order over large finite fields. The generality of the construction allows an arbitrary choice parameters involved. For instance, it possible to specify field, or class number endomorphism ring curve. This important various applications in computational theory and cryptography. Moreover, we give a method that yields all representations integer as norm imaginary quadratic field.
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sci-hub.se 参考文章(15)
Alfred Menezes, Isomorphism Classes of Elliptic Curves Over Finite Fields Springer, Boston, MA. pp. 35- 48 ,(1993) , 10.1007/978-1-4615-3198-2_3
Helmut Hasse, Abstrakte begründung der komplexen multiplikation und riemannsche vermutung in funktionenkörpern Abhandlungen Aus Dem Mathematischen Seminar Der Universitat Hamburg. ,vol. 10, pp. 325- 348 ,(1934) , 10.1007/BF02940685
Max Deuring, Die Klassenkörper der komplexen Multiplikation B.G. Teubner. ,(1958)
Harvey Cohn, Introduction to the construction of class fields ,(1985)
François Morain, Building cyclic elliptic curves modulo large primes theory and application of cryptographic techniques. ,vol. 547, pp. 328- 336 ,(1991) , 10.1007/3-540-46416-6_28
Erich Kaltofen, Noriko Yui, Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction Springer, New York, NY. pp. 149- 202 ,(1991) , 10.1007/978-1-4757-4158-2_8
F. Morain, Implementation of the Atkin-Goldwasser-Kilian primality testing algorithm INRIA. ,(1988)
Heinrich Weber, Lehrbuch der Algebra Vieweg+Teubner Verlag. ,(1921) , 10.1007/978-3-663-07282-9
Alfred Menezes, Scott Vanstone, Tatsuaki Okamoto, Reducing elliptic curve logarithms to logarithms in a finite field symposium on the theory of computing. pp. 80- 89 ,(1991) , 10.1145/103418.103434
M. Draeger, M. Deuring, Die Klassenkörper der komplexen Multiplikation (Enzyklopädie der mathematischen Wissenschaften, Band I2, Heft 10, Teil II). Herausgegeben im Auftrage der Akademien der Wissenschaften zu Berlin, Göttingen, Heidelberg, Leipzig, München und Wien sowie unter Mitwirkung zahlreicher Fachgenossen. 60 S. Stuttgart 1958. B. G. Teubner Verlagsgesellschaft. Preis brosch. 15,— DM Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik. ,vol. 40, pp. 150- 150 ,(1960) , 10.1002/ZAMM.19600400139