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Abstract: This article presents algorithms for computing discrete logarithms in class groups of quadratic number elds. In the case of imaginary quadratic elds, the algorithm is based on methods applied by Hafner and McCurley [HM89] to determine the structure of the class group of imaginary quadratic elds. In the case of real quadratic elds, the algorithm of Buchmann [Buc89] for computation of class group and regulator forms the basis. We employ the rigorous elliptic curve factorization algorithm... (Update)
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.... most ecient methods known for solving the principal ideal problem are the babystep giantstep algorithm [7] 1] and the index calculus method [29] [6] The running time of the babystepgiantstep algorithm is n O(n) R 1=2 j j o(1) where n is the degree of F , is the discriminant...
...modulo #JC (k) Hybrid strategy. It should be noted that Vollmer has proposed another strategy in the context of quadratic number elds [84] that can easily be applied to the HCDLP. His strategy is a combination of the previous two, whereby the expensive Smith normal form...
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BibTeX entry: (Update)
U. Vollmer, Asymptotically fast discrete logarithms in quadratic number elds. In Algorithmic Number Theory - ANTS4, LNCS 1838, Springer (Berlin) 2000, 581-594. http://citeseer.ist.psu.edu/vollmer00asymptotically.html More
@inproceedings{ vollmer00asymptotically,
author = "Ulrich Vollmer",
title = "Asymptotically Fast Discrete Logarithms in Quadratic Number Fields",
booktitle = "{ANTS}",
pages = "581-594",
year = "2000",
url = "citeseer.ist.psu.edu/vollmer00asymptotically.html" }
Citations (may not include all citations):352 A course in computational algebraic number theory (context) - Cohen - 1993
50 A key-exchange system based on imaginary quadratic elds (context) - Buchmann, Williams - 1988
33 Explicit bounds for primality testing and related problems (context) - Bach - 1990
25 A subexponential algorithm for the determination of class gr.. - Buchmann
24 A rigorous time bound for factoring integers (context) - Jr, Pomerance - 1992
20 Diophantine linear system solving - Mulders, Storjohann - 1999
19 Cryptographic key distribution and computation in class grou.. (context) - McCurley - 1989
15 Ein Algorithmus zur Berechnung der Klassenzahl und des Regul.. (context) - Abel - 1994
13 the computation of discrete logarithms in class groups (context) - Buchmann, llmann - 1990
13 Certifying inconsistency of sparse linear systems - Giesbrecht, Lobo et al. - 1998
11 rigorous factorization and discrete logarithm algorithms (context) - Pomerance - 1987
5 A rigorous subexpoential algorithm for computation of class .. (context) - Hafner, McCurley - 1989
5 Computing a reduced lattice basis from a generating system - Buchmann, Kessler - 1992
3 A probablistic factorization algorithm with quadratic forms .. (context) - Seysen - 1987
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