Abstract
We present an improved sequential and a parallel version of the algorithm of Hafner and McCurley for the computation of the class group of imaginary quadratic fields. We describe the implementation of this algorithm on a network of UNIX-workstations using the system LIPS.
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Bibliography
E. Bach, Explicit bounds for primality testing and related problems, Math. Comp 55 (1990), 355–380.
J. Buchmann, M. Diehl, R. Roth, LIPS — a system for distributed applications, preprint 1991.
J. Buchmann, S. Düllmann, A probabilistic class group and regulator algorithm and its implementation, Computational Number Theory (A. Pethö, M. Pohst, H.C. Williams, H.G. Zimmer, eds.), Walter de Gruiter, Berlin, 1991, 53–72.
J. Buchmann, S. Düllmann, H.C. Williams, On the complexity and efficiency of a new key exchange system, Advances in Cryptology — Proceedings EURO-CRYPT’89 (J. Quisquater, J. Vandewalle, eds.), Lecture Notes in Computer Science 434, Springer, Berlin, 1990, 597–616.
J. Buchmann, H.C. Williams, On the computation of the class number of an algebraic number field, Math. Comp. 53 (1989), 679–688.
P.D. Domich, R. Kannan, L.E. Trotter, Hermite normal form computation using modulo determinant arithmetic, Math. Op. Res. 12 (1987), 50–59.
J.L. Hafner, K.S. McCurley, A rigorous subexponential algorithm for computation of class groups, Journal AMS, to appear.
B.A. LaMacchia, A.M. Odlyzko, Computation of discrete Logarithms in Prime Fields, to appear.
C. Pomerance, Analysis and Comparison of some Integer Factoring Algorithms, Computational Methods in Number Theory (R. Tijdeman and H.W. Lenstra, Jr., eds.), Mathematisch Centrum Tract 154, Amsterdam, 1982, 89–139.
R. Schoof, Quadratic fields and factorization, Computational Methods in Number Theory (R. Tijdeman and H.W. Lenstra, Jr., eds.), Mathematisch Centrum Tract 154, Amsterdam, 1982, 235–286.
M. Seysen, A Probabilistic Factorization algorithm with quadratic Forms of Negative Discriminant, Math. Comp. 48 (1987), 737–780.
D. Shanks, Class number, a theory of factorization and genera, Proc. Symp. Pure Math. 20 (1969 Institute on number theory), Amer. Math. Soc, Providence, 1971, 415–440.
D. Shanks, On Gauss and Composition, Number Theory and Applications (R.A. Mollin, ed.), Kluwer Academic Publishers, 1989, 163–204.
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© 1992 B. G. Teubner Verlagsgesellschaft, Leipzig
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Buchmann, J., Düllmann, S. (1992). Distributed Class Group Computation. In: Buchmann, J., Ganzinger, H., Paul, W.J. (eds) Informatik. TEUBNER-TEXTE zur Informatik, vol 1. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-95233-2_5
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DOI: https://doi.org/10.1007/978-3-322-95233-2_5
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-8154-2033-1
Online ISBN: 978-3-322-95233-2
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