An algorithm of subexponential type computing the class group of quadratic orders over principal ideal domains

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1122, Issue , 1996, Pages 243-258

  Paulus, Sachar ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

C++ (PROGRAMMING LANGUAGE); CODES (SYMBOLS); COMPUTATION THEORY; COMPUTER PROGRAMMING; NUMBER THEORY;

COMPUTATIONAL REQUIREMENTS; EUCLIDEAN DOMAIN; GENERIC ALGORITHM; PRINCIPAL IDEAL DOMAIN; QUADRATIC FORM; QUADRATIC NUMBER; REDUCTION THEORY; TEMPLATE TECHNIQUE;

ALGORITHMS;

EID: 84958056339     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-61581-4_60     Document Type: Conference Paper

References (15)

1. L. M. Adleman, J. DeMarrais, M.-D. 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 877: Proceedings of ANTS-I, pp. 28-40. Berlin, Heidelberg: Springer Verlag 1994.
2. E. Artin: Quadratische Körper im Gebiete der höheren Kongruenzen L Mathematische Zeitschrift 19 (1924), pp. 153-206. In: S. Lang, J. Tate (eds.): The collected papers of Emil Artin. Reading, Mass.: Addison-Wesley 1965.
3. J. Buchmann, S. Paulus: Algorithms for finite abeiian groups. Extended Abstract. To be published in the proceedings of NTAMCS 93.;
4. D. G. Cantor: Computing in the Jacobian of a hyperelliptic curve. Mathematics of Computation 48 (1987), pp. 95-101.
5. H. Cohen: Algorithms for modules over Dedekind domains and relative extensions of number fields. Preprint.
6. R. Flassenberg, S. Paulus: Computing the rational subgroup of the Jacobian of a hyperelliptic curve over a finite field using sieving techniques. In preparation.
7. C. F. Gautβ: Disquisitiones Arithmeticae. Leipzig: Fleischer 1801.
8. J. L. Hafner, K. S. McCurley: A rigorous subexponential algorithm for the computation of class groups. Journal of the AMS 2 (1989), pp. 837-850.
9. F. Lemmermeyer: The euclidean algorithm in algebraic number fields. Expositiones Math. 13 (1995), pp. 365-416.
10. T. Papanikolaou et al.: LiDIA-Manual. Anonymous ftp: cryptl.cs.uni-sb.de
11. S. Paulus: Algorithmen für endliche abelsche Gruppen. Diplomarbeit. Universität des Saarlandes: 1992.
12. S. Paulus: Ein Algorithmus zur Berechnung der Klassengruppe quadratischer Ordnungen über Hauptidealringen. Dissertation. Universität Essen: 1995.
13. M. Seysen: A Probabilistic Factorization Algorithm with Quadratic Forms of Negative Discriminant. Mathematics of Computation 48 (1987), pp. 757-780.
14. D. Shanks: Class Number, A Theory of Factorization and Genera. Proceedings of Symposia in Pure Mathematics 20 (1970), pp. 415-440.
15. D. B. Zagier: Zetafunktionen und quadratische Körper. Berlin; Heidelberg; New York: Springer 1981.