caa a22 4500 475827147 CHVBK 20180406123831.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/s001450010013 doi (NATIONALLICENCE)springer-10.1007/s001450010013 Jacobson Michael J. Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 mjjacobs@cacr.math.uwaterloo.ca, CA aut Computing Discrete Logarithms in Quadratic Orders [Elektronische Daten] [Michael J. Jacobson] Abstract. : We present efficient algorithms for computing discrete logarithms in the class group of a quadratic order and for principality testing in a real quadratic order, based on the work of Düllmann and Abel. We show how the idea of generating relations with sieving can be applied to improve the performance of these algorithms. Computational results are presented which demonstrate that our new techniques yield a significant increase in the sizes of discriminants for which these discrete logarithm problems can be solved. International Association for Criptologic Rese, 2000 Key words. Discrete logarithm, Principal ideal testing, Quadratic order, Class group, Computational number theory nationallicence Journal of Cryptology Springer Berlin Heidelberg 13/4(2000-09-01), 473-492 0933-2790 13:4<473 2000 13 145 https://doi.org/10.1007/s001450010013 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001450010013 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Jacobson Michael J. Centre for Applied Cryptographic Research, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 mjjacobs@cacr.math.uwaterloo.ca, CA aut NATIONALLICENCE 773 0- Journal of Cryptology Springer Berlin Heidelberg 13/4(2000-09-01), 473-492 0933-2790 13:4<473 2000 13 145 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer