Picard groups and refined discrete logarithms

erschienen 31. Januar 2005 LMS Journal of Computation and Mathematics

Abstract:

Let K denote a number field, and G a finite abelian group. The ring of algebraic integers in K is denoted in this paper by O_K, and A denotes any O_K-order in K[G]. The paper describes an algorithm that explicitly computes the Picard group Pic(A), and solves the corresponding (refined) discrete logarithm problem. A tamely ramified extension L/K of prime degree l of an imaginary quadratic number field K is used as an example; the class of O_L in Pic(O_K[G]) can be numerically determined.

Links:

• Picard Groups and Refined Discrete Logarithms