7 citations · 10 across the 8 of their papers we have counts for
5 papers · 1 filter
Practical improvements to class group and regulator computation of real quadratic fields
Jean-François Biasse, Jacobson John Michael
We present improvements to the index-calculus algorithm for the computation of the ideal class group and regulator of a real quadratic field. Our improvements consist of applying t…
Security Estimates for Quadratic Field Based Cryptosystems
Jean-François Biasse, Jacobson John Michael, Silverster K. Alan
We describe implementations for solving the discrete logarithm problem in the class group of an imaginary quadratic field and in the infrastructure of a real quadratic field. The a…
Tabulation of cubic function fields via polynomial binary cubic forms
Pieter Rozenhart, Michael Jacobson, Renate Scheidler
We present a method for tabulating all cubic function fields over whose discriminant has either odd degree or even degree and the leading coefficient of …
Computing quadratic function fields with high 3-rank via cubic field tabulation
Pieter Rozenhart, Michael Jacobson, Renate Scheidler
This paper presents an algorithm for generating all imaginary and unusual discriminants up to a fixed degree bound that define a quadratic function field of positive 3-rank. Our me…
Rigorous Computation of Fundamental Units in Algebraic Number Fields
Felix Fontein, Michael J. Jacobson
We present an algorithm that unconditionally computes a representation of the unit group of a number field of discriminant , given a full-rank subgroup as input, in asymptotic…