13 citations · 27 across the 12 of their papers we have counts for
8 papers · 1 filter
Norm relations and computational problems in number fields
Jean-François Biasse, Claus Fieker, Tommy Hofmann +1
For a finite group , we introduce a generalization of norm relations in the group algebra . We give necessary and sufficient criteria for the existence of such rel…
On the computation of the HNF of a module over the ring of integers of a number field
Jean-François Biasse, Claus Fieker, Tommy Hofmann
We present a variation of the modular algorithm for computing the Hermite normal form of an -module presented by Cohen, where is the ring of integers o…
A fast algorithm for finding a short generator of a principal ideal of
Jean-Francois Biasse
We present a heuristic algorithm to compute the ideal class group, and a generator of a principal ideal in in time for $n:= deg(K…
Improvements in the computation of ideal class groups of imaginary quadratic number fields
Jean-François Biasse
We investigate improvements to the algorithm for the computation of ideal class groups described by Jacobson in the imaginary quadratic case. These improvements rely on the large p…
New techniques for computing the ideal class group and a system of fundamental units in number fields
Jean-François Biasse, Claus Fieker
We describe a new algorithm for computing the ideal class group, the regulator and a system of fundamental units in number fields under the generalized Riemann hypothesis. We use s…
An L(1/3) algorithm for discrete logarithm computation and principality testing in certain number fields
Jean-François Biasse
We analyse the complexity of solving the discrete logarithm problem and of testing the principality of ideals in a certain class of number fields. We achieve the subexponential com…
An algorithm for list decoding number field codes
Jean-François Biasse, Guillaume Quintin
We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose c…
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…