13 citations · 27 across the 12 of their papers we have counts for
15 papers
A search-to-decision reduction for the linear code equivalence problem
Jean-François Biasse, Giacomo Micheli, Benjamin Prada +1
We present a polynomial-time reduction from the search variant of the linear code equivalence problem (i.e. the search for a linear isometry between the inputs) to its decisional v…
Code Equivalence and Automorphism Problems for Codes
Jean-Francois Biasse, Alexandra V. Hostetler, Anuvrat Jaindungarwal
We study the complexity of the Code Equivalence problem and show that it is polynomially equivalent to several computational automorphism problems for codes. These problems ask for…
An efficient quantum algorithm for computing -units and its applications
Jean-Francois Biasse, Fang Song
In this paper, we provide details on the proofs of the quantum polynomial time algorithm of Biasse and Song (SODA 16) for computing the -unit group of a number field. This algor…
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…
A note on the security of CSIDH
Jean-François Biasse, Annamaria Iezzi, Michael J. Jacobson
We propose an algorithm for computing an isogeny between two elliptic curves defined over a finite field such that there is an imaginary quadratic order sat…
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…
A polynomial time algorithm for computing the HNF of a module over the integers of a number field
Jean-François Biasse, Claus Fieker
We present a variation of the modular algorithm for computing the Hermite Normal Form of an $\OK$-module presented by Cohen, where $\OK$ is the ring of integers of a number field K…
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…
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…
An L(1/3) algorithm for ideal class group and regulator computation in certain number fields
Jean-François Biasse
We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs fr…