7 citations · 9 across the 6 of their papers we have counts for
9 papers
Finding Orientations of Supersingular Elliptic Curves and Quaternion Orders
Sarah Arpin, James Clements, Pierrick Dartois +3
Orientations of supersingular elliptic curves encode the information of an endomorphism of the curve. Computing the full endomorphism ring is a known hard problem, so one might con…
On the decisional Diffie-Hellman problem for class group actions on oriented elliptic curves
Wouter Castryck, Marc Houben, Frederik Vercauteren +1
We show how the Weil pairing can be used to evaluate the assigned characters of an imaginary quadratic order in an unknown ideal class $[\mathfrak{a}] \in \mathrm{Cl}…
The supersingular isogeny path and endomorphism ring problems are equivalent
Benjamin Wesolowski
We prove that the path-finding problem in -isogeny graphs and the endomorphism ring problem for supersingular elliptic curves are equivalent under reductions of polynomial ex…
Computation of a 30750-Bit Binary Field Discrete Logarithm
Robert Granger, Thorsten Kleinjung, Arjen K. Lenstra +2
This paper reports on the computation of a discrete logarithm in the finite field , breaking by a large margin the previous record, which was set in January…
Discrete logarithms in quasi-polynomial time in finite fields of fixed characteristic
Thorsten Kleinjung, Benjamin Wesolowski
We prove that the discrete logarithm problem can be solved in quasi-polynomial expected time in the multiplicative group of finite fields of fixed characteristic. More generally, w…
Generating subgroups of ray class groups with small prime ideals
Benjamin Wesolowski
Explicit bounds are given on the norms of prime ideals generating arbitrary subgroups of ray class groups of number fields, assuming the Extended Riemann Hypothesis. These are the…
A new perspective on the powers of two descent for discrete logarithms in finite fields
Thorsten Kleinjung, Benjamin Wesolowski
A new proof is given for the correctness of the powers of two descent method for computing discrete logarithms. The result is slightly stronger than the original work, but more imp…
Isogeny graphs of ordinary abelian varieties
Ernest Hunter Brooks, Dimitar Jetchev, Benjamin Wesolowski
Fix a prime number . Graphs of isogenies of degree a power of are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the c…
Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Dimitar Jetchev, Benjamin Wesolowski
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism rin…