33 citations · 218 across the 26 of their papers we have counts for
35 papers
Mathematical Illustration: Proof, Intuition and AI
Edmund Harriss, Katherine Stange
In the French pedagogic tradition of Gaspard Monge, geometry was learned by drawing and handling models: drawing was knowing. The formalism of the early twentieth century placed il…
Extending class group action attacks via sesquilinear pairings
Joseph Macula, Katherine E. Stange
We introduce a new tool for the study of isogeny-based cryptography, namely pairings which are sesquilinear (conjugate linear) with respect to the -module structure of…
Sesquilinear pairings on elliptic curves
Katherine E. Stange
Let be an elliptic curve with complex multiplication by a ring , where is an order in an imaginary quadratic field or quaternion algebra. We define sesquilinear pairings…
On the importance of illustration for mathematical research
Rémi Coulon, Gabriel Dorfsman-Hopkins, Edmund Harriss +3
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illu…
The local-global conjecture for Apollonian circle packings is false
Summer Haag, Clyde Kertzer, James Rickards +1
In a primitive integral Apollonian circle packing, the curvatures that appear must fall into one of six or eight residue classes modulo 24. The local-global conjecture states that…
Factoring using multiplicative relations modulo : a subexponential algorithm inspired by the index calculus
Katherine E. Stange
We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdeter…