4 papers · 1 filter
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…
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…
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…
Failing to hash into supersingular isogeny graphs
Jeremy Booher, Ross Bowden, Javad Doliskani +12
An important open problem in supersingular isogeny-based cryptography is to produce, without a trusted authority, concrete examples of "hard supersingular curves" that is, equation…