18 citations · 19 across the 3 of their papers we have counts for
5 papers
Products and Polarizations of Super-Isolated Abelian Varieties
Stefano Marseglia, Travis Scholl
In this paper we study super-isolated abelian varieties, that is, abelian varieties over finite fields whose isogeny class contains a single isomorphism class. The goal of this pap…
Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant
Eric Rains, Karl Rubin, Travis Scholl +2
We show that if a rational map is constant on each isomorphism class of unpolarized abelian varieties of a given dimension, then it is a constant map. Our results are motivated by…
Adventures in Supersingularland
Sarah Arpin, Catalina Camacho-Navarro, Kristin Lauter +4
In this paper, we study isogeny graphs of supersingular elliptic curves. Supersingular isogeny graphs were introduced as a hard problem into cryptography by Charles, Goren, and Lau…
Super-Isolated Abelian Varieties
Travis Scholl
We call an abelian variety over a finite field super-isolated if its (-rational) isogeny class contains a single isomorphism class. In this paper, we u…
Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography
Travis Scholl
We call a simple abelian variety over super-isolated if its (-rational) isogeny class contains no other varieties. The motivation for considering these…