Arithmetic geometry, elliptic curves, algebraic and integer sequences, cryptography, arithmetic dynamics, Apollonian circle packings, game theory.
- The Tate pairing via elliptic nets.
- Pairing-based cryptography—Pairing 2007, 329–348, Lecture Notes in Comput. Sci., 4575, Springer, Berlin, 2007.
- Elliptic nets and elliptic curves. Algebra & Number Theory 5 (2011), no. 2, 197–229.
- Silverman, Joseph H.; Stange, Katherine E. Amicable pairs and aliquot cycles for elliptic curves. Exp. Math. 20 (2011), no. 3, 329–357.
- Levine, Lionel; Sheffield, Scott; Stange, Katherine E. A duality principle for selection games. To appear in Proceedings of the American Mathematical Society, 8 pages.
- Integral points on elliptic curves and explicit valuations of division polynomials. Preprint.
- The sensual Apollonian circle packing. Preprint.