48 citations · 63 across the 5 of their papers we have counts for
7 papers
Computing Modular Polynomials
Denis Charles, Kristin Lauter
We present a new probabilistic algorithm to compute modular polynomials modulo a prime. Modular polynomials parameterize pairs of isogenous elliptic curves and are useful in many a…
Class invariants for quartic CM fields
Eyal Z. Goren, Kristin E. Lauter
One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. We provide ex…
Improved Weil and Tate pairings for elliptic and hyperelliptic curves
Kirsten Eisentraeger, Kristin Lauter, Peter L. Montgomery
We present algorithms for computing the squared Weil and Tate pairings on elliptic curves and the squared Tate pairing for hyperelliptic curves. The squared pairings introduced in…
Primes in the denominators of Igusa Class Polynomials
Kristin Lauter
The purpose of this note is to suggest an analogue for genus 2 curves of part of Gross and Zagier's work on elliptic curves. Experimentally, for genus 2 curves with CM by a quartic…
Fast Elliptic Curve Arithmetic and Improved Weil Pairing Evaluation
Kirsten Eisentraeger, Kristin Lauter, Peter L. Montgomery
We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8 % to 8.5 % over the best known general methods when using affine coordina…
Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields
Kristin Lauter, Jean-Pierre Serre
Currently, the best upper bounds on the number of rational points on an absolutely irreducible, smooth, projective algebraic curve of genus g defined over a finite field F_q come e…