Ping Ngai Chung

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We give a general framework for uniform, constant-time one-and two-dimensional scalar multiplication algorithms for elliptic curves and Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer surface, where we can exploit faster and more uniform pseudomultiplication, before recovering the proper " signed " output back on the curve or(More)
I n 2001 Thomas Hales ([H]; see [M1, Chap. 15]) proved the Honeycomb Conjecture, which says that regular hexagons provide a least-perimeter tiling of the plane by unit-area regions. In this paper we seek perimeter-minimizing tilings of the plane by unit-area pentagons. The regular pentagon has the least perimeter, but it does not tile the plane. There are(More)
We give one-and two-dimensional scalar multiplication algorithms for Jacobians of genus 2 curves that operate by projecting to Kummer surfaces, where we can exploit faster and more uniform pseudo-multiplication, before recovering the proper " signed " output back on the Jacobian. This extends the work of López and Dahab, Okeya and Saku-rai, and Brier and(More)
The prime number theorem is one of the most fundamental theorems of analytic number theory, stating that the prime counting function, π(x), is asymptotic to x/ log x. However, it says little about the parity of π(n) as an arithmetic function. Using Selberg's sieve, we prove a positive lower bound for the proportion of positive integers n such that π(n) is r(More)
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