Halving formulae for points on elliptic curves

Abstract

Let $P$ be an arbitrary point on an elliptic curve over the complex numbers of the form $y^2=x^3+a_{4}x+a_6$ or of the form $y^2=x^3+a_2{x}^2+a_{4}x$. We provide explicit formulae to compute the points $P/2$, i.e., the points $Q$ such that $2\ast Q=P$.

6 pages