@article{amento2013efficient,
author = {Amento, B. and Rötteler, M. and Steinwandt, R. and Roetteler, Martin},
title = {Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity},
year = {2013},
month = {January},
abstract = {Elliptic curves over finite fields GF(2n) play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this paper we show that changing the curve representation allows a substantial reduction in the number of T-gates needed to implement the curve arithmetic. As a tool, we present a quantum circuit for computing multiplicative inverses in GF(2n) in depth O(n log n) using a polynomial basis representation, which may be of independent interest.},
url = {http://approjects.co.za/?big=en-us/research/publication/efficient-quantum-circuits-for-binary-elliptic-curve-arithmetic-reducing-t-gate-complexity/},
pages = {631-644},
journal = {Quant. Inform. & Comp.},
volume = {13},
edition = {Quant. Inform. & Comp.},
}