Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity
Quantum Physics
2013-12-05 v1 Data Structures and Algorithms
Emerging Technologies
Abstract
Elliptic curves over finite fields GF(2^n) 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(2^n) in depth O(n log n) using a polynomial basis representation, which may be of independent interest.
Keywords
Cite
@article{arxiv.1209.6348,
title = {Efficient quantum circuits for binary elliptic curve arithmetic: reducing T-gate complexity},
author = {Brittanney Amento and Rainer Steinwandt and Martin Roetteler},
journal= {arXiv preprint arXiv:1209.6348},
year = {2013}
}
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14 pages