On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography

Details On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography On the Design and Optimization of a Quantum Polynomial-Time Attack on Elliptic Curve Cryptography

2007-10-04

arxiv.org/abs/0710.1093v2

Quantum Information & Computation, 9(7&8):610-621, July 2009.

Physics

Quantum Physics

12 pages, 3 figures: Extended from version submitted to TQC 2008, with corrections

Scientific paper

We consider a quantum polynomial-time algorithm which solves the discrete logarithm problem for points on elliptic curves over $GF(2^m)$. We improve over earlier algorithms by constructing an efficient circuit for multiplying elements of binary finite fields and by representing elliptic curve points using a technique based on projective coordinates. The depth of our proposed implementation, executable in the Linear Nearest Neighbor (LNN) architecture, is $O(m^2)$, which is an improvement over the previous bound of $O(m^3)$ derived assuming no architectural restrictions.

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