An O(m^2)-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2^m)
Keyword(s):
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.
2002 ◽
Vol 5
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pp. 127-174
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2014 ◽
Vol 17
(A)
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pp. 203-217
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2004 ◽
Vol 7
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pp. 167-192
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2010 ◽
Vol 147
(1)
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pp. 75-104
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2004 ◽
Vol 7
◽
pp. 50-72
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