A quantum circuit to find discrete logarithms on ordinary binary elliptic curves in depth O(log^2n)
Keyword(s):
Improving over an earlier construction by Kaye and Zalka \cite{KaZa04}, in \cite{MMCP09b} Maslov et al. describe an implementation of Shor's algorithm, which can solve the discrete logarithm problem on ordinary binary elliptic curves in quadratic depth $\bigO(n^2)$. In this paper we show that discrete logarithms on such curves can be found with a quantum circuit of depth $\bigO(\log^2n)$. As technical tools we introduce quantum circuits for ${\mathbb F}_{2^n}$-multiplication in depth $\bigO(\log n)$ and for ${\mathbb F}_{2^n}$-inversion in depth $\bigO(\log^2 n)$.
2018 ◽
Vol 51
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pp. 168-182
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2018 ◽
Vol 12
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pp. 101-118
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2004 ◽
Vol 7
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pp. 167-192
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2002 ◽
Vol 5
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pp. 127-174
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2011 ◽
Vol 204-210
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pp. 1318-1321
2010 ◽
Vol 147
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pp. 75-104
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