Shor's discrete logarithm quantum algorithm for elliptic curves
نویسندگان
چکیده
منابع مشابه
Shor's discrete logarithm quantum algorithm for elliptic curves
We show in some detail how to implement Shor’s efficient quantum algorithm for discrete logarithms for the particular case of elliptic curve groups. It turns out that for this problem a smaller quantum computer can solve problems further beyond current computing than for integer factorisation. A 160 bit elliptic curve cryptographic key could be broken on a quantum computer using around 1000 qub...
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Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2003
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic3.4-3