On the Bit Security of Elliptic Curve Diffie-Hellman
نویسنده
چکیده
This paper gives the first bit security result for the elliptic curve Diffie–Hellman key exchange protocol for elliptic curves defined over prime fields. About 5/6 of the most significant bits of the x-coordinate of the Diffie–Hellman key are as hard to compute as the entire key. A similar result can be derived for the 5/6 lower bits. The paper also generalizes and improves the result for elliptic curves over extension fields, that shows that computing one component (in the ground field) of the Diffie–Hellman key is as hard to compute as the entire key.
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