Bits Security of the Elliptic Curve Diffie-Hellman Secret Keys

@inproceedings{Jetchev2008BitsSO,
  title={Bits Security of the Elliptic Curve Diffie-Hellman Secret Keys},
  author={Dimitar Jetchev and Ramarathnam Venkatesan},
  booktitle={CRYPTO},
  year={2008}
}
We show that the least significant bits (LSB) of the elliptic curve Diffie---Hellman secret keys are hardcore. More precisely, we prove that if one can efficiently predict the LSB with non-negligible advantage on a polynomial fraction of all the curves defined over a given finite field $\mathbb{F}_p$, then with polynomial factor overhead, one can compute the entire Diffie---Hellman secret on a polynomial fraction of all the curves over the same finite field. Our approach is based on random self… 

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