Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes

@inproceedings{Boneh1996HardnessOC,
  title={Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes},
  author={Dan Boneh and Ramarathnam Venkatesan},
  booktitle={Annual International Cryptology Conference},
  year={1996}
}
We show that computing the most significant bits of the secret key in a Diffie-Hellman key-exchange protocol from the public keys of the participants is as hard as computing the secret key itself. This is done by studying the following hidden number problem: Given an oracle Oα(x) that on input x computes the k most significant bits of α ċ gx mod p, find α modulo p. Our solution can be used to show the hardness of MSB'S in other schemes such s ElGamal's public key system, Shamir's message… 

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