# 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…

## 292 Citations

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### Security of the most significant bits of the Shamir message passing scheme

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For the Diffie-Hellman cryptosystem the result of Boneh and Venkatesan has been corrected and generalized and a similar analysis is given for the Shamir message passing scheme, where the results depend on some bounds of exponential sums.

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