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Hardness of Computing the Most Significant Bits of Secret Keys in Diffie-Hellman and Related Schemes
[chapter]
1996
Lecture Notes in Computer Science
We show that computing the most signicant bits of the secret key in a Die-Hellman keyexchange 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 O ; (x) that on input x computes the k most signicant bits of g x + mod p, nd ; mod p. We present many other applications of this problem including: (1) MSB's in El-Gamal encryptions, Shamir Message passing scheme etc. are hard to
doi:10.1007/3-540-68697-5_11
fatcat:s32fy6mjx5donfnt5sdkpwcayq