The Hidden Number Problem
The Hidden Number Problem (HNP) is a problem that poses the question: Are the most signficant bits of a Diffie-Hellman shared key as hard to compute as the entire secret? The original problem was defined in the paper “Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes” by Dan Boneh and Ramarathnam Venkatesan.
In this paper Boneh and Venkatesan demonstrate that a bounded number of most signifcant bits of a shared secret are as hard to compute as the entire secret itself. They also demonstrate an efficient algorithm for recovering secrets given a significant enough bit leakage. This notebook walks through some of the paper and demonstrates some of the results.