The Discrete Logarithm Hides $O(\log n)$ Bits
Douglas L. Long, Avi Wigderson · SIAM Journal on Computing · 1988
The main result of this paper is that obtaining any information about the $O(\log |p|)$ “most significant” bits of x, given $g^x (\bmod p)$, even with a tiny advantage over guessing, is equivalent to computing discrete logarithms $\bmod p$.