Rishabh Kothary

Bounds on polynomial approximations of the discrete logarithm function

We revisit a classical result of Coppersmith and Shparlinski showing bounds on how well polynomials can approximate the discrete log function. They showed that for any univariate polynomial $f(X) \in \mathbb{F}_p[X]$ with $deg(f) \leq D$, we have: $$ |\{ x \in \mathbb{F}_p^\times \mid f(x) = dlog(x) \}| \leq \sqrt{2 D...