Author

Swastik Kopparty

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Preprint Oct 2026

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...

S. Kopparty, Rishabh Kothary, Ashutosh Shankar · 0 citations

Preprint Oct 2026

Explicit Nonlinear Functions beyond the Fourier bound

We study the problem of constructing highly nonlinear vectorial maps $F: \mathbb F_2^n \to \mathbb F_2^m$. Concretely, we want an $F$ and an $A = A(m,n)>0$ as small as possible, so that for every affine map $L: \mathbb F_2^n \to \mathbb F_2^m$ (of the form $L(x) = M x + b $) we have: $$\mathrm{agree}(F, L) := |\{ x \in...

Swastik Kopparty, Rishabh Kothary, Shanthanu S. Rai · 0 citations