Assume that $NP\ne RP$. Gutfreund, Shaltiel, and Ta-Shma in [Computational Complexity 16(4):412-441 (2007)] have proved that for every randomized polynomial time decision algorithm $D$ for SAT there is a polynomial time samplable distribution such that $D$ errs with probability at least $1/6-\epsilon$ on a random formula chosen with respect to ... more >>>

We present the first truly explicit constructions of \emph{non-malleable codes} against tampering by bounded polynomial size circuits. These objects imply unproven circuit lower bounds and our construction is secure provided E requires exponential size nondeterministic circuits, an assumption from the derandomization literature.

Prior works on NMC ... more >>>

We show that one-way functions exist if and only there exists an efficient distribution relative to which almost-optimal compression is hard on average. The result is obtained by combining a theorem of Ilango, Ren, and Santhanam [STOC 2022] and one by Bauwens and Zimand [JACM, 2023].

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Trevisan and Vadhan (FOCS 2000) introduced the notion of (seedless) extractors for samplable distributions. They showed that under a very strong complexity theoretic hardness assumption (specifically, that there exists a problem in $\E=\DTIME(2^{O(n)})$ that cannot be computed by size $2^{\Omega(n)}$ circuits that have an oracle to $\Sigma_6^{\P}$) there are extractors ... more >>>