Randomness is a fundamental requirement in cryptographic systems, enabling secure encryption, commitments, and zero-knowledge proofs. However, real-world randomness sources often suffer from weaknesses that adversaries can exploit, leading to significant security vulnerabilities. While deterministic randomness extraction from a single min-entropy source is impossible, two-source extractors provide a robust solution by ... more >>>

Trevisan and Vadhan [TV00] first constructed seedless extractors for distributions samplable by poly-size circuits under the very strong complexity theoretic hardness assumption that $E=DTIME(2^{O(n)})$ is hard for exponential size circuits with oracle access to $\Sigma_6^{P}$. Their construction works when the distribution has large min-entropy $k=(1-\gamma) \cdot n$, for small constant ... more >>>

Itsykson and Sokolov identified resolution over parities, denoted by $\text{Res}(\oplus)$, as a natural and simple fragment of $\text{AC}^0[2]$-Frege for which no super-polynomial lower bounds on size of proofs are known. Building on a recent line of work, Efremenko and Itsykson proved lower bounds of the form $\text{exp}(N^{\Omega(1)})$, on the size ... more >>>