Alekseev and Itsykson (STOC 2025) proved the existence of an unsatisfiable CNF formula such that any resolution over parities (Res($\oplus$)) refutation must either have exponential size (in the formula size) or superlinear depth (in the number of variables). In this paper, we extend this result by constructing a formula with ... more >>>

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 >>>