On Recent Advances in Key Derivation via the Leftover Hash Lemma

Barak et al. showed how to significantly reduce the entropy loss, which is necessary in general, in the use of the Leftover Hash Lemma (LHL) to derive a secure key for many important cryptographic applications. If one wants this key to be secure against any additional short leakage, then the min-entropy of the source used with the LHL must be big enough. Recently, Berens came up with a notion of collision entropy that is much weaker than min-entropy and allows proving a version of the LHL with leakage robustness but without any entropy saving. We combine both approaches and extend the results of Barak et. al to the collision entropy. Summarizing, we obtain a version of the LHL with optimized entropy loss, leakage robustness and weak entropy requirements

Handy Formulas for Binomial Moments

Despite the relevance of the binomial distribution for probability theory and applied statistical inference, its higher-order moments are poorly understood. The existing formulas are either not general enough, or not structured or simplified enough for intended applications. This paper introduces novel formulas for binomial moments, in terms of \emph{variance} rather than success probability. The obtained formulas are arguably better structured and simpler compared to prior works. In addition, the paper presents algorithms to derive these formulas along with working implementation in the Python symbolic algebra package. The novel approach is a combinatorial argument coupled with clever algebraic simplifications which rely on symmetrization theory. As an interesting byproduct we establish \emph{asymptotically sharp estimates for central binomial moments}, improving upon partial results from prior works