This paper shows that the Discrete Logarithm Problem is in ZPP^(MCSP) (where MCSP is the Minimum Circuit Size Problem). This result improves the previous bound that the Discrete Logarithm Problem is in BPP^(MCSP) Allender et al. (2006). In doing so, this paper helps classify the relative difficulty of the Minimum ... more >>>

The notion of online space complexity, introduced by Karp in 1967, quantifies the amount of states required to solve a given problem using an online algorithm,
represented by a machine which scans the input exactly once from left to right.
In this paper, we study alternating machines as introduced by ... more >>>

We construct explicit two-source extractors for $n$ bit sources,
requiring $n^\alpha$ min-entropy and having error $2^{-n^\beta}$,
for some constants $0 < \alpha,\beta < 1$. Previously, constructions
for exponentially small error required either min-entropy
$0.49n$ \cite{Bou05} or three sources \cite{Li15}. The construction
combines somewhere-random condensers based on the Incidence
Theorem \cite{Zuc06,Li11}, ... more >>>