We study the implications of the existence of weak Zero-Knowledge (ZK) protocols for worst-case hard languages. These are protocols that have completeness, soundness, and zero-knowledge errors (denoted $\epsilon_c$, $\epsilon_s$, and $\epsilon_z$, respectively) that might not be negligible. Under the assumption that there are worst-case hard languages in NP, we show ... more >>>

Prange's information set algorithm is a decoding algorithm for arbitrary linear codes. It decodes corrupted codewords of any $\mathbb{F}_2$-linear code $C$ of message length $n$ up to relative error rate $O(\log n / n)$ in $\poly(n)$ time. We show that the error rate can be improved to $O((\log n)^2 / ... more >>>