We introduce Adaptive Extractors, which unlike traditional randomness extractors, guarantee security even when an adversary obtains leakage on the source \\textit{after} observing the extractor output. We make a compelling case for the study of such extractors by demonstrating their use in obtaining adaptive leakage in secret sharing schemes.<\/p>\n
Specifically, at FOCS 2020, Chattopadhyay, Goodman, Goyal, Kumar, Li, Meka, Zuckerman, built an adaptively secure leakage resilient secret sharing scheme (LRSS) with both rate and leakage rate being $\\mathcal{O}(1\/n)$, where $n$ is the number of parties. In this work, we build an adaptively secure LRSS that offers an interesting trade-off between rate, leakage rate, and the total number of shares from which an adversary can obtain leakage. As a special case, when considering $t$-out-of-$n$ secret sharing schemes for threshold $t = \\alpha n$ (constant $0<\\alpha<1$), we build a scheme with constant rate, constant leakage rate, and allow the adversary leakage from all but $t-1$ of the shares, while giving her the remaining $t-1$ shares completely in the clear. (Prior to this, constant rate LRSS scheme tolerating adaptive leakage was unknown for \\textit{any} threshold.) Finally, we show applications of our techniques to both non-malleable secret sharing and secure message transmission.<\/p>\n","protected":false},"excerpt":{"rendered":"
We introduce Adaptive Extractors, which unlike traditional randomness extractors, guarantee security even when an adversary obtains leakage on the source \\textit{after} observing the extractor output. We make a compelling case for the study of such extractors by demonstrating their use in obtaining adaptive leakage in secret sharing schemes. Specifically, at FOCS 2020, Chattopadhyay, Goodman, Goyal, 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