期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2021
卷号：21
语种：English
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：The known constructions of negligible error (non-malleable) two-source extractors can be broadly classified in three categories: (1) Constructions where one source has min-entropy rate about 12 , the other source can have small min-entropy rate, but the extractor doesn't guarantee non-malleability. (2) Constructions where one source is uniform, and the other can have small min-entropy rate, and the extractor guarantees non-malleability when the uniform source is tampered. (3) Constructions where both sources have entropy rate very close to 1 and the extractor guarantees non-malleability against the tampering of both sources. We introduce a new notion of collision resistant extractors and in using it we obtain a strong two source non-malleable extractor where we require the first source to have 08 entropy rate and the other source can have min-entropy polylogarithmic in the length of the source. We show how the above extractor can be applied to obtain a non-malleable extractor with output rate 21, which is optimal. We also show how, by using our extractor and extending the known protocol, one can obtain a privacy amplification secure against memory tampering where the size of the secret output is almost optimal.
