Non-malleable Condensers for Arbitrary Min-entropy, and Almost Optimal Protocols for Privacy Amplification

Recently, the problem of privacy amplification with an active adversary has received a lot of attention. Given a shared n-bit weak random source X with min-entropy k and a security parameter s, the main goal is to construct an explicit 2-round privacy amplification protocol that achieves entropy loss O(s). Dodis and Wichs [1] showed that optimal protocols can be achieved by constructing explicit non-malleable extractors. However, the best known explicit non-malleable extractor only achieves k = 0.49n [2] and evidence in [2] suggests that constructing explicit non-malleable extractors for smaller min-entropy may be hard. In an alternative approach, Li [3] introduced the notion of a non-malleable condenser and showed that explicit non-malleable condensers also give optimal privacy amplification protocols.

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