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Privacy Amplification from Non-malleable Codes
Authors: Eshan Chattopadhyay, Bhavana Kanukurthi, Sai Lakshmi Bhavana Obbattu, Sruthi SekarAbstract:
Non-malleable Codes give us the following property: their codewords cannot be tampered into codewords of related messages. Privacy Amplification allows parties to convert their weak shared secret into a fully hidden, uniformly distributed secret key, while communicating on a fully tamperable public channel. In this work, we show how to construct a constant round privacy amplification protocol from any augmented split-state non-malleable code. Existentially, this gives us another primitive (in addition to optimal non-malleable extractors) whose optimal construction would solve the long-standing open problem of building constant round privacy amplification with optimal entropy loss. Instantiating our code with the current best known NMC gives us an 8-round privacy amplification protocol with entropy loss O(\log(n)+ \kappa \log (\kappa)) and min-entropy requirement \Omega(\log(n) +\kappa\log (\kappa)), where \kappa is the security parameter and n is the length of the shared weak secret. In fact, for our result, even the weaker primitive of Non-malleable Randomness Encoders suffice. We view our result as an exciting connection between two of the most fascinating and well-studied information theoretic primitives, non-malleable codes and privacy amplification.
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