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In privacy amplification, two mutually trusted parties aim to amplify thesecrecy of an initial shared secret $X$ in order to establish a shared privatekey $K$ by exchanging messages over an insecure communication channel. If thechannel is authenticated the task can be solved in a single round ofcommunication using a strong randomness extractor; choosing a quantum-proofextractor allows one to establish security against quantum adversaries.  In the case that the channel is not authenticated, Dodis and Wichs (STOC'09)showed that the problem can be solved in two rounds of communication using anon-malleable extractor, a stronger pseudo-random construction than a strongextractor.  We give the first construction of a non-malleable extractor that is secureagainst quantum adversaries. The extractor is based on a construction by Li(FOCS'12), and is able to extract from source of min-entropy rates larger than$1/2$. Combining this construction with a quantum-proof variant of thereduction of Dodis and Wichs, shown by Cohen and Vidick (unpublished), weobtain the first privacy amplification protocol secure against active quantumadversaries.

A Quantum-Proof Non-Malleable Extractor, With Application to Privacy Amplification against Active Quantum Adversaries