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

TL;DR

This paper introduces the first quantum-proof non-malleable extractor, enabling privacy amplification secure against active quantum adversaries, and demonstrates its application in quantum-secure key establishment.

Contribution

It presents the first construction of a quantum-secure non-malleable extractor and applies it to develop a privacy amplification protocol resilient to active quantum attacks.

Findings

First quantum-proof non-malleable extractor constructed

Achieves extraction from sources with min-entropy rate > 1/2

Enables privacy amplification against active quantum adversaries

Abstract

In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret $X$ in order to establish a shared private key $K$ by exchanging messages over an insecure communication channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor; choosing a quantum-proof extractor 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 a non-malleable extractor, a stronger pseudo-random construction than a strong extractor. We give the first construction of a non-malleable extractor that is secure against 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this construction with a quantum-proof variant of the reduction of Dodis and Wichs, shown by Cohen and Vidick (unpublished), we obtain the first privacy amplification protocol secure against active quantum adversaries.