Quantum secure non-malleable-extractors
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We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015]. 1) We construct the first explicit quantum secure non-malleable-extractor for (source) min-entropy k ≥(log( n/ϵ)) (n is the length of the source and ϵ is the error parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that the inner-product based non-malleable-extractor proposed by Li [2012] is quantum secure, however it required linear (in n) min-entropy and seed length. Using the connection between non-malleable-extractors and privacy amplification (established first in the quantum setting by Cohen and Vidick [2017]), we get a 2-round privacy amplification protocol that is secure against active quantum adversaries with communication (log( n/ϵ)), exponentially improving upon the linear communication required by the protocol due to [2019]. 2) We construct an explicit quantum secure 2-source non-malleable-extractor for min-entropy k ≥ n- n^Ω(1), with an output of size n^Ω(1) and error 2^- n^Ω(1). 3) We also study their natural extensions when the tampering of the inputs is performed t-times. We construct explicit quantum secure t-non-malleable-extractors for both seeded (t=d^Ω(1)) as well as 2-source case (t=n^Ω(1)).
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