We construct non-interactive non-malleable commitments with respect to replacement, without setup in the plain model, under well-studied assumptions.

First, we construct non-interactive non-malleable commitments with respect to commitment for $\epsilon \log \log n$ tags for a small constant $\epsilon>0$, under the following assumptions:

- Sub-exponential hardness of factoring or discrete ... more >>>

After presentations of the oracle separation of BQP and PH result by Raz and Tal [ECCC TR18-107], several people
(e.g. Ryan O’Donnell, James Lee, Avishay Tal) suggested that the proof may be simplified by
stochastic calculus. In this short note, we describe such a simplification.

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In a recent breakthrough result, Chattopadhyay, Mande and Sherif [ECCC TR18-17] showed an exponential separation between the log approximate rank and randomized communication complexity of a total function $f$, hence refuting the log approximate rank conjecture of Lee and Shraibman [2009]. We provide an alternate proof of their randomized communication ... more >>>