We construct, under standard hardness assumptions, the first non-malleable commitments secure against quantum attacks. Our commitments are statistically binding and satisfy the standard notion of non-malleability with respect to commitment. We obtain the following instantiations:

begin{itemize}
item A $log^star(lambda)$-round classical protocol based on quantum fully-homomorphic encryption and the quantum hardness of Learning with Errors.

item A polynomial-round classical protocol based on post-quantum oblivious transfer.

item A polynomial-round quantum protocol based on post-quantum one-way functions.
end{itemize}

Previously, non-malleable commitments with quantum security were only known against a restricted class of adversaries known as synchronizing adversaries. At the heart of our results is a general technique that allows to modularly obtain non-malleable commitments from any extractable commitment protocol, obliviously of the underlying extraction strategy (black-box or non-black-box), round complexity, and whether communication is quantum or classical. The transformation preserves the quantum security of the underlying extractable commitments, and is new even in the classical setting.

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