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.
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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