Cryptographic protocols with adaptive security ensure that security holds against an adversary who can dynamically determine which parties to corrupt as the protocol progresses---or even after the protocol is finished. In the setting where all parties may potentially be corrupted, and secure erasure is not assumed, it has been a long-standing open question to design secure-computation protocols with adaptive security running in constant rounds.
Here, we show a constant-round, universally composable protocol for computing any functionality, tolerating a malicious, adaptive adversary corrupting any number of parties. Interestingly, our protocol can compute all functionalities, not just adaptively well-formed ones.
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