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We construct the first general secure computation protocols that require no trusted infrastructure other than authenticated communication, and that satisfy a meaningful notion of security that is preserved under universal composition---{em assuming only the existence of enhanced trapdoor permutations.} The notion of security is a generalization of the ``angel-based'' notion of Prabhakaran and Sahai (STOC'04) and implies super-polynomial time simulation security.

A key element in our construction is a new notion of security for commitment schemes. The new notion, security against chosen-commitment-attacks (CCA security), means that security holds even if the attacker has access to a {em decommitment oracle.} This notion is stronger than concurrent non-malleability and is of independent interest. Our main technical contribution is constructing CCA-secure commitments based on standard one-way functions, and with no trusted set-up. This provides a construction of a primitive whose emph{adaptive hardness} can be based on standard assumptions without set-up.

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