Abstract. We present a new construction of non-committing encryption schemes. Unlike the previous constructions of Canetti et al. (STOC ’96) and of Damg˚ard and Nielsen (Crypto ’00), our construction achieves all of the following properties: – Optimal round complexity. Our encryption scheme is a 2-round protocol, matching the round complexity of Canetti et al. and improving upon that in Damg˚ard and Nielsen. – Weaker assumptions. Our construction is based on trapdoor simulatable cryptosystems, a new primitive that we introduce as a relaxation of those used in previous works. We also show how to realize this primitive based on hardness of factoring. – Improved efficiency. The amortized complexity of encrypting a single bit is O(1) public key operations on a constant-sized plaintext in the underlying cryptosystem. As a result, we obtain the first non-committing public-key encryption schemes under hardness of factoring and worst-case lattice assumptions; previously, such schemes were only known under the CDH and RSA assumptions. Combined with existing work on secure multi-party computation, we obtain protocols for multi-party computation secure against a malicious adversary that may adaptively corrupt an arbitrary number of parties under weaker assumptions than were previously known. Specifically, we obtain the first adaptively secure multi-party protocols based on hardness of factoring in both the stand-alone setting and the UC setting with a common reference string. Key words: public-key encryption, adaptive corruption, non-committing encryption, secure multi-party computation.