Non-committing Encryption from Φ-hiding

A multiparty computation protocol is said to be adaptively secure if it retains its security even in the presence of an adversary who can corrupt participants as the protocol proceeds. This is in contrast to the static corruption model where the adversary is forced to choose which participants to corrupt before the protocol begins. A central tool for constructing adaptively secure protocols is non-committing encryption (Canetti, Feige, Goldreich and Naor, STOC ’96). The original protocol of Canetti et al. had ciphertext expansion that was quadratic in the security parameter, and prior to this work, the best known constructions had ciphertext expansion that was linear in the security parameter. In this work, we present the first non-committing encryption scheme that achieves ciphertext expansion that is logarithmic in the message length. Our construction has optimal round complexity (2-rounds), where (just as in all previous constructions) the first message consists of a public-key of size Õ(nλ) where n is the message length and λ is the security parameter. The second message consists of a ciphertext of size O(n logn+ λ). The security of our scheme is proved based on the Φ-hiding problem. ∗The work of R. Ostrovsky was supported in part by NSF grants CCF-0916574, IIS-1065276, CCF-1016540, CNS-1118126, CNS-1136174; US-Israel BSF grant 2008411; OKAWA Foundation Research Award; IBM Faculty Research Award; Xerox Faculty Research Award; B. John Garrick Foundation Award; Teradata Research Award; and Lockheed-Martin Corporation Research Award. This material is also based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014-11-1-0392. †Work supported by ISF grant no. 1255/12 and by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 307952. Part of this work done while visiting UCLA.