An Efficient Non-interactive Universally Composable String-Commitment Scheme
This paper presents a new non-interactive string-commitment scheme that achieves universally composable security. Security is proven under the decisional composite residuosity (DCR) assumption (or the decisional Diffie-Hellman (DDH) assumption) in the common reference string (CRS) model. The universal composability (UC) is a very strong security notion. If cryptographic protocols are proven secure in the UC framework, then they remain secure even if they are composed with arbitrary protocols and polynomially many copies of the protocols are run concurrently. Many UC commitment schemes in the CRS model have been proposed, but they are either interactive commitment or bit-commitment (not string-commitment) schemes. We note, however, that although our scheme is the first non-interactive UC string-commitment scheme, a CRS is not reusable. We use an extension of all-but-one trapdoor functions (ABO-TDFs) proposed by Peikert and Waters at STOC 2008 as an essential building block. Our main idea is to extend (original deterministic) ABO-TDFs to probabilistic ones by using the homomorphic properties of their function indices. The function indices of ABO-TDFs consist of ciphertexts of homomorphic encryption schemes (such as EIGamal, and Damgard-Jurik encryption). Therefore we can re-randomize the output of ABO-TDFs by re-randomization of ciphertexts. This is a new application of ABO-TDFs.
universal composability commitment all-but-one trapdoor function homomorphic encryption