Semi-honest to Malicious Oblivious Transfer—The Black-Box Way

Until recently, all known constructions of oblivious transfer protocols based on general hardness assumptions had the following form. First, the hardness assumption is used in a black-box manner (i.e., the construction uses only the input/output behavior of the primitive guaranteed by the assumption) to construct a

semi-honest

oblivious transfer, a protocol whose security is guaranteed to hold only against adversaries that follow the prescribed protocol. Then, the latter protocol is “compiled” into a (malicious) oblivious transfer using non-black techniques (a Karp reduction is carried in order to prove an NP statement in zero-knowledge).

In their recent breakthrough result, Ishai, Kushilevitz, Lindel and Petrank (STOC ’06) deviated from the above paradigm, presenting a black-box reduction from oblivious transfer to enhanced trapdoor permutations and to homomorphic encryption. Here we generalize their result, presenting a black-box reduction from oblivious transfer to semi-honest oblivious transfer. Consequently, oblivious transfer can be black-box reduced to each of the hardness assumptions known to imply a semi-honest oblivious transfer in a black-box manner. This list currently includes beside the hardness assumptions used by Ishai et al., also the existence of families of dense trapdoor permutations and of non trivial single-server private information retrieval.