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 zeroknowledge). In their recent breakthrough result, Ishai, Kushilevitz, Lindel and Petrank (STOC ’06) deviated from the above paradigm, presenting a blackbox 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.