k out of n Oblivious Transfer Protocols from Bilinear Pairings

Two non-interactive three parties k out of n oblivious transfer protocols k n OT (where 0<k<n) from bilinear pairings are proposed in this paper. In these protocols, a sender can obliviously transfer n messages to a receiver without communication with him/her. The public keys that a sender used to encrypt his/her messages are made by a third party. The receiver can extract k out of n messages at his/her choices by using the corresponding secret keys. The choices of the receiver are unconditionally secure. The sender's secrecy is guaranteed if the receiver is semi-honest in the standard model since the decision bilinear Diffie-Hellman problem (DBDH) is hard and the sender's secrecy is achieved when the receiver is a malicious party in the random oracle model since the bilinear DiffieHellman problem assumption (BDHA) holds. When a sender is a cheating party, the receiver will detect him/her and halt the protocol. A precise proof of the security of the protocols is presented.