Homomorphic Encryption based k-out-of-n Oblivious Transfer Protocols

Oblivious Transfer (OT) is an important cryptographic tool, which has found its usage in many crypto protocols, such as Secure Mul- tiparty Computations (9), Certified E-mail (2) and Simultaneous Con- tract Signing (20). In this paper, we propose three k-out-of-n OT (OTnk) protocols based on additive homomorphic encryption. Two of these pro- tocols prohibit malicious behaviors from both sender and receiver. We also achieve efficient communication complexity bounded by O(l· n) in bits, where l is the size of the encryption key. The computational com- plexity is same or better than the most efficient existing protocols. Due to the semantic security property, the sender cannot get receiver's selec- tion. When the receiver tries to retrieve more than k values, the receiver is caught cheating with 1 1/m probability (Protocol II) or the receiver is unable to get any value at all (Protocol III). We introduce a novel technique based on the solvability of linear equations, which could find its way into other applications. We also provide an experimental analysis to compare the efficiency of the protocols.