Abstract
In this paper, we focus on lowering the complexity of t-out-of-n string/bit OTs for large t. The notion of oblivious public-key cryptosystem (OPKC) is introduced, in which Bob possesses n public keys but only t private keys and no one knows which t private keys Bob possesses. If the sender, say, Alice, encrypts each message using the n oblivious public keys, resp., the receiver, Bob, can obtain only t messages by t decryptions with his known t private keys. This approach can be directly applied to t-out-of-n bit OT. However, it is very inefficient due to heavy message expansion and many encryption/decryption operations. To construct t-out-of-n bit OT, we introduce bit oblivious public-key cryptosystem (BOPKC), which is a special public-key cryptosystem with a message space of n bits, and the private key only enables its owner to decrypt t bits of n secret bits. After an offline generation of such a BOPKC, it requires only one encryption, one decryption and one ciphertext. Finally, we show the concrete implementations of OPKC/BOPKC based on ElGamal/Paillier cryptosystem, and efficient t-out-of-n string/bit OTs are achieved.
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Wu, Q., Qin, B., Wang, C., Chen, X., Wang, Y. (2005). t-Out-of-n String/Bit Oblivious Transfers Revisited. In: Deng, R.H., Bao, F., Pang, H., Zhou, J. (eds) Information Security Practice and Experience. ISPEC 2005. Lecture Notes in Computer Science, vol 3439. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31979-5_35
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