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Journal of Computer Research and Development

An Efficient 1-out-of-n Oblivious Transfer Protocol with Full Simulation

Xiaochao Wei, Han Jiang, Qianchuan Zhao

Published Nov 1, 2016• 2 citations
Publisher
DOI
10.7544/issn1000-1239.2016.20150505

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In this paper, a universally composable 1-out-of-N oblivious transfer protocol with low communication is built. This protocol obtained full simulation security based on the modulo learning with rounding (Mod-LWR) assumption. It can achieve universally composable security in the random oracle machine (ROM) model by combining random OT based on the key exchange protocol with the authentication encryption algorithm. It can be proven to resist static adversary attacks by simulating all corruption cases. Based on computer simulation and detailed mathematical derivation, this protocol was practicable and had better efficiency and lower communication.
We construct a universal composable framework for two-message oblivious transfer protocols based on lattice-assumption. Compared with the paper proposed by Liu and Hu, we modify a framework proposed by Liu and Hu by adding three tools, which are XOR, Bit Commitment and Smooth Projective Hash Function (SPHF). We instantiate Hash Function as SPHF, which can be more secure in practical application and can achieve full-simulatable in security proof. Compared with Hash Function used as Random Oracle in security proof, this construction is more secure and efficient in security proof. In particular, we mainly consider full-simulatable in simulation, which simulator can simulate any corruption cases. So we mainly consider non-adaptively malicious adversary in Oblivious Transfer protocols.
Bringer et al. proposed two cryptographic protocols for the computation of Hamming distance. Their first scheme uses oblivious transfer and provides security in the semi-honest model. The other scheme uses committed oblivious transfer and is claimed to provide full security in the malicious case. The proposed protocols have direct implications to biometric authentication schemes between a prover and a verifier where the verifier has biometric data of the users in plain form. In this paper, we show that their protocol is not actually fully secure against malicious adversaries. More precisely, our attack breaks the soundness property of their protocol where a malicious user can compute a Hamming distance, which is different from the actual value. For biometric authentication systems, this attack allows a malicious adversary to pass the authentication without knowledge of the honest user's input with at most O(n) complexity instead of O(2n), where n is the input length. We propose an enhanced version of their protocol where this attack is eliminated. The security of our modified protocol is proven using the simulation-based paradigm. Furthermore, as for efficiency concerns, the modified protocol utilizes verifiable oblivious transfer, which does not require the commitments to outputs, which improves its efficiency significantly.