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Lecture notes in computer science

Efficient Committed Oblivious Transfer of Bit Strings

Mehmet Sabır Kiraz, Berry Schoenmakers, José Villegas

Published Jan 1, 2007• 16 citations
Publisher
DOI
10.1007/978-3-540-75496-1_9

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Committed oblivious transfer is the natural fusion of one-out-of-two oblivious transfer and bit commitment. Unfortunately, the protocols proposed before are not only complicated but also very inefficient. This paper describes a new committed oblivious transfer protocol based on a first two round string oblivious transfer and bit commitment with XOR. With a first two round string oblivious transfer, the protocol can avoid performing a large number of bit oblivious transfers. And with bit commitment with XOR, zero knowledge proofs are very easy. The protocol is conceptually simple and more efficient. The security and complexity of the protocol are also discussed in this paper.
Commitment schemes are essential to many cryptographic protocols and schemes with applications that include privacy-preserving computation on data, privacy-preserving authentication, and in particular also in oblivious transfer protocols. For quantum oblivious transfer (qOT) protocols, unconditionally binding commitment schemes that do not rely on hardness assumptions from structured mathematical problems are required. These additional constraints severely limit the choice of commitment schemes to random oracle-based constructions or Naor’s bit commitment scheme. As these protocols commit to individual bits, the use of such commitment schemes comes at a high bandwidth and computational cost.In this work, we investigate improvements to the efficiency of commitment schemes used in qOT protocols and propose an extension of Naor’s commitment scheme requiring the existence of one-way functions (OWF) to reduce communication complexity for 2-bit strings. Additionally, we provide an interactive string commitment scheme with preprocessing to enable a fast and efficient computation of commitments.