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Journal of Circuits and Systems

An efficient PMPC protocol

Jianhua Ge

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The private multi-party computation protocol proposed by Claude Crepeau etc.is not only complicated but very inefficient.This paper describes a new protocol with an efficient global commitment transfer sub-protocol.With a first two round string oblivious transfer,the protocol can avoid performing a large mount of bit oblivious transfers.And with bit commitment with XOR,zero knowledge proofs are very easy.This PMPC protocol is conceptually simple and more efficient.The security and complexity of the protocol are also discussed in this paper.

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The private multi-party computation protocol proposed by Claude Crepeau etc.is not only complicated but very inefficient.This paper describes a new protocol with an efficient global commitment transfer sub-protocol.With a first two round string oblivious transfer,the protocol can avoid performing a large mount of bit oblivious transfers.And with bit commitment with XOR,zero knowledge proofs are very easy.This PMPC protocol is conceptually simple and more efficient.The security and complexity of the protocol are also discussed in this paper.
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.
The problem of secure multi-party computation(SMPC) is one of the most fundamental problems in information security. First, we introduce the basic concept of SMPC and four SMPC basic agreement: key distribution,oblivious transfer, bit commitment and zero knowledge proof. Secondly, we separately illustrate commitment schemes  commitment transfer protocol, commitment sharing protocol and commitment multiplication protocol. Finally, we present unconditionally secure multi-party computation with a passive adversary, an active adversary, general adversary structures.
We consider the problem of designing an efficient oblivious transfer (OT) protocol that is provably secure in a concurrent setting, i.e., where many OT sessions may be running concurrently with their messages interleaved arbitrarily. Known OT protocols use zero-knowledge proofs, and no concurrent zero-knowledge proofs are known that use less than a poly-logarithmic number of rounds (at least without requiring a pre-processing phase, a public random string, an auxiliary string, timing constraints, or pre-distributed public keys). We introduce a model for proving security of concurrent OT protocols, and present a protocol that is proven secure in this model based on the decisional Diffie-Hellman problem. The protocol is efficient, requiring only a slightly non-constant number of rounds.
We present a round-efficient black-box construction of a general multi-party computation (MPC) protocol that satisfies composability in the plain model. The security of our protocol is proven in the angel-based UC framework [Prabhakaran and Sahai, STOC’04] under the minimal assumption of the existence of semi-honest oblivious transfer protocols. The round complexity of our protocol is max⁡(O~(log⁡2n),O(ROT))\max (\widetilde{O}(\log ^2n), O(R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))max(O(log2n),O(ROT​)) when the round complexity of the underlying oblivious transfer protocol is ROTR_{{{{\mathsf {O}}}{{\mathsf {T}}}}}ROT​ . Since constant-round semi-honest oblivious transfer protocols can be constructed under standard assumptions (such as the existence of enhanced trapdoor permutations), our result gives a O~(log⁡2n)\widetilde{O}(\log ^2n)O(log2n) -round protocol under these assumptions. Previously, only an O(max⁡(nϵ,ROT))O(\max (n^{\epsilon }, R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))O(max(nϵ,ROT​)) -round protocol was shown, where ϵ>0\epsilon >0ϵ>0 is an arbitrary constant. We obtain our MPC protocol by constructing a O~(log⁡2n)\widetilde{O}(\log ^2n)O(log2n) -round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.
A two-party oblivious circuit evaluation (2P- OCE) protocol is a way for a party Alice owns a secret x and another party Bob owns a secret y to compute the value of an agreed upon function f(x,y), where f can be computed by a polynomial sized Boolean circuit. This is done in such a way that Alice learns nothing about y and Bob learns nothing about x, except for what can be inferred from one's private input and the public value of f(x,y). This paper presents a general, correct, fair, honest, and maximum privacy 2P-OCE protocol that is based on a set of reductions to more simple cryptographic primitives. The protocol uses the primitives of one-out-of-two oblivious transfer (1-2-OT) and bit commitment (BC) as black boxes. Consequently, the protocol may be implemented with or without computational assumptions, depending on the type of 1-2-OT and BC used by participants.