Cryptology ePrint Archive: Report 2010/462

Unconditionally Secure Rational Secret Sharing in Standard Communication Networks

Zhifang Zhang

Abstract: Rational secret sharing protocols in both the two-party and multi-party settings are proposed. These protocols are built in standard communication networks and with unconditional security. Namely, the protocols run over standard point-to-point networks without requiring physical assumptions or simultaneous channels, and even a computationally unbounded player cannot gain more than $\epsilon$ by deviating from the protocol. More precisely, for the $2$-out-of-$2$ protocol the $\epsilon$ is a negligible function in the size of the secret, which is caused by the information-theoretic MACs used for authentication. The $t$-out-of-$n$ protocol is $(t-1)$-resilient and the $\epsilon$ is exponentially small in the number of participants. Although secret recovery cannot be guaranteed in this setting, a participant can at least reduce the Shannon entropy of the secret to less than $1$ after the protocol. When the secret-domain is large, every rational player has great incentive to participate in the protocol.

Category / Keywords: cryptographic protocols / rational secret sharing, $\epsilon$-Nash equilibrium, unconditional security

Date: received 30 Aug 2010, last revised 1 Nov 2010

Contact author: zfz at amss ac cn

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Version: 20101102:022421 (All versions of this report)

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