Efficient multi-party computation with collusion-deterred secret sharing

Abstract

Many secure multiparty computation (SMC) protocols use Shamir's Secret Sharing (SSS) scheme as a building block. Unlike other cryptographic SMC techniques such as garbled circuits (GC), SSS requires no data expansion and achieves information theoretic security. A weakness of SSS is the possibility of collusion attacks from participants. In this paper, we propose an evolutionary game-theoretic (EGT) approach to deter collusion in SSS-based protocols. First, we consider the possibility of detecting the leak of secret data caused by collusion, devise an explicit retaliation mechanism, and show that the evolutionary stable strategy of this game is not to collude if the technology to detect the leakage of secret is readily available. Then, we consider the situation in which data-owners are unaware of the leakage and thereby unable to retaliate. Such behaviors are deterred by injecting occasional fake collusion requests, and detected by a censorship scheme that destroys subliminal communication. Comparison results show that our collusion-deterred SSS system significantly outperforms GC, while game simulations confirm the validity of our EGT framework on modeling collusion behaviors.