Secure Multiparty Sorting Protocols with Covert Privacy

We introduce the notion of covert privacy for secret-sharingbased secure multiparty computation (SMC) protocols. We show how covertly or actively private SMC protocols, together with recently introduced verifiable protocols allow the construction of SMC protocols secure against active adversaries. For certain computational problems, the relative overhead of our protocols, when compared to protocols secure against passive adversaries only, approaches zero as the problem size increases. We analyse the existing adaptations of sorting algorithms to SMC protocols and find that unless they are already using actively secure primitive protocols, none of them are covertly private or verifiable. We propose a covertly private sorting protocol based on radix sort, the relative overhead of which again approaches zero, when compared to the passively secure protocol. Our results reduce the computational effort needed to counteract active adversaries for a significant range of SMC applications, where sorting is used as a subroutine.