A Collusion-Resistant Distributed Scalar Product Protocol With Application To Privacy-Preserving Computation of Trust

Private scalar product protocols have proved to be interesting in various applications such as data mining, data integration, trust computing, etc. In 2007, Yao et al. proposed a distributed scalar product protocol with application to privacy-preserving computation of trust [1]. This protocol is split in two phases: an homorphic encryption computation; and a private multi-party summation protocol. The summation protocol has two drawbacks: first, it generates a non-negligible communication overhead; and second, it introduces a security flaw. The contribution of this present paper is two-fold. We first prove that the protocol of [1] is not secure in the semi-honest model by showing that it is not resistant to collusion attacks and we give an example of a collusion attack, with only four participants. Second, we propose to use a superposed sending round as an alternative to the multi-party summation protocol, which results in better security properties and in a reduction of the communication costs. In particular, regarding security, we show that the previous scheme was vulnerable to collusions of three users whereas in our proposal we can fix t is an element of [1..n - 1] and define a protocol resisting to collusions of up to t users.