On Secure Multi-party Computation in Black-Box Groups

Abstract. We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function fG(x1, . . . , xn) = x1 · x2 · · · xn in an arbitrary finite group (G, ·), where the input of party Pi is xi ∈ G for i = 1, . . . , n. For flexibility, we are interested in protocols for fG which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G, ·) is non-abelian and n ≥ 4, then no n/2 -private protocol for computing fG exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for fG based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinato...

• Type: Conference
• Year: 2007
• Where: CRYPTO
• Authors: Yvo Desmedt, Josef Pieprzyk, Ron Steinfeld, Huaxiong Wang
• Keywords: Colouring Construction, CRYPTO 2007, Graph Colouring, Group Elements