Client-Aided Bit-Composition Protocol with Guaranteed Output Delivery

Secure multiparty computation (MPC) enables par-ties to compute an arbitrary function without revealing each party's inputs. A typical MPC is the secret sharing based MPC (SS-MPC). In the SS-MPC, each party distributes its inputs, and the computation proceeds with secret shares that just look like random numbers distributed among the parties. In the SS-MPC protocol, the parties can compute any function represented as a circuit by using shares locally and communicating among the parties. In particular, when the parties compute a complex function composed of binary and arithmetic circuits, an efficient share conversion protocol facilitates the computation of it. An important conversion protocol is the bit-composition protocol that converts a k-dimensional vector with the shares on Z
₂
(i.e., shares of binary sequence) to the shares on Z
₂
k (i.e., shares of decimal value). The previous work proposed a maliciously secure bit-composition protocol with guaranteed output delivery (GOD), which is the security notion that all the parties learn the correct output regardless of the attacker's behaviour. However, its security is proved in the random oracle model.In this paper, we propose a new bit-composition protocol with GOD by introducing additional clients just helping the parties during computation. Our protocol is based on a maliciously secure four-party protocol with one corruption using replicated secret sharing. The security of our protocol is proved in the standard model (which is weaker than the random oracle model). Our protocol achieves the efficiency and strongest security simultaneously. We also propose a protocol for the Hamming distance with GOD by modifying our bit-composition protocol. It achieves a secure iris recognition service via MPC with GOD.