Optimal message transmission protocols with flexible parameters

Abstract

In Secure message transmission (SMT) protocols two nodes in a network want to communicate securely, given that some of the nodes in the network are corrupted by an adversary with unlimited computational power. An SMT protocol uses multiple paths between the sender and a receiver to guarantee privacy and reliability of the message transmission. An (ϵ, δ)-SMT protocol bounds the adversary's success probability of breaking privacy and reliability to ε and δ, respectively. Rate optimal SMT protocols have the smallest transmission rate (amount of communication per one bit of message). Rate optimal protocols have been constructed for a restricted set of parameters.In this paper we use wire virtualization method to construct new optimal protocols for a wide range of parameters using previously known optimal protocols. In particular, we design, for the first time, an optimal 1-round (0, δ)-SMT protocol for n = (2 + c)t, c ≥ 1 t , where n is the number of paths between the sender and the receiver, up to t of which are controlled by the adversary. We also design an optimal 2-round (0, 0)-SMT protocol for n = (2 + c)t, c ≥ 1 t , with communication cost better than the known protocols. The wire virtualization method can be used to construct other protocols with provable properties from component protocols.

A General Construction for 1-Round δ-RMT and (0, δ)-SMT

“…For this network our approach will need q ≥ 16000, q 4 computation, the list size will be q 3 and δ = 42 q 4 = 6(10 −6 ), where q is the base field size. For q = 16000, the δ for the protocol in [22] is 0.0263. whereas, δ for the protocol in [21] is not defined (the protocol needs larger field size). To have the same δ as our protocol, [21] needs field size to be 1.2 × 10 14 .…”

“…On the other hand, for N = (2 + c)t, c > 1 t , there are two optimal and efficient 1-round (0, δ)-SMT protocols [22,21]. The protocol of [21] uses two SMT protocols in two levels.…”

“…The protocol of [21] uses two SMT protocols in two levels. The first SMT protocol for the lowest connectivity is used many times on different subsets of the wires.…”

“…There has been two other optimal (transmission rate) and efficient (computation) 1-round (0, δ)-SMT protocols for higher connectivity (N = (2 + c)t, c > 1 t ) [21,22]. The protocol presented in Section 4.2 has the least δ.…”