Asymptotically Secure Network Code for Active Attacks

Perfectly Secure Message Transmission Against Rational Adversaries

“…More specifically, 1 The papers studied more general problems of secure network coding. By considering a simple n-link network as in SMT and assuming the adversary who eavesdrops and tampers with the same links, the coding schemes of [33], [7], [34] give constructions of almost-reliable SMT protocols for t < n/2.…”

“…2 Perfect security against a timid adversary can be achieved by an almost reliable SMT if (i) there is no information leaked to the adversary in the protocol execution, and (ii) a legitimate user can identify which channels are modified with high probability. Since the network coding schemes of [7], [34] satisfy the two conditions, they are PSMT protocols against timid adversaries for t < n/2. See [34,Theorem 3] for condition (i) and [34, for condition (ii) of the scheme [34].…”

“…Since the network coding schemes of [7], [34] satisfy the two conditions, they are PSMT protocols against timid adversaries for t < n/2. See [34,Theorem 3] for condition (i) and [34, for condition (ii) of the scheme [34]. See [7, Theorem 3] with Z I = 0 for the scheme [7].…”

Reduction Theorem for Secrecy over Linear Network Code for Active Attacks

“…In fact, as explained in Subsection III-G, this extension is essential because there exists an attack model over a network model such that the secrecy and the detectability of the error are possible with multiple uses of the same network while it is impossible with the single use of the network. Also, another paper will discuss the application of these results to the asymptotic setting [30].…”

“…Thus, we can apply Theorem 2 to the multiple unicast case. The detail discussion for this extension is discussed in the paper [30].…”