Towards Optimal and Efficient Perfectly Secure Message Transmission

Abstract

Abstract. Perfectly secure message transmission (PSMT), a problem formulated by Dolev, Dwork, Waarts and Yung, involves a sender S and a recipient R who are connected by n synchronous channels of which up to t may be corrupted by an active adversary. The goal is to transmit, with perfect security, a message from S to R. PSMT is achievable if and only if n > 2t.For the case n > 2t, the lower bound on the number of communication rounds between S and R required for PSMT is 2, and the only known efficient (i.e., polynomial in n) two-round protocol involves a communication complexity of O(n 3 ) bits, where is the length of the message. A recent solution by Agarwal, Cramer and de Haan is provably communication-optimal by achieving an asymptotic communication complexity of O(n ) bits; however, it requires the messages to be exponentially large, i.e., = Ω(2 n ). In this paper we present an efficient communication-optimal tworound PSMT protocol for messages of length polynomial in n that is almost optimally resilient in that it requires a number of channels n ≥ (2 + ε)t, for any arbitrarily small constant ε > 0. In this case, optimal communication complexity is O( ) bits.

Error decodable secret sharing and one-round perfectly secure message transmission for general adversary structures

“…Kurosawa points out that in the case of a threshold adversary, this results in the need to transmit considerably more information over each of the channels in T than if an ideal threshold scheme were used [16], a result whose secret-sharing analogue is well-known (see [14], for example). If an ideal threshold scheme is used then the resulting overhead is precisely n. However, it is possible to do better than this, as illustrated by the following corollary to Theorem 5.6, which re-proves a result that appears in [10].…”

Quantum Key Management

“…Moreover, it constitutes a necessity for perfectly secure communication, as has rigorously been proven by Wang & Desmedt (2008), Fitzi et al (2007) and Ashwin Kumar et al (2002). The remaining problem with these results still is their limited applicability in real-life networks, as many known criteria for perfectly secure communication impose strong requirements on the graph's (vertex) connectivity.…”

Secure Message Transmission with Small Public Discussion

“…The goal is to send the message both privately and reliably. Since its introduction, SMT has been widely studied and optimized with respect to several different settings of parameters (for example, see [SA96,SNP04,ACH06,FFGV07,KS08]). …”

“…For 1-round PSMT, Fitzi et al [FFGV07] show that transmission rate ≥ n n−3t is necessary and sufficient. (Recall that n > 3t is required in this case.)…”