Perfectly Secure Message Transmission Research Articles

Perfectly Secure Message Transmission Against Rational Adversaries

Secure Message Transmission (SMT) is a two-party cryptographic protocol by which the sender can securely and reliably transmit messages to the receiver using multiple channels. An adversary can corrupt a subset of the channels and commit eavesdropping and tampering attacks over the channels. In this work, we introduce a game-theoretic security model for SMT in which adversaries have some preferences for protocol execution. We define rational “timid” adversaries who prefer to violate security requirements but do not prefer the tampering to be detected. First, we consider the basic setting where a single adversary attacks the protocol. We construct perfect SMT protocols against any rational adversary corrupting all but one of the channels. Since minority corruption is required in the traditional setting, our results demonstrate a way of circumventing the cryptographic impossibility results by a game-theoretic approach. Next, we study the setting in which all the channels can be corrupted by multiple adversaries who do not cooperate. Since we cannot hope for any security if a single adversary corrupts all the channels or multiple adversaries cooperate maliciously, the scenario can arise from a game-theoretic model. We also study the scenario in which both malicious and rational adversaries exist.

Efficient Protocols for Perfectly Secure Message Transmission With Applications to Secure Network Coding

In the model that has become known as “Perfectly Secure Message Transmission” (PSMT), a sender Alice is connected to a receiver Bob through $n$ parallel two-way channels. A computationally unbounded adversary Eve controls $t$ of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve gains no information about the message while Bob is able to recover it completely. We focus on PSMT protocols that work in two transmission rounds for $n= 2t+1$ . We break from previous work by following a conceptually simpler blueprint. This has two consequences: first, we obtain improved efficiency, namely, we reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from $\mathcal {O}(n^{3}\log n)$ to $\mathcal {O}(n^{2}\log n)$ . Our solution also reaches optimal transmission rate for a secret of size $\mathcal {O}(n \log n)$ , thus answering the hitherto open question of attaining a threshold below $\mathcal {O}(n^{2} \log n)$ bits. Second, our construction can be adapted to more general scenarios relevant to Network Coding, where the adversary is given more power.

Round-efficient perfectly secure message transmission scheme against general adversary

In the model of Perfectly Secure Message Transmission Schemes (PSMTs), there are n channels between a sender and a receiver, and they share no key. An infinitely powerful adversary A can corrupt (observe and forge) the messages sent through some subset of n channels. For non-threshold adversaries called Q 2, Kumar et al. showed a many round PSMT (Ashwin Kumar et al. On perfectly secure communication over arbitrary networks. PODC 2002, pp. 193---202, 2002). In this paper, we show round efficient PSMTs against Q 2-adevrsaries. We first give a 3-round PSMT which runs in polynomial time in the size of the underlying linear secret sharing scheme. We next present a 2-round PSMT which is inefficient in general. (However, it is efficient for some special case.)

Secure message transmission in asynchronous networks

In the Perfectly Secure Message Transmission (PSMT) problem, a sender S and a receiver R are part of a distributed network and connected through n node disjoint paths, also called as wires, among which at most t wires are controlled by a static, Byzantine adversary A t s t a t i c , having unbounded computing power. S has a message m , which S intends to send to R. The challenge is to design a protocol, such that at the end of the protocol, R should correctly output m without any error (perfect reliability) and A t s t a t i c should not get any information about m , whatsoever, in information theoretic sense (perfect security). The problem of Statistically Secure Message Transmission (SSMT) is same as PSMT, except that R should correctly output m with very high probability. Sayeed and Abu-Amara (1995) [37] have given a PSMT protocol in an asynchronous network tolerating A t s t a t i c , where S and R are connected by n = 2 t + 1 wires. However, we show that their protocol does not provide perfect security. We then prove that in an asynchronous network, if all the n wires are directed from S to R, then any PSMT protocol tolerating A t s t a t i c is possible iff n > 3 t . Surprisingly, we also prove that even if all the n wires are bi-directional, then any PSMT protocol in asynchronous network tolerating A t s t a t i c is possible iff n > 3 t . This is quite surprising because for synchronous networks, by the results of Dolev et al. (1993) [16], if all the wires are unidirectional (directed from S to R), then PSMT tolerating A t s t a t i c is possible iff n > 3 t , where as if all the wires are bi-directional then PSMT tolerating A t s t a t i c is possible iff n > 2 t . This shows that asynchrony of the network demands higher connectivity of the network for the existence of PSMT protocols. Interestingly, we further show that n > 2 t wires are necessary and sufficient for the existence of any SSMT protocol in asynchronous network tolerating A t s t a t i c , irrespective of whether the n wires are unidirectional from S to R or the n wires are bi-directional. By the results of Franklin and Wright (2000) [18] and Kurosawa and Suzuki (2009) [22], n > 2 t wires are necessary and sufficient for the existence of SSMT in synchronous networks, irrespective of whether the n wires are unidirectional from S to R or the n wires are bi-directional. This shows that asynchrony of the network does not demand higher connectivity of the network for SSMT protocols.

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

An error decodable secret-sharing scheme is a secret-sharing scheme with the additional property that the secret can be recovered from the set of all shares, even after a coalition of participants corrupts the shares they possess. In this paper, schemes that can tolerate corruption by sets of participants belonging to a monotone coalition structure are considered. This coalition structure may be unrelated to the authorised sets of the secret-sharing scheme. This is generalisation of both a related notion studied in the context of multiparty computation, and the well-known error-correction properties of threshold schemes based on Reed-Solomon codes. Necessary and sufficient conditions for the existence of such schemes are deduced, and methods for reducing the storage requirements of a technique of Kurosawa for constructing error-decodable secret-sharing schemes with efficient decoding algorithms are demonstrated. In addition, the connection between one-round perfectly secure message transmission (PSMT) schemes with general adversary structures and secret-sharing schemes is explored. We prove a theorem that explicitly shows the relation between these structures. In particular, an error decodable secret-sharing scheme yields a one-round PSMT, but the converse does not hold. Furthermore, we are able to show that some well-known results concerning one-round PSMT follow from known results on secret-sharing schemes. These connections are exploited to investigate factors affecting the performance of one-round PSMT schemes such as the number of channels required, the communication overhead, and the efficiency of message recovery.

Truly Efficient $2$-Round Perfectly Secure Message Transmission Scheme

In the model of perfectly secure message transmission (PSMT) schemes, there are n channels between a sender and a receiver. An infinitely powerful adversary A may corrupt (observe and forge) the messages sent through t out of n channels. The sender wishes to send a secret s to the receiver perfectly privately and perfectly reliably without sharing any key with the receiver. In this paper, we show the first 2-round PSMT for n = 2t + 1 such that not only the transmission rate is O(n) but also the computational costs of the sender and the receiver are both polynomial in n. This means that we solve the open problem raised by Agarwal, Cramer, and de Haan at CRYPTO 2006. The main novelty of our approach is to introduce a notion of pseudobasis to the coding theory. It will be an independent interest for coding theory, too.

Perfectly reliable and secure message transmission tolerating mobile adversary

We study the problem of perfectly reliable message transmission (PRMT) and perfectly secure message transmission (PSMT) in an undirected synchronous network tolerating an all powerful threshold mobile Byzantine adversary. Specifically, we show that the mobility of the threshold adversary does not affect the possibility and optimality of PRMT and PSMT protocols. We also characterise PSMT in directed networks tolerating mobile adversary. All existing PRMT and PSMT protocols abstract the paths between the sender and the receiver as wires, neglecting the intermediate nodes in the paths, thus causing significant over estimation in the communication and round complexity of protocols. Here, we consider the underlying paths as a whole instead of abstracting them as wires and derive a tight bound on the number of rounds required to achieve reliable communication tolerating a threshold mobile adversary with arbitrary roaming speed. Finally, we briefly study PRMT and PSMT protocols in the presence of non-threshold mobile Byzantine adversary. Even though the characterisation for PRMT/PSMT is shown to be same against both threshold static and threshold mobile adversary (in this article), we show that the characterisation for PRMT/PSMT against non-threshold static and non-threshold mobile adversary are not same.

Perfectly Reliable Message Transmission

We consider the problem of reliable message transmission between two synchronous players connected by n wires, some t < n 2 of which may be faulty. We show how to get reliability “for free”—reliable transmission of b bits involves a total communication of only O ( b ) bits, when b is large enough. We also construct an efficient Perfectly Secure Message Transmission Protocol.