How to share a secret with cheaters
Journal of Cryptology
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Perfectly secure message transmission
Journal of the ACM (JACM)
Size of shares and probability of cheating in threshold schemes
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Robust vector space secret sharing schemes
Information Processing Letters
Detection of Cheaters in Vector Space Secret Sharing Schemes
Designs, Codes and Cryptography
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
Designs, Codes and Cryptography
Robust key establishment in sensor networks
ACM SIGMOD Record
Optimum Secret Sharing Scheme Secure against Cheating
SIAM Journal on Discrete Mathematics
Almost Secure (1-Round, n-Channel) Message Transmission Scheme
Information Theoretic Security
Towards optimal and efficient perfectly secure message transmission
TCC'07 Proceedings of the 4th conference on Theory of cryptography
International Journal of Applied Cryptography
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
Almost optimum secret sharing schemes secure against cheating for arbitrary secret distribution
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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In the Secure Message Transmission (SMT) problem, a sender $\cal S$ is connected to a receiver $\cal R$ through n node-disjoint paths in the network, a subset of which are controlled by an adversary with unlimited computational power. $\cal{S}$ wants to send a message m to $\cal{R}$ in a private and reliable way. Constructing secure and efficient SMT protocols against a threshold adversary who can corrupt at most t out of n wires, has been extensively researched. However less is known about SMT problem for a generalized adversary who can corrupt one out of a set of possible subsets. In this paper we focus on 1-round (0,δ)-SMT protocols where privacy is perfect and the chance of protocol failure (receiver outputting NULL ) is bounded by δ. These protocols are especially attractive because of their possible practical applications. We first show an equivalence between secret sharing with cheating and canonical 1-round (0, δ)-SMT against a generalized adversary. This generalizes a similar result known for threshold adversaries. We use this equivalence to obtain a lower bound on the communication complexity of canonical 1-round (0, δ)-SMT against a generalized adversary. We also derive a lower bound on the communication complexity of a general 1-round (0, 0)-SMT against a generalized adversary. We finally give a construction using a linear secret sharing scheme and a special type of hash function. The protocol has almost optimal communication complexity and achieves this efficiency for a single message (does not require block of message to be sent).