The complexity of perfect zero-knowledge
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Journal of the ACM (JACM)
Perfectly secure message transmission
Journal of the ACM (JACM)
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Fault-tolerant Computation in the Full Information Model
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Approximation Hardness and Secure Communication in Broadcast Channels
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Issues of fault tolerance in concurrent computations (databases, reliability, transactions, agreement protocols, distributed computing)
Revisiting colored networks and privacy preserving censorship
CRITIS'06 Proceedings of the First international conference on Critical Information Infrastructures Security
Algorithm for proving the knowledge of an independent vertex set
EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
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From a cryptographic aspect zero-knowledge protocols for graph isomorphisms, graph non-isomorphisms, and graph-coloring are artificial problems, that received lots of attention. Due to recent work in network security in a broadcast setting, it seems important to design efficient zero-knowledge protocols for the following graph problems: independent set problem, neighbor independent set problem, and disjoint broadcast lines problem. In this paper, we will introduce a new concept of k-independent set problem which is a generalization of independent set and neighbor independent set problems, and we will present efficient zero-knowledge protocols for these problems. In the end of the paper we will give some cryptographic applications of k-independent set. Especially, we will point out the applications to the concept of "threshold" and appropriate access structures. Note that k-independent set also has applications outside cryptography, such as biology, methodology of scientific research, ethics, etc., which are beyond the scope of this paper.