How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Provably secure session key distribution: the three party case
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Communications of the ACM
Using encryption for authentication in large networks of computers
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Handbook of Applied Cryptography
Handbook of Applied Cryptography
A Simple Publicly Verifiable Secret Sharing Scheme and Its Application to Electronic
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Efficient Identification and Signatures for Smart Cards
CRYPTO '89 Proceedings of the 9th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Efficient Group Signature Schemes for Large Groups (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
ISC '01 Proceedings of the 4th International Conference on Information Security
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Publicly verifiable secret sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Distributed Pseudo-random functions and KDCs
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Quasi-efficient revocation of group signatures
FC'02 Proceedings of the 6th international conference on Financial cryptography
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In [16], Naor, Pinkas and Reingold introduced schemes in which some groups of servers distribute keys among a set of users in a distributed way. They gave some specific proposals both in the unconditional and in the computational security framework. Their computationally secure scheme is based on the Decisional Diffie-Hellman Assumption. This model assumes secure and authenticated communication between users and servers. Furthermore it requires users to do some expensive computations in order to obtain a key.In this paper we modify the model introduced in [16]. Our model makes the user's computations easier, because most computations of the protocol are carried out by servers, keeping to a more realistic situation. Furthermore, this new model requires only authenticated channels between users and servers.We propose a basic scheme, that makes use of ElGamal cryptosystem, and that fits in with this model in the case of a passive adversary. Then we add zero-knowledge proofs and verifiable secret sharing to prevent from the action of an active adversary. We consider general structures (not only the threshold ones) for those subsets of servers that can provide a key to a user and for those tolerated subsets of servers that can be corrupted by the adversary. We find necessary combinatorial conditions on these structures in order to provide security to our scheme.