A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Diffie-Hellman key distribution extended to group communication
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Breaking generalized Diffie-Hellman modulo a composite is no easier than factoring
Information Processing Letters
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Provably authenticated group Diffie-Hellman key exchange
CCS '01 Proceedings of the 8th ACM conference on Computer and Communications Security
Authenticated Diffie-Hellman Key Agreement Protocols
SAC '98 Proceedings of the Selected Areas in Cryptography
A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Dynamic Group Diffie-Hellman Key Exchange under Standard Assumptions
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Provably Authenticated Group Diffie-Hellman Key Exchange - The Dynamic Case
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Group Diffie-Hellman Key Exchange Secure against Dictionary Attacks
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Key Agreement Protocols and Their Security Analysis
Proceedings of the 6th IMA International Conference on Cryptography and Coding
The Decision Diffie-Hellman Problem
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Group Diffie-Hellman Key Exchange Secure against Dictionary Attacks
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Provably secure authenticated group Diffie-Hellman key exchange
ACM Transactions on Information and System Security (TISSEC)
International Journal of Wireless and Mobile Computing
Authenticated wireless roaming via tunnels: making mobile guests feel at home
Proceedings of the 4th International Symposium on Information, Computer, and Communications Security
A generalization of DDH with applications to protocol analysis and computational soundness
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Efficient key agreement for merging clusters in ad-hoc networking environments
EUC'05 Proceedings of the 2005 international conference on Embedded and Ubiquitous Computing
N-Party encrypted diffie-hellman key exchange using different passwords
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
An access control scheme for partially ordered set hierarchy with provable security
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
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In this paper we study generalizations of the Diffie-Hellman problems recently used to construct cryptographic schemes for practical purposes. The Group Computational and the Group Decisional Diffie-Hellman assumptions not only enable one to construct efficient pseudo-random functions but also to naturally extend the Diffie-Hellman protocol to allow more than two parties to agree on a secret key. In this paper we provide results that add to our confidence in the GCDH problem. We reach this aim by showing exact relations among the GCDH, GDDH, CDH and DDH problems.