Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Communications of the ACM
The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
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
Secure Integration of Asymmetric and Symmetric Encryption Schemes
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Applications of Multiple Trust Authorities in Pairing Based Cryptosystems
InfraSec '02 Proceedings of the International Conference on Infrastructure Security
Attribute-based encryption for fine-grained access control of encrypted data
Proceedings of the 13th ACM conference on Computer and communications security
Ciphertext-Policy Attribute-Based Encryption
SP '07 Proceedings of the 2007 IEEE Symposium on Security and Privacy
Discrete Applied Mathematics
A length-flexible threshold cryptosystem with applications
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
The twin Diffie-Hellman problem and applications
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
An interpretation of identity-based cryptography
Foundations of security analysis and design IV
The twin bilinear diffie-Hellman inversion problem and applications
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
The n-Diffie-Hellman problem and its applications
ISC'11 Proceedings of the 14th international conference on Information security
Identity based encryption without redundancy
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Security proof of sakai-kasahara's identity-based encryption scheme
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
The n-Diffie-Hellman problem and its applications
ISC'11 Proceedings of the 14th international conference on Information security
OAKE: a new family of implicitly authenticated diffie-hellman protocols
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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The main contributions of this paper are twofold. On the one hand, the twin Diffie-Hellman (twin DH) problem proposed by Cash, Kiltz and Shoup is extended to the n-Diffie-Hellman (n-DH) problem for an arbitrary integer n, and this new problem is shown to be at least as hard as the ordinary DH problem. Like the twin DH problem, the n-DH problem remains hard even in the presence of a decision oracle that recognizes solution to the problem. On the other hand, observe that the double-size key in the Cash et al. twin DH based encryption scheme can be replaced by two separated keys each for one entity, that results in a 2-party encryption scheme which holds the same security feature as the original scheme but removes the key redundancy. This idea is further extended to an n-party case, which is also known as n-out-of-n encryption. As examples, a variant of ElGamal encryption and a variant of Boneh-Franklin IBE have been presented; both of them have proved to be CCA secure under the computational DH assumption and the computational bilinear Diffie-Hellman (BDH) assumption respectively, in the random oracle model. The two schemes are efficient, due partially to the size of their ciphertext, which is independent to the value n.