How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Diffie-Hellman key distribution extended to group communication
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
Security of most significant bits of gx2
Information Processing Letters
The Group Diffie-Hellman Problems
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
Towards Realizing Random Oracles: Hash Functions That Hide All Partial Information
CRYPTO '97 Proceedings of the 17th 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
A Tool Box of Cryptographic Functions Related to the Diffie-Hellman Function
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress 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
Number-theoretic constructions of efficient pseudo-random functions
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Completeness theorems for the Abadi-Rogaway language of encrypted expressions
Journal of Computer Security - Special issue on WITS'02
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
Public-key encryption in a multi-user setting: security proofs and improvements
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Adaptive security of symbolic encryption
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Hierarchical identity based encryption with constant size ciphertext
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
On the protocol composition logic PCL
Proceedings of the 2008 ACM symposium on Information, computer and communications security
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
CoSP: a general framework for computational soundness proofs
Proceedings of the 16th ACM conference on Computer and communications security
Computational soundness of non-malleable commitments
ISPEC'08 Proceedings of the 4th international conference on Information security practice and experience
Formal proofs of cryptographic security of Diffie-Hellman-based protocols
TGC'07 Proceedings of the 3rd conference on Trustworthy global computing
Computational soundness of equational theories
TGC'07 Proceedings of the 3rd conference on Trustworthy global computing
Calibrating the power of schedulers for probabilistic polynomial-time calculus
Journal of Computer Security - Security Issues in Concurrency (SecCo'07)
Computationally sound analysis of protocols using bilinear pairings
Journal of Computer Security - 7th International Workshop on Issues in the Theory of Security (WITS'07)
Inductive trace properties for computational security
Journal of Computer Security - 7th International Workshop on Issues in the Theory of Security (WITS'07)
Computational soundness of symbolic zero-knowledge proofs
Journal of Computer Security - 7th International Workshop on Issues in the Theory of Security (WITS'07)
On the equality of probabilistic terms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
A Survey of Symbolic Methods in Computational Analysis of Cryptographic Systems
Journal of Automated Reasoning
Information Sciences: an International Journal
ICISC'11 Proceedings of the 14th international conference on Information Security and Cryptology
Adaptive soundness of static equivalence
ESORICS'07 Proceedings of the 12th European conference on Research in Computer Security
Fast transmission to remote cooperative groups: a new key management paradigm
IEEE/ACM Transactions on Networking (TON)
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In this paper we identify the (P,Q)-DDH assumption, as an extreme, powerful generalization of the Decisional Diffie-Hellman (DDH) assumption: virtually all previously proposed generalizations of DDH are instances of the (P,Q)-DDH problem. We prove that our generalization is no harder than DDH through a concrete reduction that we show to be rather tight in most practical cases. One important consequence of our result is that it yields significantly simpler security proofs for protocols that use extensions of DDH. We exemplify in the case of several group-key exchange protocols (among others we give an elementary, direct proof for the Burmester-Desmedt protocol). Finally, we use our generalization of DDH to extend the celebrated computational soundness result of Abadi and Rogaway [1] so that it can also handle exponentiation and Diffie-Hellman-like keys. The extension that we propose crucially relies on our generalization and seems hard to achieve through other means.