A public-key cryptosystem with worst-case/average-case equivalence
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Breaking generalized Diffie-Hellman modulo a composite is no easier than factoring
Information Processing Letters
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Proceedings of the nineteenth annual ACM symposium on Principles of distributed computing
Key Agreement in Dynamic Peer Groups
IEEE Transactions on Parallel and Distributed Systems
Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Digital Payment Systems with Passive Anonymity-Revoking Trustees
ESORICS '96 Proceedings of the 4th European Symposium on Research in Computer Security: Computer Security
Designing and Detecting Trapdoors for Discrete Log Cryptosystems
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Algorithms for Black-Box Fields and their Application to Cryptography (Extended Abstract)
CRYPTO '96 Proceedings of the 16th 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
"Indirect Discourse Proof": Achieving Efficient Fair Off-Line E-cash
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Equitable Key Escrow with Limited Time Span (or, How to Enforce Time Expiration Cryptographically)
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
A Note on Security Proofs in the Generic Model
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Anonymous Fingerprinting with Direct Non-repudiation
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Anonymity Control in E-Cash Systems
FC '97 Proceedings of the First International Conference on Financial Cryptography
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
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
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
Efficient Certificateless Signature Schemes
ACNS '07 Proceedings of the 5th international conference on Applied Cryptography and Network Security
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient and Provably Secure Self-certified Signature Scheme
AMT '09 Proceedings of the 5th International Conference on Active Media Technology
Fully Robust Tree-Diffie-Hellman Group Key Exchange
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Enhanced short signature scheme with hybrid problems
Computers and Electrical Engineering
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
Directed transitive signature scheme
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
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The security of many cryptographic constructions relies on assumptions related to Discrete Logarithms (DL), e.g., the Diffie-Hellman, Square Exponent, Inverse Exponent or Representation Problem assumptions. In the concrete formalizations of these assumptions one has some degrees of freedom offered by parameters such as computational model, the problem type (computational, decisional) or success probability of adversary. However, these parameters and their impact are often not properly considered or are simply overlooked in the existing literature. In this paper we identify parameters relevant to cryptographic applications and describe a formal framework for defining DL-related assumptions. This enables us to precisely and systematically classify these assumptions. In particular, we identify a parameter, termed granularity, which describes the underlying probability space in an assumption. Varying granularity we discover the following surprising result: We prove that two DL-related assumptions can be reduced to each other for medium granularity but we also show that they are provably not reducible with generic algorithms for high granularity. Further we show that reductions for medium granularity can achieve much better concrete security than equivalent high-granularity reductions.