Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Algorithms
CRYPTO '94 Proceedings of the 14th 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
Generic Lower Bounds for Root Extraction and Signature Schemes in General Groups
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Security of Signed ElGamal Encryption
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application 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
Adapting the Weaknesses of the Random Oracle Model to the Generic Group Model
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
The Exact Security of ECIES in the Generic Group Model
Proceedings of the 8th IMA International Conference on Cryptography and Coding
Generic Groups, Collision Resistance, and ECDSA
Designs, Codes and Cryptography
Short Signatures Without Random Oracles and the SDH Assumption in Bilinear Groups
Journal of Cryptology
On Black-Box Ring Extraction and Integer Factorization
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
On the equivalence of RSA and factoring regarding generic ring algorithms
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Abstract models of computation in cryptography
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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The generic group model (GGM) is a commonly used tool in cryptography, especially in the analysis of fundamental cryptographic problems, such as the complexity of the discrete logarithm problem [1,2,3] or the relationship between breaking RSA and factoring integers [4,5,6]. Moreover, the GGM is frequently used to gain confidence in the security of newly introduced computational problems or cryptosystems [7,8,9,10,11]. The GGM serves basically as an idealization of an abstract algebraic group: An algorithm is restricted to basic group operations, such as computing the group law, checking for equality of elements, and possibly additional operations, without being able to exploit any specific property of a given group representation. Different models formalizing the notion of generic groups have been proposed in the literature. Although all models aim to capture the same notion, it is not obvious that a security proof in one model implies security in the other model. Thus the validity of a proven statement may depend on the choice of the model. In this paper we prove the equivalence of the models proposed by Shoup [2] and Maurer [3].