Random oracles are practical: a paradigm for designing efficient protocols
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
REACT: Rapid Enhanced-Security Asymmetric Cryptosystem Transform
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
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
Relations Among Notions of Security for Public-Key Encryption Schemes
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Minimizing the use of random oracles in authenticated encryption schemes
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Orthogonality between Key Privacy and Data Privacy, Revisited
Information Security and Cryptology
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
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Recently various public key encryption schemes such as DHIES by Abdalla, Bellare and Rogaway and REACT by Okamoto and Pointcheval, whose security against adaptive chosen ciphertext attack (CCA) is based on the Gap problems, have been proposed. Although the Gap problems were proved to be a sufficient assumption for those schemes to be secure against adaptive chosen-cipertext attack, a necessary condition for CCA security of those schemes has not been explicitly discussed.In this paper we clarify the necessary condition for CCA security of those schemes. Namely we prove (in the random oracle model) that the Gap Diffie-Hellman is not only sufficient, but also a necessary assumption for the CCA security of DHIES and Diffie-Hellman version of REACT. We also show that our result applies to a wider class of public key encryption schemes. Furthermore we show that our result implies the equivalence, in the random oracle model, between 'Strong Diffie-Hellman' and 'Oracle Diffie-Hellman' assumptions proposed by Abdalla, Bellare and Rogaway. Our results may be used as criteria for distinguishing public key encryption schemes whose CCA security is based on strong assumptions (such as Gap Diffie-Hellman) from those schemes based on weaker ones (such as Computational Diffie-Hellman).