Abstract
To describe the design approaches of IND-CCA2 (adaptive chosen ciphertext attack) secure public key encryption schemes systematically, the gaps between different kinds of intractable problems and IND-CCA2 security are studied. This paper points out that the construction of IND-CCA2 secure schemes is essentially to bridge these gaps. These gaps are categorized, analyzed and measured. Finally the methods to bridge these gaps are described. This explains the existing design approaches and gives an intuition about the difficulty of designing IND-CCA2 secure public key encryption schemes based on different types of assumptions.
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References
Naor M, Yung M. Public-key cryptosystems provably-secure against chosen-ciphertext attacks [C]// 22nd ACM Symposium on Theory of Computing. New York: ACM, 1990: 427–437.
Rivest R L, Shamir A, Adleman L. A method for obtaining digital signatures and public-key cryptosystems [J]. Communications of the ACM, 1978, 21(2): 120–126.
El Gamal T. A public key cryptosystem and signature scheme based on discrete logarithms [J]. IEEE Transaction on Information Theory, 1985, 31(4): 469–472.
Okamoto T, Pointcheval D. REACT: Rapid enhanced-security asymmetric cryptosystem transform [C]//RSA 2001. Berlin/Heidelberg: Springer-Verlag, 2001: 159–174.
Cash D, Kiltz E, Shoup V. The twin Diffie-Hellman problem and applications [C]//Advances in Cryptology-EUROCRYPT 2008. Berlin/Heidelberg: Springer-Verlag, 2008: 127–145.
Cramer R, Shoup V. A practical public key cryptosystem provably secure against chosen ciphertext attack [C]//Advances in Cryptology-Crypto1998. Berlin/Heidelberg: Springer-Verlag, 1998: 13–25.
Kiltz E. Chosen-ciphertext secure key encapsulation based on hashed gap decisional Diffie-Hellman [C]// Proceedings of the 10th International Workshop on Practice and Theory in Public Key Cryptography, PKC 2007. Berlin/Heidelberg: Springer-Verlag, 2007: 282–297.
Abdalla M, Bellare M, Rogaway P. The oracle Diffie-Hellman assumptions and an analysis of DHIES [C]//Topics in Cryptology-CT-RSA 2001. Berlin/Heidelberg: Springer-Verlag, 2001: 143–158.
Bellare M, Rogaway P. Random oracles are practical: A paradigm for designing efficient protocols [C]//1st ACM CCCS. New York: ACM, 1993: 62–73.
Hanaoka G, Kurosawa K. Efficient chosen ciphertext secure public key encryption under the computational Diffie-Hellman assumption [EB/OL]. [2008-08-10]. http://eprint.iacr.org/2008/211.
Canetti R, Halevi S, Katz J. Chosen-ciphertext security from identity-based encryption [C]//Advances in Cryptology-Eurocrypt 2004. Berlin/Heidelberg: Springer-Verlag, 2004: 207–222.
Boneh D, Katz J. Improved efficiency for CCAsecure cryptosystems built using identity based encryption [C]//Proceedings of RSA-CT 2005. Berlin/Heidelberg: Springer-Verlag, 2005: 87–103.
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Foundation item: the National Natural Science Foundation of China (Nos. 60573032, 60773092, 90604036)
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Lu, Xh., Lai, Xj. & He, Dk. The gap between intractable problem and adaptive chosen ciphertext security. J. Shanghai Jiaotong Univ. (Sci.) 14, 90–93 (2009). https://doi.org/10.1007/s12204-009-0090-7
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DOI: https://doi.org/10.1007/s12204-009-0090-7