A CCA Secure Hybrid Damgård's ElGamal Encryption

ElGamal encryption, by its efficiency, is one of the most used schemes in cryptographic applications. However, the original ElGamal scheme is only provably secure against passive attacks. Damgard proposed a slight modification of ElGamal encryption scheme (named Damgard's ElGamal scheme) that provides security against non-adaptive chosen ciphertext attacks under a knowledge-of-exponent assumption. Recently, the CCA1-security of Damgard's ElGamal scheme has been proven under more standard assumptions. In this paper, we study the open problem of CCA2-security of Damgard's ElGamal. By employing a data encapsulation mechanism, we prove that the resulted hybrid Damgard's ElGamal Encryption is secure against adaptive chosen ciphertext attacks. The down side is that the proof of security is based on a knowledge-of-exponent assumption. In terms of efficiency, this scheme is more efficient (e.g. one exponentiation less in encryption) than Kurosawa-Desmedt scheme, the most efficient scheme in the standard model so far.

[1]  Ivan Damgård,et al.  Towards Practical Public Key Systems Secure Against Chosen Ciphertext Attacks , 1991, CRYPTO.

[2]  Victor Shoup,et al.  Using Hash Functions as a Hedge against Chosen Ciphertext Attack , 2000, EUROCRYPT.

[3]  Pil Joong Lee,et al.  Advances in Cryptology — ASIACRYPT 2001 , 2001, Lecture Notes in Computer Science.

[4]  Mihir Bellare,et al.  The Knowledge-of-Exponent Assumptions and 3-Round Zero-Knowledge Protocols , 2004, CRYPTO.

[5]  David Pointcheval.  Topics in Cryptology - CT-RSA 2006, The Cryptographers' Track at the RSA Conference 2006, San Jose, CA, USA, February 13-17, 2006, Proceedings , 2006, CT-RSA.

[6]  Silvio Micali,et al.  Probabilistic Encryption , 1984, J. Comput. Syst. Sci..

[7]  Michael Wiener,et al.  Advances in Cryptology — CRYPTO’ 99 , 1999 .

[8]  Alexander W. Dent,et al.  The Hardness of the DHK Problem in the Generic Group Model , 2006, IACR Cryptol. ePrint Arch..

[9]  Hugo Krawczyk,et al.  Secure Hashed Diffie-Hellman over Non-DDH Groups , 2004, EUROCRYPT.

[10]  Yvo Desmedt,et al.  A New Paradigm of Hybrid Encryption Scheme , 2004, CRYPTO.

[11]  Victor Shoup,et al.  Lower Bounds for Discrete Logarithms and Related Problems , 1997, EUROCRYPT.

[12]  Ronald Cramer,et al.  A Practical Public Key Cryptosystem Provably Secure Against Adaptive Chosen Ciphertext Attack , 1998, CRYPTO.

[13]  Daniel R. Simon,et al.  Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack , 1991, CRYPTO.

[14]  Kristian Gjøsteen,et al.  A New Security Proof for Damgård's ElGamal , 2006, CT-RSA.

[15]  Jiang Wu,et al.  On The Security of The ElGamal Encryption Scheme and Damgard's Variant , 2008, IACR Cryptol. ePrint Arch..

[16]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[17]  Matthew Franklin,et al.  Advances in Cryptology – CRYPTO 2004 , 2004, Lecture Notes in Computer Science.

[18]  Rosario Gennaro,et al.  A Note on An Encryption Scheme of Kurosawa and Desmedt , 2004, IACR Cryptol. ePrint Arch..

[19]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[20]  Mihir Bellare,et al.  Towards Plaintext-Aware Public-Key Encryption Without Random Oracles , 2004, ASIACRYPT.

[21]  Aggelos Kiayias,et al.  Traceable Signatures , 2004, EUROCRYPT.

[22]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[23]  Moni Naor,et al.  Public-key cryptosystems provably secure against chosen ciphertext attacks , 1990, STOC '90.

[24]  Taher El Gamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, IEEE Trans. Inf. Theory.

[25]  Ronald Cramer,et al.  Design and Analysis of Practical Public-Key Encryption Schemes Secure against Adaptive Chosen Ciphertext Attack , 2003, SIAM J. Comput..