Abstract
ElGamal encryption is the most extensively used alternative to RSA. Easily adaptable to many kinds of cryptographic groups, ElGamal encryption enjoys homomorphic properties while remaining semantically secure providing that the DDH assumption holds on the chosen group. Its practical use, unfortunately, is intricate: plaintexts have to be encoded into group elements before encryption, thereby requiring awkward and ad hoc conversions which strongly limit the number of plaintext bits or may partially destroy homomorphicity. Getting rid of the group encoding (e.g., with a hash function) is known to ruin the standard model security of the system.
This paper introduces a new alternative to group encodings and hash functions which remains fully compatible with standard model security properties. Partially homomorphic in customizable ways, our encryptions are comparable to plain ElGamal in efficiency, and boost the encryption ratio from about 13 for classical parameters to the optimal value of 2.
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Abdalla, M., Bellare, M., Rogaway, P.: DHAES: An Encryption Scheme Based on the Diffie-Hellman Problem. Submission to IEEE P1363a (September 1998), Available from http://grouper.ieee.org/groups/1363/
Bellare, M., Rogaway, P.: Optimal Asymmetric Encryption – How to Encrypt with RSA. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)
Bresson, E., Catalano, D., Pointcheval, D.: A Simple Public-Key Cryptosystem with a Double Trapdoor Decryption Mechanism and its Applications. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 37–54. Springer, Heidelberg (2003)
Chevassut, O., Fouque, P.-A., Gaudry, P., Pointcheval, D.: The Twist-Augmented Technique for Key Exchange. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T.G. (eds.) PKC 2006. LNCS, vol. 3958, pp. 410–426. Springer, Heidelberg (2006)
Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)
Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–137. Springer, Heidelberg (2001)
Diffie, W., Hellman, M.E.: New Directions in Cryptography. IEEE Transactions on Information Theory IT-22(6), 644–654 (1976)
El Gamal, T.: A Public Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory IT-31(4), 469–472 (1985)
Fujisaki, E., Okamoto, T.: How to Enhance the Security of Public-Key Encryption at Minimum Cost. In: Imai, H., Zheng, Y. (eds.) PKC 1999. LNCS, vol. 1560, pp. 53–68. Springer, Heidelberg (1999)
Fujisaki, E., Okamoto, T.: Secure Integration of Asymmetric and Symmetric Encryption Schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)
Fujisaki, E., Okamoto, T.: How to Enhance the Security of Public-Key Encryption at Minimum Cost. IEICE Transaction of Fundamentals of Electronic Communications and Computer Science E83-A(1), 24–32 (2000)
Gennaro, R., Krawczyk, H., Rabin, T.: Secure Hashed Diffie-Hellman over Non-DDH Groups. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 361–381. Springer, Heidelberg (2004)
Goldwasser, S., Micali, S.: Probabilistic Encryption. Journal of Computer and System Sciences 28, 270–299 (1984)
Koblitz, N.: Elliptic Curve Cryptosystems. Mathematics of Computation 48(177), 203–209 (1987)
Miller, V.: Uses of Elliptic Curves in Cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417–426. Springer, Heidelberg (1986)
Naccache, D., Stern, J.: A New Public-Key Cryptosystem. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 27–36. Springer, Heidelberg (1997)
Okamoto, T., Pointcheval, D.: REACT: Rapid Enhanced-security Asymmetric Cryptosystem Transform. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 159–175. Springer, Heidelberg (2001)
Okamoto, T., Uchiyama, S.: A New Public Key Cryptosystem as Secure as Factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)
Paillier, P.: Public-Key Cryptosystems Based on Composite-Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Pointcheval, D.: Chosen-Ciphertext Security for any One-Way Cryptosystem. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 129–146. Springer, Heidelberg (2000)
Rabin, M.O.: Digitalized Signatures and Public Key Functions as Intractible as Factorization. Technical Report MIT/LCS/TR-212, Massachusetts Institute of Technology - Laboratory for Computer Science (January 1979)
Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
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Chevallier-Mames, B., Paillier, P., Pointcheval, D. (2006). Encoding-Free ElGamal Encryption Without Random Oracles. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds) Public Key Cryptography - PKC 2006. PKC 2006. Lecture Notes in Computer Science, vol 3958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11745853_7
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DOI: https://doi.org/10.1007/11745853_7
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