Abstract
IND-CCA secure public key encryption schemes based on the CDH assumption in the standard model use a hardcore function as a key derivation function for a shared key. Therefore, many secret and public key size are necessary for sending a sufficiently long shared key. Yamada et al. [17,16] and Haralambiev et al. [12] proposed efficient public key encryption schemes based on the CDH assumption. Moreover, they proposed a method that drastically reduces the secret and the public key sizes by using a bilinear map, and they also proposed IND-CCA secure public key encryption based on the bilinear DH assumption. Unfortunately, many secret and public key sizes are still necessary in general cyclic groups that lack known efficient bilinear map.
In this paper, we propose a compact public key scheme based on the CDH assumption in the standard model. The public and secret key sizes are trivially reduced by sending several block of the ciphertext. By using batch verification, our scheme succeeded in reducing the ciphertext size compared with that in the case of the trivially extended scheme. To prove IND-CCA security of our scheme, we define a new computational assumption, namely, the extended hashed strong twin Diffie-Hellman assumption. Moreover, we construct an extended trapdoor test to simulate a decisional oracle, and prove that if the CDH assumption holds and the hash function is the hardcore function for DH key, then the extended hashed strong twin DH assumption also holds. Our reducing technique is also applicable to other schemes [17,16,15] based on the CDH assumption.
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Hanatani, Y., Muratani, H., Yonemura, T. (2011). Toward Compact Public Key Encryption Based on CDH Assumption via Extended Twin DH Assumption. In: Boyen, X., Chen, X. (eds) Provable Security. ProvSec 2011. Lecture Notes in Computer Science, vol 6980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24316-5_11
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DOI: https://doi.org/10.1007/978-3-642-24316-5_11
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