Cryptology ePrint Archive: Report 2022/127

CCA secure ElGamal encryption over an integer group where ICDH assumption holds

Gyu-Chol.Kim and Jae-Yong.Sin and Yong-Bok.Jong

Abstract: In order to prove the ElGamal CCA (Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group (i.e., ICDH group) where ICDH assumption holds. Until now, only bilinear group where ICDH assumption is equivalent to CDH assumption has been known as the ICDH group. In this paper, we introduce another ICDH group in which ICDH assumption holds under the RSA assumption. Based on this group, we propose the CCA secure ElGamal encryption. And we describe the possibility to speed up decryption by reducing CRT (Chinese Remainder Theorem) exponents in CCA secure ElGamal.

Category / Keywords: public-key cryptography / ElGamal, CCA security, Interactive Computational Diffie Hellman problem, random oracle, RSA

Date: received 4 Feb 2022

Contact author: kgc841110 at star-co net kp

Available format(s): PDF | BibTeX Citation

Version: 20220209:085308 (All versions of this report)

Short URL: ia.cr/2022/127