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Proxy ReEncryption That Supports Homomorphic Operations for ReEncrypted Ciphertexts
Yutaka KAWAI Takahiro MATSUDA Takato HIRANO Yoshihiro KOSEKI Goichiro HANAOKA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E102A
No.1
pp.8198 Publication Date: 2019/01/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E102.A.81
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security) Category: Keyword: Proxy Reencryption, homomorphic encryption,
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Summary:
Homomorphic encryption (HE) is useful to analyze encrypted data without decrypting it. However, by using ordinary HE, a user who can decrypt a ciphertext that is generated by executing homomorphic operations, can also decrypt ciphertexts on which homomorphic evaluations have not been performed, since homomorphic operations cannot be executed among ciphertexts which are encrypted under different public keys. To resolve the above problem, we introduce a new cryptographic primitive called Homomorphic Proxy ReEncryption (HPRE) combining the “keyswitching” property of Proxy ReEncryption (PRE) and the homomorphic property of HE. In our HPRE, original ciphertexts (which have not been reencrypted) guarantee CCA2 security (and in particular satisfy nonmalleability). On the other hand, reencrypted ciphertexts only guarantee CPA security, so that homomorphic operations can be performed on them. We define the functional/security requirements of HPRE, and then propose a specific construction supporting the group operation (over the target group in bilinear groups) based on the PRE scheme by Libert and Vergnaud (PKC 2008) and the CCA secure public key encryption scheme by Lai et al. (CTRSA 2010), and prove its security in the standard model. Additionally, we show two extensions of our HPRE scheme for the group operation: an HPRE scheme for addition and an HPRE scheme for degree2 polynomials (in which the number of degree2 terms is constant), by using the technique of the recent work by Catalano and Fiore (ACMCCS 2015).

