IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Online ISSN : 1745-1337
Print ISSN : 0916-8508
Special Section on Cryptography and Information Security
Proxy Re-Encryption That Supports Homomorphic Operations for Re-Encrypted Ciphertexts
Yutaka KAWAITakahiro MATSUDATakato HIRANOYoshihiro KOSEKIGoichiro HANAOKA
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2019 Volume E102.A Issue 1 Pages 81-98

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Abstract

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 Re-Encryption (HPRE) combining the “key-switching” property of Proxy Re-Encryption (PRE) and the homomorphic property of HE. In our HPRE, original ciphertexts (which have not been re-encrypted) guarantee CCA2 security (and in particular satisfy non-malleability). On the other hand, re-encrypted 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. (CT-RSA 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 degree-2 polynomials (in which the number of degree-2 terms is constant), by using the technique of the recent work by Catalano and Fiore (ACMCCS 2015).

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© 2019 The Institute of Electronics, Information and Communication Engineers
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