International Association
for Cryptologic Research

In homomorphic encryption schemes, anyone can perform homomorphic operations, and therefore, it is difficult to manage when, where and by whom they are performed. In addition, the property that anyone can \\lq\\lq freely\'\' perform the operation inevitably means that ciphertexts are malleable, and it is well-known that adaptive chosen ciphertext (CCA) security and the homomorphic property can never be achieved simultaneously.

In this paper, we show that CCA security and the homomorphic property can be simultaneously handled in situations that the user(s) who can perform homomorphic operations on encrypted data should be controlled/limited, and propose a new concept of homomorphic public-key encryption, which we call \\emph{keyed-homomorphic public-key encryption} (KH-PKE). By introducing a secret key for homomorphic operations, we can control who is allowed to perform the homomorphic operation. To construct KH-PKE schemes, we introduce a new concept, a \\emph{homomorphic transitional universal hash family}, and present a number of KH-PKE schemes through hash proof systems. We also present a practical construction of KH-PKE from the DDH assumption. For $\\ell$-bit security, our DDH-based scheme yields only $\\ell$-bit longer ciphertext size than that of the Cramer-Shoup PKE scheme.