Paper 2013/390

Chosen Ciphertext Secure Keyed-Homomorphic Public-Key Encryption

Keita Emura, Goichiro Hanaoka, Koji Nuida, Go Ohtake, Takahiro Matsuda, and Shota Yamada

Abstract

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, \emph{transitional universal property}, and present a practical KH-PKE scheme from the DDH assumption. For $\ell$-bit security, our DDH-based KH-PKE scheme yields only $\ell$-bit longer ciphertext size than that of the Cramer--Shoup PKE scheme. Finally, we consider an identity-based analogue of KH-PKE, called \emph{keyed-homomorphic identity-based encryption} (KH-IBE) and give its concrete construction from the Gentry IBE scheme.

Note: Add keyed-homomorphic identity-based encryption (KH-IBE) and some related works, and improve the presentation of security proofs.