With the emerging of new types of network forms, services and cloud computation, the situation has transformed from one party to many parties at least one of both communication ends, that is "one-to-many," "many-to-one," and "many-to-many" situations. Most of the existing fully homomorphic encryption schemes only allow one party to encrypt the plaintext and another party to decrypt the ciphertext without the decryption keys. This form of cryptography loses efficiency under the demands of "one-to-many," "many-to-one," and "many-to-many" scenarios. In this paper, we combine the fully homomorphic encryption with proxy re-encryption to propose the fully homomorphic proxy re-encryption scheme which can be applied to "many-to-one" scenario, that is the fully homomorphic proxy re-encryption scheme allows one party to compute arbitrary functions over encrypted data for many parties without the decryption keys. Finally, IND-CPA, KP-CPA and master secret security proof of our proposal are given.
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