Method of constructing a semi-public key system in qap-based homomorphic encryption

Abstract

The method of constructing QAP-based Homomorphic Encryption (HE) in the semi-public setting is introduced, which comprises: encryption, computation, and decryption. The data receiver produces a semi-public key Key. The data provider can encode his k-qubit plaintext |xto a k-qubit ciphertext |ψ=Q|xvia a k-qubit invertible operator Qrandomly generated by Key. From the provider, the message En(ζ) of Qencoded by a cryptosystem Gin Keyis transmitted to the receiver through a small-resource communication channel and the ciphertext |ψis conveyed to the cloud. The receiver creates the instruction of encoded computation U=PMQand transports to the cloud, where M is the required k-qubit arithmetic operation, P a k-qubit permutation, anda k-qubit operator to mingle with M. According the instruction, the cloud performs the encrypted evaluation U|ψand transfer to the receiver. The decryption KeyU|ψis conducted by the receiver via the private key Key=P, a complex-transpose of the product P, to obtain the final result M|x.