METHOD OF CONSTRUCTING A PUBLIC-KEY SYSTEM IN QAP-BASED HOMOMORPHIC ENCRYPTION

A public-key scheme of Homomorphic Encryption (HE) in the framework Quotient Algebra Partition (QAP) comprises: encryption, computation and decryption. With the data receiver choosing a partition or a QAP, [n, k, C], a public key Keypub=(VQen, Gen) and a private key Keypriv=†P† are produced, where VQen is the product of an n-qubit permutation V and an n-qubit encoding operator Qen, Gen an error generator randomly provides a dressed operator Ē=V†EV spinor error E of [n, k, C]. Then, by Keypub, the sender can encode his k-qubit plaintext Ix) into an n-qubit ciphertext |ψen, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation Uen=PV†Qen† for a given k-qubit action M and sends to cloud, where is the error-correction operator of [n, k, C], =I2⊗M the tensor product of the (n−k)-qubit identity I2and M , and V†Q†en and P the complex-transposes of VQen and †P† respectively. The cloud executes the homomorphic encryption computation Uen|ψen) and conveys the encrypted result to receiver. The receiver performs the decryption KeyprivUen|ψen and obtains the final result M|x.