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

Abstract

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 Key=(VQ, Gen) and a private key Key=Pare produced, where VQis the product of an n-qubit permutation V and an n-qubit encoding operator Q, Genan error generator randomly provides a dressed operator Ē=VEV spinor error E of [n, k, C]. Then, by Key, the sender can encode his k-qubit plaintext Ix) into an n-qubit ciphertext |ψ, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation U=PVQfor a given k-qubit action M and sends to cloud, whereis the error-correction operator of [n, k, C],=I⊗M the tensor product of the (n−k)-qubit identity Iand M , and VQand Pthe complex-transposes of VQandPrespectively. The cloud executes the homomorphic encryption computation U|ψ) and conveys the encrypted result to receiver. The receiver performs the decryption KeyU|ψand obtains the final result M|x.