National Applied Research Laboratories

Ming-Chung Tsai

Zheng-Yao Su

The present inventive concept discloses a method of designing a one-way computational system in QAP-based homomorphic encryption applied to the n-qubit encode operations of a k-qubit action M for public-key and semi-public-key schemes respectively, n≥k, wherein the method comprises: preparing a tensor-product operator=I⊗M=and decomposing it into two parts, whereinis composed of elementary gates, and let=and=; providing a correction operator,=for public-key and=Ifor semi-public-key, and an encoding operator, QV=WWfor public-key and Q=WWfor semi-public-key, both composed of elementary gates; providing appropriate permutations P, Pand P, while P=Pfor semi-public-key, to obey the nilpotent condition PWP=I for the identity operator; through process of merging operators according to sets of identities of gates, including Id-GateELIM, Id-GateEx and Id-GateREP, there obtain the mixed encode for public-key scheme, U=PQV=(PWWP)(PP)(PWWP) (PW), and that for semi-public key, U=PMQ=(PWWP)(PW) with n=k,==Iand P=P.

Method of designing one-way computational system in QAP-based homomorphic encryption

A method of designing a multi-party system in quotient algebra partition-based homomorphic encryption (QAPHE), which is based on the framework of quotient algebra partition (QAP) and the computation of homomorphic encryption (HE), wherein the method comprises: increasing single model provider A to multiple ones, wherein the number of the multiple model providers is L and let Aand L≥2; increasing single data provider B to multiple ones, wherein the number of the multiple data providers is R and let Band R≥2; and encoding plaintexts, each of which is of kqubits, from all data providers into ciphertexts respectively; aggregating the ciphertexts by a form of tensor product and generating an encoded state for computation; and preparing a model operation to conduct the encrypted computation via an encoded operator and the encoded state in a cloud. The method can improve the security of public-key/semi-public-key system and be applied to a threshold HE or a multi-key HE to solve actual problems.

Method of designing of multi-party system in QAP-based homomorphic encryption

A method of constructing a procedural threshold in quotient algebra partition-based fault tolerance quantum computation, which is based on the framework of quotient algebra partition (QAP) applied in the fault tolerance quantum computation (FTQC), wherein an n-qubit fault tolerant encode of a k-qubit quantum gate M, is feasible to a threshold, wherein the method comprises: preparing a quantum code, with a stabilizer; creating an n-qubit encoding, in the quantum code, and obtaining an n-qubit fault tolerant encode of M; factorizing each encoded component, of this n-qubit fault tolerant encode; and producing a detection-correction operator by placing n-k ancilla qubits with the original system of n qubits, wherein the detection-correction operator comprises a conditional detection operator and a conditional correction operator to remove r-qubit spinor error. In terms of this invention, a fault-tolerant computation is conducted by the following criteria given a threshold 0<δ<1: a qubit keeps unchanged if it has the fidelity >δand needs an error-correction if it has the fidelity <δ. Based on this concept, a fault tolerant method is constructed to be feasible to practical experiments composed of noisy systems, leading to scalable fault tolerance quantum computation.

Method of procedural thresholds in QAP-based fault tolerance quantum computation

A method for constructing an n-qubit fault tolerant encode for any k-qubit quantum gate M, in any given quantum code [n, k, C], comprising: choosing a number n−k of independent spinors Sfrom the first stabilizer C and a first ordered set Sconsists of the independent spinors S; choosing a number n−k of independent spinors Ŝfrom a second stabilizer Ĉ in the intrinsic coordinate and a second ordered set Ŝconsists of the independent spinors Ŝconsist; implementing an encoding Q, wherein the encoding Qconverts the first ordered set Sto the second ordered set S, wherein the encoding Qis a sequential product provided by sequential operations of a number n−k of unitary operators Q; wherein each of the unitary operator Qis composed of a single s-rotation or a product of two s-rotations; and wherein the encoding Qconverts and maps the rindependent spinor Sin the first ordered set Sto the rindependent spinor Ŝin the second ordered set Scorrespondingly; a fault tolerant action Û in the quantum code [n, k, C] generated by the second stabilizer Ĉ in the intrinsic coordinate, wherein the fault tolerant action Û is a direct sum of a basis state operator Λ and a correction operator Ω; and acquiring a fault tolerant encode in the quantum code [n, k, C] generated by the first stabilizer C, wherein the fault tolerant encode is a sequential product of the encoding Q, the fault tolerant action Û and a complex conjugate Qof the encoding Q.

Method for constructing a fault tolerant encode using a quantum computational model

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 |&#x3c8;=Q|xvia a k-qubit invertible operator Qrandomly generated by Key. From the provider, the message En(&#x3b6;) of Qencoded by a cryptosystem Gin Keyis transmitted to the receiver through a small-resource communication channel and the ciphertext |&#x3c8;is 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|&#x3c8;and transfer to the receiver. The decryption KeyU|&#x3c8;is conducted by the receiver via the private key Key=P, a complex-transpose of the product P, to obtain the final result M|x.

Method of constructing a semi-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 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 &#x112;=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 |&#x3c8;, 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&#x2297;M the tensor product of the (n&#x2212;k)-qubit identity Iand M , and VQand Pthe complex-transposes of VQandPrespectively. The cloud executes the homomorphic encryption computation U|&#x3c8;) and conveys the encrypted result to receiver. The receiver performs the decryption KeyU|&#x3c8;and obtains the final result M|x.

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Hsinchu, Taiwan

Ming-Chung Tsai