QAP-Based Homomorphic Encryption for Exact Blind Computation
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Solution Overview
Problem
Current homomorphic encryption schemes based on lattice cryptography suffer from noise-induced computational errors, requiring approximated solutions and excessive computational overhead, and reveal algorithms and operators during computation, limiting their efficiency and security.
Innovation Solution
A method for constructing a semi-public key system in quotient algebra partition (QAP)-based homomorphic encryption that enables exact solutions through encoded arithmetic operations using delicately-designed invertible gates, such as spinor, CNOT, Toffoli, and SWAP gates, allowing blind computations and reducing communication resources between data providers and receivers, thereby eliminating the need for error-correction overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If lattice-based homomorphic encryption is used, then encryption security is provided, but noise-induced computational errors occur requiring approximated solutions and excessive computational overhead
Solution Approach 1:
The patent transitions from lattice-based cryptography to QAP-based homomorphic encryption, fundamentally changing the cryptographic parameter framework. This involves switching from polynomial ring operations with noise terms to multilinear map operations over finite fields, thereby eliminating noise-induced errors while maintaining security through different mathematical hardness assumptions (e.g., multilinear decisional Diffie-Hellman problem).
Solution Approach 2:
The patent replaces the lattice-based cryptographic mechanism with a QAP-based mechanism. Specifically, it substitutes polynomial multiplication and noise management in lattice schemes with arithmetic circuit evaluation over encrypted data in QAP schemes. This substitution eliminates the need for error correction while enabling exact computation on encrypted data.
2Reliability
If lattice-based homomorphic encryption is used, then encryption is achieved, but algorithms and operators are revealed during computation
Solution Approach 1:
The patent segments the computation process into independent arithmetic operations that can be performed on encrypted data without revealing the underlying algorithm. By representing computations as arithmetic circuits in QAP format, each gate operation (AND, OR, NOT) is executed independently on encrypted inputs, preventing inference of the overall algorithm structure during computation.
Solution Approach 2:
The patent introduces encrypted intermediate representations as mediators between plaintext algorithms and ciphertext computations. The QAP evaluation process uses encrypted witnesses and polynomial commitments as intermediaries, allowing the system to compute algorithm outputs on encrypted data without exposing the algorithm itself. The evaluator never sees the plaintext algorithm or intermediate plaintext values.
3Measurement precision
If error-correction processes are implemented in QAPHE, then computational accuracy is improved, but computational cost increases
Solution Approach 1:
The patent extracts and removes the error-correction mechanism from the QAP-based homomorphic encryption system. Since QAP operates over finite fields with exact arithmetic rather than noisy approximate arithmetic, there are no errors to correct. The system achieves computational accuracy through the mathematical properties of multilinear maps and polynomial interpolation, making error-correction codes unnecessary and reducing computational overhead.
Data Source
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AI summary
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 Keys-pub.The data provider can encode his k-qubit plaintext |x〉 to a k-qubit ciphertext |ψen〉 = QP |x〉 via a k-qubit invertible operator QP randomly generated by Keys-pub. From the provider, the message En(ζp) of QP encoded by a cryptosystem Gcrypt in Keys-pub is transmitted to the receiver through a small-resource communication channel and the ciphertext |ψen〉 is conveyed to the cloud. The receiver creates the instruction of encoded computation Uen = P MQP and transports to the cloud, where M is the required k-qubit arithmetic operation, P a k-qubit permutation, and a k-qubit operator to mingle with M. According the instruction, the cloud performs the encrypted evaluation Uen |ψen〉 and transfer to the receiver. The decryption Keypriv Uen |ψen〉 is conducted by the receiver via the private key Keypriv = A†P†, a complex-transpose of the product P A, to obtain the final result M|x〉.