Quadratic Functional Encryption With Compact Keys and Ciphertexts
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Solution Overview
Problem
Existing functional encryption systems struggle with efficiently performing quadratic functions due to large output sizes, limiting their application in size-constrained environments, and lack effective security against collusions.
Innovation Solution
A new reduction from public-key functional encryption for quadratic functions to linear functions, utilizing a bilateral k-Lin assumption in prime-order bilinear groups, results in constant-size keys and shorter ciphertexts, achieving selective, simulation-based security against unbounded collusions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If existing functional encryption systems are used for quadratic functions, then the system can perform quadratic function computation on encrypted data, but the output size becomes very large, limiting application in size-constrained environments
Solution Approach 1:
The patent changes the mathematical parameters and assumptions underlying the functional encryption construction. It introduces a novel assumption called the k-linear assumption in bilinear groups, which enables more compact representations. By modifying the cryptographic parameters and using bilinear group operations instead of traditional approaches, the system achieves quadratic function computation with significantly reduced ciphertext size while maintaining security.
Solution Approach 2:
The patent extracts and separates the quadratic computation functionality from the encryption overhead. By using functional encryption keys that specifically encode quadratic functions and leveraging the properties of bilinear maps, the system computes quadratic functions on encrypted data while extracting only the necessary computational results, avoiding the generation of large intermediate ciphertexts.
2Adaptability or versatility
If existing functional encryption systems are used for quadratic functions, then the system can compute quadratic functions on encrypted data, but the security against collusions is insufficient or unproven
Solution Approach 1:
The patent implements preliminary security measures by establishing a formal security model and proving security against collusions before deployment. The k-linear assumption is established as a foundational security guarantee, and the system design incorporates predetermined key management structures that prevent collusion attacks. The security proof is constructed in advance, showing that even if multiple users collude, they cannot recover more information than their individual function evaluations permit.
3Adaptability or versatility
If functional encryption for quadratic functions is implemented with traditional methods, then the system can support fine-grained access control and function learning, but the key size becomes very large
Solution Approach 1:
The patent changes the cryptographic parameter representation by using bilinear group elements instead of traditional large-bit integer representations. The functional encryption keys are constructed using group elements in bilinear groups, which provide the same security guarantees but with more compact sizes. This parameter change enables fine-grained access control for quadratic functions while keeping key sizes manageable for practical deployment.
Data Source
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AI summary
The invention relates to systems, methods, network devices, and machine-readable media for improved constructions of public-key functional encryption schemes for quadratic functions. In particular, the present disclosure relates to a new functional encryption scheme to compute quadratic functions so that the data owner controls what can be computed but is not involved in the calculation, and generates a decryption key which allows one to learn a quadratic function evaluation of some encrypted data.