Garbled Circuit SIMD Homomorphic Encryption Comparison
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Solution Overview
Problem
Current homomorphic encryption systems face inefficiencies due to the inability to perform non-linear operations using Single-Instruction/Multiple-Data (SIMD) operations, which limits processing speed and efficiency, especially when trying to execute complex operations like comparisons.
Innovation Solution
Integration of garbled circuits into SIMD FHE programs allows for interactive non-linear operations by embedding a garbled circuit between a garbler device and an evaluator device, enabling efficient execution of non-linear operations while maintaining the benefits of SIMD parallelization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If SIMD operations are used in homomorphic encryption, then processing efficiency is improved, but the ability to perform non-linear operations is lost
Solution Approach 1:
The system segments the computation into two distinct parts: a garbler that prepares garbled circuits for non-linear operations, and an evaluator that executes SIMD operations on homomorphically encrypted data. This segmentation allows each component to specialize in its strength - the garbler handles non-linear operations through garbled circuits while the evaluator maintains SIMD efficiency for linear operations.
Solution Approach 2:
Garbled circuits serve as an intermediary mechanism between the garbler and evaluator, enabling the transfer of non-linear operation capabilities to the SIMD-FHE evaluator without sacrificing processing efficiency. The garbled circuit acts as a mediator that translates non-linear operations into a form compatible with SIMD evaluation.
2Adaptability or versatility
If garbled circuits are embedded in SIMD FHE programs, then non-linear operations are enabled, but processing efficiency is reduced
Solution Approach 1:
The system dynamically selects which operations are performed by the garbler and which by the evaluator based on the operation type. Linear operations that benefit from SIMD parallelization are dynamically assigned to the evaluator, while non-linear operations are routed to the garbler. This dynamic allocation optimizes overall processing efficiency while maintaining versatility.
Solution Approach 2:
The invention changes the operational parameters of the homomorphic encryption system by introducing garbled circuits with specific security parameters and circuit complexity thresholds. Operations below a certain complexity threshold are executed directly by the evaluator, while more complex non-linear operations trigger garbler involvement, optimizing the balance between versatility and efficiency.
3Adaptability or versatility
If multiple bootstrapping operations are used for comparisons, then non-linear operations are achieved, but processing speed decreases
Solution Approach 1:
Instead of performing multiple bootstrapping operations on the original homomorphically encrypted data, the system creates a copied representation through garbled circuits. The garbler generates garbled versions of the input data that encode the necessary non-linear operation logic, allowing the evaluator to perform comparisons efficiently without repeated bootstrapping.
Data Source
AI summary
A multi-party system comprising a garbler and an evaluator for interactively executing homomorphic SIMD operations using garbled circuits. The garbler and evaluator may each store a unique share of a shared secret key, a ciphertext, and a shared public key. The garbler and evaluator may each partially decrypt the ciphertext using its key share to generate a unique data share. The garbler may linearize and reduce the size of the unique garbler data share. The garbler may send to the evaluator a garbled circuit, a garbling of the linear unique garbled data share, and garbled potential wires for the evaluator to garble its linear unique evaluator data share by oblivious transfer. The evaluator may evaluate the garbled circuit to execute a SIMD program to combine, in parallel, multiple indices of the linear garbler and evaluator unique data shares to efficiently generate an encrypted result of the garbled circuit.