Homomorphic Circuit Multiplicative Depth Reduction
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Solution Overview
Problem
Homomorphic encryption schemes are slower than their non-homomorphic counterparts due to inefficiencies in evaluating functions on encrypted data, particularly due to high multiplicative depth in homomorphic circuits.
Innovation Solution
Optimizing homomorphic circuits by reducing multiplicative depth through techniques such as parallelizing operations across loop iterations and using mixed encoding units, allowing for more efficient matrix and vector multiplications, and implementing bootstrapping to support functions of unbounded multiplicative depth.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic encryption is used to enable computation on encrypted data, then security is improved, but computational speed deteriorates
Solution Approach 1:
The patent segments the computation process into distinct homomorphic operations (addition, multiplication, rotation, addition before rotation) that can be independently optimized and executed. By breaking down complex functions into smaller operational units, the system can apply specific optimizations to each segment, improving overall computational efficiency while maintaining security.
Solution Approach 2:
The patent changes key parameters of the homomorphic encryption scheme by introducing mixed encoding units with different precision levels and implementing optimized evaluation algorithms. By adjusting parameters such as encoding unit size, precision allocation, and computational depth, the system achieves faster computation while preserving cryptographic security.
2Adaptability or versatility
If homomorphic circuits are designed to evaluate complex functions, then functionality is improved, but multiplicative depth increases causing slower performance
Solution Approach 1:
The patent implements dynamic circuit optimization by adaptively selecting evaluation strategies based on the specific function being computed. The system dynamically adjusts the homomorphic circuit structure, encoding unit configurations, and operation ordering to minimize multiplicative depth for each particular computational task, thereby reducing computation time while maintaining full functionality.
Solution Approach 2:
The patent introduces a new dimension of optimization by using mixed encoding units with varying precision levels across different parts of the computation. This dimensional approach allows the system to allocate computational resources more efficiently, performing operations in parallel across different precision levels and reducing the overall multiplicative depth of the circuit.
3Device complexity
If standard encoding units are used throughout the computation, then simplicity is maintained, but computational efficiency deteriorates
Solution Approach 1:
The patent applies local quality by using different encoding unit precisions in different regions of the computation based on the specific requirements of each operation. Critical operations that require high precision use finer encoding units, while less critical operations use coarser units. This localized optimization improves overall computational efficiency without significantly increasing system complexity.
Solution Approach 2:
The patent creates a composite encoding structure by combining multiple encoding units with different precision levels into a unified homomorphic computation system. This composite approach allows the system to leverage the strengths of different encoding types, achieving high computational efficiency while maintaining a manageable level of complexity through standardized interfaces and protocols.
Data Source
AI summary
Techniques to improve the operation of homomorphic circuits. Systems and methods described herein may improve the operation of a homomorphic circuit by analyzing a circuit to reduce the multiplicative depth of the circuit. Techniques described herein may be utilized to perform linear algebra operations with mixed encoding units, according to a homomorphic encryption scheme.