Homomorphic Evaluation Key Switching Noise Management
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Solution Overview
Problem
Current homomorphic encryption techniques are limited by their inability to efficiently perform complex operations on encrypted data without decrypting it, as they often require converting between different representations and suffer from high memory and computational costs, especially when evaluating deep circuits.
Innovation Solution
The implementation of a method that performs homomorphic evaluation using a public key encryption scheme with multiple secret keys and moduli, employing key-switching and modulus-switching transformations to maintain low noise levels and optimize operations, allowing for efficient computation on encrypted data by keeping ciphertexts in evaluation representation and minimizing the need for coefficient representation conversions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If homomorphic evaluation is performed using conventional encryption techniques, then security is maintained, but computational time and memory requirements increase significantly
Solution Approach 1:
The patent segments the homomorphic evaluation process into distinct phases: key-switching transformations, modulus-switching transformations, and evaluation operations. By dividing the computation into manageable segments with specific purposes, the system maintains security while reducing overall computational time through optimized execution of each segment
Solution Approach 2:
The patent changes parameters dynamically during evaluation by switching between different moduli (q0, q1, ..., qt-1) and keys (s0, s1, ..., st-1). This parameter switching allows the system to balance security requirements with computational efficiency at different stages of the evaluation process
2Reliability
If homomorphic evaluation is performed using conventional encryption techniques, then security is maintained, but memory requirements increase significantly
Solution Approach 1:
The patent segments ciphertext representations into coefficient form and evaluation form, using each form where it is most memory-efficient. By maintaining only necessary components in memory at any given time and switching between representations strategically, the system reduces overall memory requirements while preserving security
Solution Approach 2:
The patent changes the representation parameter of ciphertexts between coefficient representation and evaluation representation based on computational needs. This dynamic parameter change reduces memory usage by storing data in the most compact form possible at each stage of the evaluation
3Adaptability or versatility
If conversions between coefficient representation and evaluation representation are performed frequently, then computational flexibility is improved, but computational time increases
Solution Approach 1:
The patent performs preliminary key-switching and modulus-switching transformations to prepare ciphertexts in the appropriate representation before evaluation operations. By pre-positioning data in the correct form, the system avoids time-consuming conversions during the actual evaluation, thus improving computational flexibility without sacrificing time
4Ease of operation
If noise levels in ciphertexts are not controlled, then operational simplicity is maintained, but evaluation accuracy deteriorates
Solution Approach 1:
The patent incorporates noise level monitoring and control through modulus-switching transformations. By periodically reducing noise levels during the evaluation process, the system maintains evaluation accuracy without significantly complicating the operational flow, thus balancing simplicity with precision
Data Source
AI summary
Homomorphic evaluations of functions are performed. The functions include operation(s). Variants of key switching and modulus switching are described and are performed prior to or after the operation(s). A key switching transformation converts a ciphertext with respect to a first secret key and a first modulus to a ciphertext with respect to a second secret key and a second modulus. A key switching transformation converts a first version of a ciphertext with respect to a first secret key and with some number r bits of precision to a second version of the selected ciphertext with respect to a second keys and with some other number r′ bits of precision. The ciphertexts may be operated on as polynomials represented using evaluation representation, which has benefits for multiplication and automorphism. Further, ciphertexts are associated with an estimate of noise, which is used to determine when to perform modulus switching on the ciphertexts.