Blind Rotation for FHE Bootstrapping With One External Product
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Solution Overview
Problem
Existing fully homomorphic encryption (FHE) schemes face significant computational overhead when increasing the number of possible values for secret key digits beyond bits, particularly in bootstrapping operations, due to the increased number of external multiplications required.
Innovation Solution
A computer-implemented blind rotation method for FHE that iterates over secret key digits, performing at most one external product per digit, allowing for more flexible parameter selection without increasing the number of external multiplications, by using encrypted multiplier polynomials computed as linear combinations of bootstrapping keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the number of possible values for secret key digits is increased beyond bits, then the security and flexibility of FHE is improved, but the computational overhead and number of external multiplications increases significantly
Solution Approach 1:
The patent segments the secret key into multiple digits, each digit being processed independently through iterative blind rotation operations. This segmentation allows the system to handle larger key spaces by breaking down the problem into manageable units, where each digit contributes to the overall security without proportionally increasing the computational burden of the entire system.
Solution Approach 2:
The patent employs dynamic parameter selection where the number of iterations and rotation steps are adjusted based on the specific requirements of the FHE scheme. The system dynamically adapts the computational parameters to balance security requirements against computational efficiency, allowing flexible optimization for different security levels without fixed overhead.
2Adaptability or versatility
If more external multiplications are performed to support higher radix secret keys, then the functionality and security of FHE is enhanced, but the computational time and resource consumption increases
Solution Approach 1:
The patent performs preliminary blind rotation operations during key generation and setup phases, preparing the cryptographic primitives in advance. This preliminary action reduces the computational burden during actual FHE operations, as the expensive rotation and multiplication operations have already been pre-computed and stored in an optimized form.
Solution Approach 2:
The patent changes computational parameters such as the modulus, polynomial degree, and rotation steps to optimize the balance between functionality and computational time. By adjusting these parameters, the system can support higher radix secret keys with enhanced functionality while keeping computational time within acceptable bounds through careful parameter selection.
Data Source
AI summary
Some embodiments are directed to a computer-implemented blind rotation method for use in fully homomorphic encryption (FHE). The method comprises rotating a polynomial (210) over a masked value and iterating over secret key digits, e.g., they may be ternary. The secret key digits can have at least three different values. An iteration further blind rotating the polynomial as indicated by a current secret key digit and a corresponding masking value. In the iteration an encrypted multiplier polynomial may be computed from bootstrapping keys and the masking values. One external product may be done in an iteration with the encrypted multiplier polynomial to further blind rotate the polynomial.