Modular Calculation via Bit-Reversed Prime Numbers
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Solution Overview
Problem
Fully homomorphic encryption's bootstrapping process is slowed by the need for large homomorphic calculations and high-degree polynomials, requiring a significant increase in processing time.
Innovation Solution
A calculation apparatus and method that generates prime number information necessary for modular multiplication by reversing bits of pre-stored base prime number information, allowing for efficient modular calculations using a combination of exponentiations of 2, and storing only base prime number information to reduce memory requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If bootstrapping is performed using traditional methods with large homomorphic calculations and high-degree polynomials, then the security and correctness of homomorphic encryption is maintained, but the processing speed is significantly reduced
Solution Approach 1:
The patent segments the large homomorphic calculation into multiple smaller modular multiplications. By breaking down the bootstrapping process into sequential modular operations with smaller moduli, the system maintains security requirements while reducing the computational burden of each individual operation, thereby improving overall processing speed.
Solution Approach 2:
The patent performs preliminary preparation by pre-calculating and storing prime number information and its bit-reversed form. This preliminary action allows the bootstrapping process to use pre-computed values during execution, avoiding the need to perform complex calculations in real-time and significantly accelerating the bootstrapping speed while maintaining correctness.
2Speed
If all prime number information necessary for modular multiplication is pre-stored, then the calculation speed is improved, but the memory usage increases
Solution Approach 1:
The patent applies bit-reversal transformation to the stored prime number information. By storing the bit-reversed form of prime numbers and performing corresponding bit-reversal operations during calculation, the system enables faster modular multiplication through optimized hardware operations while storing only the essential base prime number information, thus reducing memory requirements.
Solution Approach 2:
The patent creates a transformed copy of the prime number information through bit-reversal. Instead of storing multiple versions or all possible prime number variants, the system stores the base prime number information in bit-reversed form and uses transformation operations to generate the necessary values during calculation, reducing storage requirements while maintaining calculation efficiency.
Data Source
AI summary
Disclosed is a calculation apparatus. The calculation apparatus comprises a memory which stores at least one instruction and a processor which executes the at least one instruction, wherein the processor executes the at least one instruction to store a predetermined base prime number, invert the bits of information about the pre-stored base prime number to generate first prime number information different from the base prime number information, and perform modular calculation on a plurality of ciphertexts by using the generated first prime number information.