Parallel NTT Coefficient Processing for Lattice Cryptography
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing hardware accelerators designed for classical public-key cryptography are inefficient for polynomial computations required in lattice-based post-quantum cryptography due to differences in coefficient sizes and arithmetic operations.
Innovation Solution
A method for performing number theoretic transforms (NTTs) on polynomials by dividing input polynomials into multiple polynomials with fewer coefficients, processing these in parallel using a coprocessor with word-length registers, and executing cryptographic operations based on the transformed results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing hardware accelerators for classical public-key cryptography are used, then device complexity is reduced, but productivity deteriorates due to inefficiency in polynomial computations
Solution Approach 1:
The patent segments the polynomial coefficients into multiple groups that can be processed in parallel. Specifically, it divides the input polynomial with n coefficients into multiple polynomials with fewer coefficients each, allowing parallel processing using the coprocessor's word-length registers. This segmentation enables efficient utilization of existing hardware without requiring complete architectural redesign.
2Loss of time
If polynomial coefficients are processed individually, then manufacturing precision is maintained, but loss of time increases due to sequential processing
Solution Approach 1:
The patent merges multiple coefficient processing operations into parallel butterfly operations. By organizing coefficients into segments that fit within the coprocessor's word-length registers, it combines multiple individual coefficient transformations into simultaneous parallel operations, significantly reducing total computational time while maintaining accuracy.
3Ease of operation
If coprocessor registers are used for storage, then loss of substance is reduced, but ease of operation deteriorates due to word length constraints
Solution Approach 1:
The patent changes the parameter representation by transforming polynomial coefficients into a segmented format that matches the coprocessor's word length constraints. It applies number theoretic transforms and modular arithmetic to reorganize data so that coefficients are grouped into segments fitting within register word lengths, enabling efficient in-register processing without requiring complex external memory operations.
Data Source
AI summary
Electronic device and method for performing number theoretic transforms (NTTs) on polynomials for cryptography uses an arithmetic transformation on an input polynomial with n coefficients to divide the input polynomial into multiple polynomials each with less than n coefficients such that the coefficients of the multiple polynomials add up to n. An NTT transformation is executed on the multiple polynomials such that the coefficients of each of the multiple polynomials are processed in parallel butterfly operations. A cryptographic operation is performed based on the results of the NTT transformation.