Cryptographic Matrix Compression Using Delta and Entropy Coding
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Solution Overview
Problem
Storing matrices for cryptographic operations requires significant storage space and computational resources, which is a challenge for advanced computing devices, especially in post-quantum cryptographic techniques like the Dilithium algorithm.
Innovation Solution
Delta-encoding and entropy-encoding the matrix coefficients, followed by shuffling, to reduce storage requirements and computational overhead, using techniques such as asymmetric numeral system (ANS) entropy encoding.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If matrices are stored for cryptographic operations, then encryption and decryption operations can be performed efficiently, but storage space requirements increase significantly
Solution Approach 1:
The patent extracts only the essential characteristics of matrices needed for cryptographic operations. Instead of storing complete large-dimensional matrices, the invention uses matrix compression techniques that retain only the critical information required for encryption and decryption, thereby reducing storage space while maintaining operational capability
Solution Approach 2:
The patent transforms matrix representation by changing parameters such as using different basis representations, applying coordinate transformations, or utilizing algebraic normal forms. These parameter changes allow the same cryptographic functionality to be achieved with more compact data structures that require less storage space
2Quantity of substance
If matrices are re-generated for cryptographic operations, then storage space is reduced, but computational resources and time increase
Solution Approach 1:
The patent performs preliminary processing of matrices into compressed forms that can be quickly reconstructed or utilized. By pre-computing and storing compressed matrix representations with efficient reconstruction algorithms, the system avoids the need to regenerate full matrices during cryptographic operations, thus reducing both storage requirements and computational overhead
Solution Approach 2:
The patent creates simplified copies or representations of matrices that capture essential properties needed for cryptographic operations. These compressed copies use less storage space and can be processed more efficiently, maintaining the necessary cryptographic functionality while reducing both storage and computational demands
3Reliability
If large matrices are used for post-quantum cryptographic techniques, then security strength is improved, but device complexity and resource requirements increase
Solution Approach 1:
The patent segments large cryptographic matrices into smaller blocks or components that can be processed independently. This segmentation maintains the overall security strength by preserving the mathematical relationships needed for cryptographic operations while reducing the complexity of individual processing steps and enabling more efficient implementation on computing devices
Data Source
AI summary
Systems and techniques are described herein for compressing data used in cryptographic operations. For example, a process may include obtaining a first data structure, wherein the first data structure comprises polynomials; generating a second data structure based on the first data structure, wherein the second data structure comprises coefficients of the polynomials; sorting the second data structure in an ascending order to obtain a sorted second data structure; updating the sorted second data structure based on differences between elements of the sorted second data structure to obtain a delta-encoded data structure; performing an entropy coding on the delta-encoded data structure to obtain an entropy-encoded output; recovering an updated first data structure using the entropy-encoded output, wherein the updated first data structure corresponds to the first data structure with a different order of first data structure elements; and performing a cryptographic operation using the updated first data structure.