Lattice Cryptography Compression Using Error-Mediated Division
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Solution Overview
Problem
Existing lattice-based cryptographic systems are vulnerable to attacks, and there is a need to improve their security by enhancing the compression function used in these systems.
Innovation Solution
A method is introduced to compile a compression function for lattice-based cryptographic mechanisms, utilizing a lossy compression function that determines an error based on integer division loss, allowing the output to be computed without directly computing the integer division.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a standard compression function using integer division is used in lattice-based cryptography, then the compression operation can be performed, but the system becomes vulnerable to attacks
Solution Approach 1:
The patent introduces an intermediary error term that mediates between the integer division operation and the final compression output. By computing the compression function as floor((x + error) / q) where error represents the division loss, the system achieves secure compression without directly exposing the vulnerable integer division operation to attackers.
Solution Approach 2:
The patent transforms the compression function by changing the parameter representation from direct integer division to a form that incorporates an error term. This parameter transformation allows the same mathematical operation to be performed in a way that is resistant to cryptographic attacks while maintaining computational efficiency.
2Ease of operation
If integer division is computed directly in the compression function, then the operation is straightforward, but it introduces security vulnerabilities to the cryptographic system
Solution Approach 1:
The patent converts the harmful effect of integer division loss into a beneficial security feature by explicitly modeling the error term. What was previously a source of vulnerability (the loss from integer division) becomes a protected component of the compression function, where the error is deliberately computed and incorporated to prevent attacks.
3Reliability
If lossy compression is used to improve security, then resistance to attacks increases, but computation of the error term adds operational complexity
Solution Approach 1:
The error term computation is designed to be self-service to the main compression operation. The error is computed as a byproduct of the compression process itself rather than as a separate, expensive operation. This allows the security-enhancing error term to be generated efficiently within the existing computational flow.
Data Source
AI summary
Compiling a compression function of a lattice-based cryptographic mechanism by (i) basing the compression function on a lossy compression function, (ii) determining an error based on a loss introduced by an integer division, and (iii) determining an output of the compression function based on the error.