Punctured Reed-Muller Generator Matrix for Secure McEliece Keys
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Solution Overview
Problem
The McEliece encryption system using a Reed-Muller (RM) code generator matrix is vulnerable to attacks due to its special structure, which increases the risk of exposure of important data, as the private key can be easily guessed, and existing methods for defending against such attacks are inadequate.
Innovation Solution
The solution involves puncturing specific bit values in the columns of the generator matrix of the RM code to create a punctured generator matrix, which changes the structure and generates a public key for encryption, thereby enhancing security against third-party attacks by altering the generator matrix's structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a Reed-Muller code generator matrix is used in the McEliece encryption system, then error correction capability is provided, but the special structure of the RM code makes the private key easy to guess, increasing security vulnerability
Solution Approach 1:
The patent extracts specific bit values from predetermined column points of the Reed-Muller code generator matrix to create a punctured generator matrix. This extraction process removes the problematic structural patterns while preserving the essential error correction capabilities, thereby eliminating the security vulnerability caused by the special RM code structure.
Solution Approach 2:
The patent applies local modification by puncturing only specific bit values at predetermined column points rather than changing the entire matrix structure. This localized change maintains the overall error correction functionality while altering the specific structural patterns that make the private key vulnerable to guessing attacks.
2Object-affected harmful factors
If the generator matrix structure is modified to defend against attacks, then security is enhanced, but the complexity of key generation and processing increases
Solution Approach 1:
The patent performs preliminary puncturing of the generator matrix during the key generation phase, creating a punctured generator matrix before encryption operations. This advance preparation eliminates the need for complex runtime modifications and simplifies the encryption/decryption processes while maintaining enhanced security.
Solution Approach 2:
The patent changes the parameters of the generator matrix by puncturing specific bit values at predetermined column points. This parameter modification transforms the original RM code structure into a secure variant that maintains error correction capabilities while providing resistance against structural attacks, without requiring fundamentally new algorithms.
Data Source
AI summary
Disclosed are a data encryption apparatus and a data encryption method using an encryption key based on puncturing of a generator matrix. Bit values located in a column at a specific point are punctured from a generator matrix of a Reed-Muller (RM) code and thereafter, encryption of a message is performed through a public key generated by using the punctured generator matrix to defend an attack from a third party based on a structure of the RM code by change of the structure of the generator matrix, thereby solving security vulnerability caused as the existing McEliece encryption system uses the generator matrix of the RM code having a special structure as it is.