Generalized Concatenated Codes with Restricted Errors for Smaller Keys
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current code-based cryptographic systems face challenges with large public keys due to the need for long codes to achieve sufficient security, making them inefficient and vulnerable to structural attacks, especially against Information Set Decoding (ISD) attacks.
Innovation Solution
The implementation of generalized concatenated codes (GCC) with restricted error values, utilizing inner codes over Gaussian or Eisenstein integers and binary BCH codes, which enhance error correction capabilities and reduce public key sizes by limiting error values, thereby increasing security against ISD and structural attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If very long codes are used to achieve sufficient security in code-based cryptographic systems, then security level is improved, but public key size increases
Solution Approach 1:
The code is segmented into multiple blocks that are processed independently through parallel decoding steps. The decoding process is divided into sequential stages where each stage handles a portion of the error correction, allowing the system to achieve high security with shorter overall code length by distributing the computational workload across multiple smaller units.
Solution Approach 2:
The decoding process employs dynamic adaptive strategies where the system adjusts its approach based on the detected error patterns. The parallel decoding steps can be selectively activated or modified based on the specific error configuration, enabling efficient correction with reduced code length requirements compared to static decoding methods.
2Device complexity
If conventional error correction codes are used, then implementation simplicity is maintained, but vulnerability to Information Set Decoding attacks increases
Solution Approach 1:
The code structure is segmented into multiple blocks with specific algebraic properties that complicate ISD attacks. Each block can be decoded independently using simplified procedures, maintaining implementation ease while the overall segmented structure provides enhanced security against information set decoding attacks compared to conventional unsegmented codes.
Solution Approach 2:
The error correction code combines multiple algebraic structures (Gaussian integers, Eisenstein integers, binary BCH codes) into a composite code structure. This composite approach maintains relative implementation simplicity through modular design while providing superior resistance to ISD attacks compared to single-structure conventional codes.
3Productivity
If higher code rates are achieved, then data transmission efficiency is improved, but error correction capability may be reduced
Solution Approach 1:
The parallel decoding steps provide dynamic error correction capability that adapts to the actual error patterns in the received data. This dynamic approach allows the system to achieve higher effective code rates by concentrating correction resources on blocks with errors, while maintaining strong error correction capability through the coordinated operation of all decoding steps.
Solution Approach 2:
By segmenting the code into multiple independently decodable blocks, the system achieves higher overall code rates while maintaining error correction capability. Each block can be corrected with lower redundancy requirements, and the collective segmentation strategy ensures that the entire code maintains robust error correction performance despite the higher rate.
Data Source
AI summary
The present disclosure relates to error correction coding based on generalized concatenated codes with restricted error values for code-based cryptography. The error correction encoding comprises encoding the information according to a McEliece cryptosystem or according to a Niederreiter cryptosystem, in each case using an error vector containing at most t E N non-zero error values; and a combination of: a permutation operation, a scrambling operation; and a coding operation involving a p-ary generalized concatenated code, GCC, having an error correction capability t up to which it can correct all possible error patterns. The GCC comprises multiple outer codes A(1) with different dimensions n1 and 1=0, . . . , N, and an inner code B, the inner code B being one of an error correction code over Gaussian integers, an error correction code over Eisenstein integers, or a binary BCH error correction code, wherein q is a natural number with q>2 in the case of an error correction code over Gaussian integers or Eisenstein integers and with q=2 in the case of a binary BCH error correction code. A corresponding decoding method comprises applying erase decoding such that all decoding errors, if any, are recognized during the decoding of the GCC.