Non-linear Data Transformation Apparatus Using Small S-boxes and MDS Matrices
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Solution Overview
Problem
Current cryptographic algorithms, particularly common-key blockcipher cryptography, face challenges in achieving high security and performance due to limitations in the design of S-boxes used for non-linear transformation processing, which are vulnerable to various cryptanalytic attacks and have long critical paths, making it difficult to implement efficient and secure cryptographic systems.
Innovation Solution
The proposed solution involves a data transformation apparatus and method that utilize a combination of small non-linear transformation parts and a linear transformation part using a highly branched matrix for optimal diffusion mappings, specifically employing MDS matrices over an extension field to perform non-linear transformation processing, thereby enhancing security and reducing the critical path length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional S-boxes are used for non-linear transformation processing, then the implementation is simpler, but the resistance to cryptanalytic attacks is reduced
Solution Approach 1:
The patent divides the non-linear transformation processing into multiple small non-linear transformation parts (first and second non-linear transformation parts) instead of using a single conventional S-box. This segmentation allows each part to be simpler while the combination provides enhanced security against cryptanalytic attacks through optimal diffusion mappings.
2Productivity
If conventional linear transformation matrices are used, then the implementation is easier, but the diffusion process is less efficient
Solution Approach 1:
The patent changes the parameters of the linear transformation by using highly branched matrices with a number of branches not less than m (where m is the matrix dimension). This parameter change optimizes the diffusion process, ensuring that changes in input bits propagate efficiently to output bits, thereby improving diffusion efficiency without excessive complexity.
3Reliability
If larger matrices are used for linear transformation, then the diffusion mapping is more optimal, but the critical path length increases
Solution Approach 1:
The patent segments the linear transformation into multiple stages with highly branched matrices, where each stage processes a portion of the data. This segmentation allows optimal diffusion mappings to be achieved through the branching structure rather than through a single large matrix, thereby maintaining shorter critical path lengths while preserving diffusion quality.
Solution Approach 2:
The patent introduces the dimension of matrix branching (number of branches) as a new structural parameter. Instead of increasing matrix size to improve diffusion, the invention uses highly branched matrices that spread data transformation across multiple output lines, achieving optimal diffusion mappings without proportionally increasing the critical path length.
Data Source
AI summary
A non-linear transformation processing structure having a high implementation efficiency and a high security is realized. Data transformation is performed using a first non-linear transformation part performing non-linear transformation using a plurality of small S-boxes; a linear transformation part receiving all the outputs from the first non-linear transformation part and performing data transformation using a matrix for performing optimal diffusion mappings; and a second non-linear transformation part including a plurality of small non-linear transformation parts that perform non-linear transformation on individual data units into which output data from the linear transformation part is divided. With this structure, appropriate data diffusion can be achieved without excessively increasing a critical path, and a structure with a high implementation efficiency and a high security can be achieved.