Quasi-Cyclic Matrix Authentication for Low-Storage Devices
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Solution Overview
Problem
Current cryptographic authentication methods, such as those based on the RSA algorithm, are inefficient on low-cost devices like smart cards and radio frequency tags due to high computational requirements, and existing error-correcting code decoding methods face storage and calculation speed limitations.
Innovation Solution
Implementing a cryptographic authentication method using a quasi-cyclic matrix for error-correcting code decoding, which reduces storage needs by storing only the baseline of circulating blocks and facilitates fast calculations through the properties of quasi-cyclic matrices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a random public matrix is used in error-correcting code decoding authentication protocols, then security is improved, but storage requirements increase significantly
Solution Approach 1:
The patent changes the structure parameter of the public matrix from a random matrix to a quasi-cyclic matrix. This structural parameter change allows the matrix to be defined by a smaller generating set (first and second generating rows) rather than storing all elements, significantly reducing storage requirements while maintaining the security properties needed for authentication.
Solution Approach 2:
The quasi-cyclic matrix structure allows copying the pattern of the first generating row across multiple rows through cyclic permutations. Instead of storing all matrix elements uniquely, the system copies the generating row pattern to create the entire matrix, reducing the effective storage requirement from the full matrix size to just the generating row size.
2Reliability
If RSA algorithm is used for cryptographic authentication, then security is improved through mathematical difficulty of factoring large integers, but calculation speed decreases on low-cost devices
Solution Approach 1:
The patent changes the computational parameter from RSA's discrete exponential calculations to error-correcting code decoding calculations. This parameter change in the type of mathematical operation enables faster execution on low-cost devices while maintaining security through the NP-completeness of the decoding problem.
Solution Approach 2:
The patent substitutes the RSA authentication mechanism with an error-correcting code-based mechanism. This replacement uses syndrome decoding operations that are computationally lighter and faster than RSA operations, making the system suitable for low-cost cryptographic devices while preserving security.
3Quantity of substance
If a quasi-cyclic matrix is used instead of a random matrix, then storage requirements are reduced, but calculation complexity may increase
Solution Approach 1:
The quasi-cyclic matrix is segmented into repeating circular blocks defined by the generating rows. This segmentation allows the matrix to be represented compactly by its generating structure rather than all elements, reducing storage. The modular block structure also simplifies calculation operations by breaking them down into repeated patterns.
Solution Approach 2:
The generating rows serve multiple functions: they define the matrix structure for storage efficiency, provide the basis for syndrome calculation, and enable fast matrix-vector multiplication through cyclic permutation properties. This multi-functionality reduces overall system complexity despite the specialized matrix structure.
Data Source
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AI summary
The invention relates to a cryptographic method of authentication using a decoding of an error correcting code on the basis of a public matrix, in which the public matrix is a quasi-cyclic matrix. The invention pertains also to a cryptographic device comprising computation means arranged so as to implement this method. The invention makes it possible to reduce the amount of public data to be stored in a cryptographic authentication method using a decoding of an error correcting code on the basis of a public matrix.