Quasi-Cyclic Public Matrix Authentication for Low-Memory Devices
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Solution Overview
Problem
Current cryptographic methods of authentication, 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 methods using error-correcting codes with random public matrices face storage constraints and slow calculations.
Innovation Solution
A cryptographic method using a quasi-cyclic matrix for error-correcting code decoding, which reduces storage needs by storing only a base row of circulant blocks and enables quick calculations through circular permutations, allowing implementation on devices with limited processing and storage capacity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a large random public matrix is used for authentication, then security is improved, but storage requirements increase making it incompatible with low-cost devices
Solution Approach 1:
The public matrix is segmented into multiple circulant blocks, where each block has a structured form that allows compression. Instead of storing the entire large random matrix, only the generator vectors of the circulant blocks need to be stored, significantly reducing memory requirements while maintaining the matrix's cryptographic properties
Solution Approach 2:
The matrix structure is changed from completely random to quasi-cyclic with circulant blocks. This parameter change in the matrix structure allows for compact representation through generator vectors, reducing storage from kilobits to much smaller size, while the cryptographic security is preserved through the mathematical properties of the transformed matrix
2Reliability
If RSA algorithm is used for authentication, then security is achieved, but calculation speed decreases on low-cost devices
Solution Approach 1:
The cryptographic system substitutes the RSA mathematical operations (large integer factorization, discrete exponentiation) with error-correcting code operations (syndrome decoding). This replacement changes the computational mechanism from heavy arithmetic operations to more efficient bitwise operations, achieving comparable security with much faster execution on resource-constrained devices
3Quantity of substance
If a pseudo-random generator is implemented to reduce storage, then storage requirements decrease, but device complexity increases beyond low-cost device capabilities
Solution Approach 1:
Instead of using a pseudo-random generator to create the matrix, the system uses explicit mathematical construction of circulant blocks from generator vectors. This copying approach generates deterministic structured matrices that achieve the same storage reduction as pseudo-random generation but without requiring complex generator algorithms, keeping device complexity low
Data Source
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.