Structural Properties of Twisted Reed-Solomon Codes with Applications to Cryptography
This work addresses the need for robust cryptographic primitives resistant to attacks, though it appears incremental as it builds upon existing code structures.
The authors tackled the problem of constructing secure code-based cryptographic systems by generalizing Twisted Reed-Solomon codes to create a new large class of MDS codes, proving that a subfamily resists existing structural attacks on Reed-Solomon-like codes.
We present a generalisation of Twisted Reed-Solomon codes containing a new large class of MDS codes. We prove that the code class contains a large subfamily that is closed under duality. Furthermore, we study the Schur squares of the new codes and show that their dimension is often large. Using these structural properties, we single out a subfamily of the new codes which could be considered for code-based cryptography: These codes resist some existing structural attacks for Reed-Solomon-like codes, i.e. methods for retrieving the code parameters from an obfuscated generator matrix.