APPLICATION OF MATRIX REPRESENTATIONS IN CRYPTOGRAPHIC ALGORITHMS
Keywords:
vector space, linear mappings, matrix mappings, MDS matrices, finite fields, modern ciphersAbstract
Matrix reflections are one of the main mechanisms of modern cryptographic algorithms. They play an important role in increasing the diffusion strength, creating protection against linearity, forming complex structures in lattice-based public-key schemes, and mathematically representing the evolution of the internal state in stream ciphers. This article provides an in-depth analysis of the theoretical foundations of matrix reflections, their role in block and stream ciphers, the construction of MDS matrices, as well as the cryptographic significance of basis matrices in lattice cryptosystems.
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