Generating efficient circulant-like MDS matrices for implementation
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https://doi.org/10.54654/isj.v2i22.1049Keywords:
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The exploration of maximal distance separable codes (MDS codes) has been a longstanding focus in error-correcting code theory and holds significant relevance in cryptography. Numerous approaches have been investigated for constructing MDS matrices, including deriving them from MDS codes, utilizing Hadamard matrices, Cauchy matrices, Vandermonde matrices, circulant matrices, circulant-like matrices, among others. However, a major challenge for cryptography designers is finding MDS matrices with low implementation cost. In this paper, we propose algorithms for generating efficient circulant-like MDS matrices of size , and for implementation. Subsequently, we evaluate the fixed points, the number of XOR operations of the proposed MDS matrices, and compare them with MDS matrices of other well-known ciphers. These proposed MDS matrices can become promising candidates for many cryptographic algorithms in the future.
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