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A Framework for McEliece-Like Cryptosystems Based on Gabidulin Matrix Codes.
Rel. Roberto Garello. Politecnico di Torino, Corso di laurea magistrale in Communications Engineering, 2026
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Abstract
Code-based cryptography is one of the main candidates for post-quantum cryptography. In fact, its security relies on the hardness of decoding a random-looking linear code, a problem believed to remain difficult even for quantum computers. In particular, rank-metric code-based cryptosystems have attracted significant interest due to their ability to achieve smaller key sizes compared to classical Hamming-metric constructions. Gabidulin codes, which are the rank-metric analogues of Reed–Solomon codes, play a central role among rank-metric codes thanks to their optimal error-correction capability. However, their strong algebraic structure makes them vulnerable to structural attacks, such as Overbeck’s attack, which can distinguish these codes from random ones and recover the hidden structure.
To address this issue, some recent cryptographic proposals rely on Gabidulin matrix codes, obtained by expanding Gabidulin codes defined over extension fields into equivalent representations over the base field
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