Encryption scheme based on expanded Reed-Solomon codes

Abstract

<p style='text-indent:20px;'>We present a code-based public-key cryptosystem, in which we use Reed-Solomon codes over an extension field as secret codes and disguise it by considering its shortened expanded code over the base field. Considering shortened expanded codes provides a safeguard against distinguisher attacks based on the Schur product. Moreover, without using a cyclic or a quasi-cyclic structure we obtain a key size reduction of nearly <inline-formula><tex-math id="M1">\begin{document}$ 45 \% $\end{document}</tex-math></inline-formula> compared to the classic {McE}liece cryptosystem proposed by Bernstein <i>et al.</i>