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 expanded code over the base field. Considering the expanded codes provide a safeguard against distinguisher attacks based on the Schur product. Moreover, without using cyclic or quasi-cyclic structure we obtain a key size reduction of nearly 60% compared to the classic McEliece cryptosystem proposed by Bernstein et al.
In this paper we generalize the Ball-Collision Algorithm by Bernstein, Lange, Peters from the binary field to a general finite field. We also provide a complexity analysis and compare the asymptotic complexity to other generalized information set decoding algorithms.
<p style='text-indent:20px;'>In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric. We first prove that the decisional version of the problem is NP-complete, by a reduction from the <inline-formula><tex-math id="M1">\begin{document}$ 3 $\end{document}</tex-math></inline-formula>-dimensional matching problem. Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel solutions. For the analyzed algorithms, we assess the computational complexity in the asymptotic regime and compare it to the corresponding algorithms in the Hamming metric.</p>
Let n and m be positive integers such that n < m. In this paper we compute the density of rectangular unimodular n by m matrices over the ring of algebraic integers of a number field.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.