Titlebook: Algebra, Codes and Cryptology; First International Cheikh Thiecoumba Gueye,Edoardo Persichetti,Johann Conference proceedings 2019 Springer

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On the Computation of Minimal Free Resolutions with Integer CoefficientsLet . be an ideal of .. We introduce in this paper the concept of .ideal . of . which is a proper ideal of . and we propose a technique for computing a weak Gr?bner basis for .. This result is central and leads to the computation of a minimal free resolution for . as an .module.

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On the Splitting Field of Some Polynomials with Class Number OneLet .(.) be an irreducible monic polynomial of ., . be the discriminant of .(.) and . be the splitting field of .(.). In this paper, we study the class number one problem for the splitting field . or the condition for which the class number of . is equal to 1 using an algebraic approach based on the Hilbert class field towers of some fields.

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Politics of Citizenship and Migrationduce the public key size. In our scheme the underlying Generalized Reed-Solomon code is not secret, so the classical attacks such as square code or folding attacks have no more purpose against it. In addition one part of the security of this scheme is based on hard problems in coding theory like ..

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https://doi.org/10.1007/978-3-031-23379-1ately, most of these variants are vulnerable to structural attacks because of the algebraic structure of the underlying codes. In this work, we propose the first efficient secure scheme based on polar codes (i.e., .), which is inspired by RLCE scheme, a candidate for the NIST post-quantum cryptograp

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