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# Computer algebra in coding theory and cryptanalysis: Polynomial system solving for decoding linear codes and algebraic cryptanalysis

## Abstract

his book that represents the author's Ph.D. thesis is devoted to applying symbolic methods to the problems of decoding linear codes and of algebraic cryptanalysis. The initial problems are reformulated in terms of systems of polynomial equations over a finite field, which solution(s) should yield a way to solve the initial problems. Solutions of such systems are obtained using Gröbner bases. The first part is devoted to an application of system solving to decoding linear codes. The original method for arbitrary linear codes, which in some sense generalizes the Newton identities method widely known for cyclic codes, is proposed. Since for the method to work the „field equations“ are not needed, it is possible to handle quite large codes. The second part is about the algebraic cryptanalysis of the AES. The systems usually considered in this area have many auxiliary variables that are not needed for the key recovery. Therefore, here the approach is provided where these variables are eliminated and a resulting system in key-variables only is then solved. This is shown to be effective for small scale variants of the AES especially when using several plain-/ciphertext pairs.

Item Type: Book 2009 Bulygin, Stanislav Computer algebra in coding theory and cryptanalysis: Polynomial system solving for decoding linear codes and algebraic cryptanalysis ["languages_typename_1" not defined] his book that represents the author's Ph.D. thesis is devoted to applying symbolic methods to the problems of decoding linear codes and of algebraic cryptanalysis. The initial problems are reformulated in terms of systems of polynomial equations over a finite field, which solution(s) should yield a way to solve the initial problems. Solutions of such systems are obtained using Gröbner bases. The first part is devoted to an application of system solving to decoding linear codes. The original method for arbitrary linear codes, which in some sense generalizes the Newton identities method widely known for cyclic codes, is proposed. Since for the method to work the „field equations“ are not needed, it is possible to handle quite large codes. The second part is about the algebraic cryptanalysis of the AES. The systems usually considered in this area have many auxiliary variables that are not needed for the key recovery. Therefore, here the approach is provided where these variables are eliminated and a resulting system in key-variables only is then solved. This is shown to be effective for small scale variants of the AES especially when using several plain-/ciphertext pairs. Südwestdeutscher Verlag für Hochschulschriften 978-3-8381-0948-0 Secure Data LOEWE > LOEWE-Zentren > CASED – Center for Advanced Security Research DarmstadtLOEWE > LOEWE-ZentrenLOEWE 30 Dec 2016 20:23 TUD-CS-2009-0227 ASCII CitationSimple MetadataEP3 XMLT2T_XMLDublin CoreRDF+XMLReference ManagerMultiline CSVHTML CitationAtomJSONMODSEndNoteBibTeX TUfind oder in Google Send an inquiry

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