A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes.
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| Title: | A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes. |
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| Authors: | Joundan, Issam Abderrahman1 joundan.fsb@gmail.com, Nouh, Said1, Azouazi, Mohamed1, Namir, Abdelwahed1 |
| Source: | International Journal of Electrical & Computer Engineering (2088-8708). Apr2019, Vol. 9 Issue 2, p1232-1239. 8p. |
| Subjects: | Multipliers (Mathematical analysis), Cryptosystems, Error-correcting codes, Public key cryptography, Cyclic codes, Coding theory, Permutations |
| Abstract: | BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity. ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Joundan%2C+Issam+Abderrahman%22">Joundan, Issam Abderrahman</searchLink><relatesTo>1</relatesTo><i> joundan.fsb@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Nouh%2C+Said%22">Nouh, Said</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Azouazi%2C+Mohamed%22">Azouazi, Mohamed</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Namir%2C+Abdelwahed%22">Namir, Abdelwahed</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Electrical+%26+Computer+Engineering+%282088-8708%29%22">International Journal of Electrical & Computer Engineering (2088-8708)</searchLink>. Apr2019, Vol. 9 Issue 2, p1232-1239. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Multipliers+%28Mathematical+analysis%29%22">Multipliers (Mathematical analysis)</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptosystems%22">Cryptosystems</searchLink><br /><searchLink fieldCode="DE" term="%22Error-correcting+codes%22">Error-correcting codes</searchLink><br /><searchLink fieldCode="DE" term="%22Public+key+cryptography%22">Public key cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Cyclic+codes%22">Cyclic codes</searchLink><br /><searchLink fieldCode="DE" term="%22Coding+theory%22">Coding theory</searchLink><br /><searchLink fieldCode="DE" term="%22Permutations%22">Permutations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: BCH codes represent an important class of cyclic error-correcting codes; their minimum distances are known only for some cases and remains an open NP-Hard problem in coding theory especially for large lengths. This paper presents an efficient scheme ZSSMP (Zimmermann Special Stabilizer Multiplier Permutation) to find the true value of the minimum distance for many large BCH codes. The proposed method consists in searching a codeword having the minimum weight by Zimmermann algorithm in the sub codes fixed by special stabilizer multiplier permutations. These few sub codes had very small dimensions compared to the dimension of the considered code itself and therefore the search of a codeword of global minimum weight is simplified in terms of run time complexity. ZSSMP is validated on all BCH codes of length 255 for which it gives the exact value of the minimum distance. For BCH codes of length 511, the proposed technique passes considerably the famous known powerful scheme of Canteaut and Chabaud used to attack the public-key cryptosystems based on codes. ZSSMP is very rapid and allows catching the smallest weight codewords in few seconds. By exploiting the efficiency and the quickness of ZSSMP, the true minimum distances and consequently the error correcting capability of all the set of 165 BCH codes of length up to 1023 are determined except the two cases of the BCH(511,148) and BCH(511,259) codes. The comparison of ZSSMP with other powerful methods proves its quality for attacking the hardness of minimum weight search problem at least for the codes studied in this paper. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal of Electrical & Computer Engineering (2088-8708) is the property of Institute of Advanced Engineering & Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.11591/ijece.v9i2.pp1232-1239 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 1232 Subjects: – SubjectFull: Multipliers (Mathematical analysis) Type: general – SubjectFull: Cryptosystems Type: general – SubjectFull: Error-correcting codes Type: general – SubjectFull: Public key cryptography Type: general – SubjectFull: Cyclic codes Type: general – SubjectFull: Coding theory Type: general – SubjectFull: Permutations Type: general Titles: – TitleFull: A new efficient way based on special stabilizer multiplier permutations to attack the hardness of the minimum weight search problem for large BCH codes. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Joundan, Issam Abderrahman – PersonEntity: Name: NameFull: Nouh, Said – PersonEntity: Name: NameFull: Azouazi, Mohamed – PersonEntity: Name: NameFull: Namir, Abdelwahed IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 20888708 Numbering: – Type: volume Value: 9 – Type: issue Value: 2 Titles: – TitleFull: International Journal of Electrical & Computer Engineering (2088-8708) Type: main |
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