S-box Construction Based on Linear Fractional Transformation and Permutation Function
Substitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/5/826 |
| _version_ | 1797567707717042176 |
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| author | Liyana Chew Nizam Chew Eddie Shahril Ismail |
| author_facet | Liyana Chew Nizam Chew Eddie Shahril Ismail |
| author_sort | Liyana Chew Nizam Chew |
| collection | DOAJ |
| description | Substitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically strong S-box depends on its construction technique. This work aims to design and develop a cryptographically strong 8 × 8 S-box for block ciphers. In this work, the construction of the S-box is based on the linear fractional transformation and permutation function. Three steps involved in producing the S-box. In step one, an irreducible polynomial of degree eight is chosen, and all roots of the primitive irreducible polynomial are calculated. In step two, algebraic properties of linear fractional transformation are applied in Galois Field GF (2<sup>8</sup>). Finally, the produced matrix is permuted to add randomness to the S-box. The strength of the S-box is measured by calculating its potency to create confusion. To analyze the security properties of the S-box, some well-known and commonly used algebraic attacks are used. The proposed S-box is analyzed by nonlinearity test, algebraic degree, differential uniformity, and strict avalanche criterion which are the avalanche effect test, completeness test, and strong S-box test. S-box analysis is done before and after the application of the permutation function and the analysis result shows that the S-box with permutation function has reached the optimal properties as a secure S-box. |
| first_indexed | 2024-03-10T19:46:18Z |
| format | Article |
| id | doaj.art-08142933835d45d1aeb10c682ce40e4f |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T19:46:18Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-08142933835d45d1aeb10c682ce40e4f2023-11-20T00:46:32ZengMDPI AGSymmetry2073-89942020-05-0112582610.3390/sym12050826S-box Construction Based on Linear Fractional Transformation and Permutation FunctionLiyana Chew Nizam Chew0Eddie Shahril Ismail1Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, MalaysiaDepartment of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 UKM, Selangor, MalaysiaSubstitution boxes (S-box) with strong and secure cryptographic properties are widely used for providing the key property of nonlinearity in block ciphers. This is critical to be resistant to a standard attack including linear and differential cryptanalysis. The ability to create a cryptographically strong S-box depends on its construction technique. This work aims to design and develop a cryptographically strong 8 × 8 S-box for block ciphers. In this work, the construction of the S-box is based on the linear fractional transformation and permutation function. Three steps involved in producing the S-box. In step one, an irreducible polynomial of degree eight is chosen, and all roots of the primitive irreducible polynomial are calculated. In step two, algebraic properties of linear fractional transformation are applied in Galois Field GF (2<sup>8</sup>). Finally, the produced matrix is permuted to add randomness to the S-box. The strength of the S-box is measured by calculating its potency to create confusion. To analyze the security properties of the S-box, some well-known and commonly used algebraic attacks are used. The proposed S-box is analyzed by nonlinearity test, algebraic degree, differential uniformity, and strict avalanche criterion which are the avalanche effect test, completeness test, and strong S-box test. S-box analysis is done before and after the application of the permutation function and the analysis result shows that the S-box with permutation function has reached the optimal properties as a secure S-box.https://www.mdpi.com/2073-8994/12/5/826cryptographysubstitution boxblock cipher |
| spellingShingle | Liyana Chew Nizam Chew Eddie Shahril Ismail S-box Construction Based on Linear Fractional Transformation and Permutation Function Symmetry cryptography substitution box block cipher |
| title | S-box Construction Based on Linear Fractional Transformation and Permutation Function |
| title_full | S-box Construction Based on Linear Fractional Transformation and Permutation Function |
| title_fullStr | S-box Construction Based on Linear Fractional Transformation and Permutation Function |
| title_full_unstemmed | S-box Construction Based on Linear Fractional Transformation and Permutation Function |
| title_short | S-box Construction Based on Linear Fractional Transformation and Permutation Function |
| title_sort | s box construction based on linear fractional transformation and permutation function |
| topic | cryptography substitution box block cipher |
| url | https://www.mdpi.com/2073-8994/12/5/826 |
| work_keys_str_mv | AT liyanachewnizamchew sboxconstructionbasedonlinearfractionaltransformationandpermutationfunction AT eddieshahrilismail sboxconstructionbasedonlinearfractionaltransformationandpermutationfunction |