Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space
Among the multiple important properties that characterize strong S-boxes for symmetric cryptography and are used in their designs, this study focuses on two: the non-linearity property, a classical security metric, and the confusion coefficient variance property, a statistical proxy for side channel...
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MDPI AG
2025-06-01
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| author | Ismel Martínez-Díaz Carlos Miguel Legón-Pérez Guillermo Sosa-Gómez |
| author_facet | Ismel Martínez-Díaz Carlos Miguel Legón-Pérez Guillermo Sosa-Gómez |
| author_sort | Ismel Martínez-Díaz |
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| description | Among the multiple important properties that characterize strong S-boxes for symmetric cryptography and are used in their designs, this study focuses on two: the non-linearity property, a classical security metric, and the confusion coefficient variance property, a statistical proxy for side channel resistance under the Hamming weight leakage model. Given an S-box, two sets can be created: the set of affine-shifted S-boxes, where S-boxes have the same non-linearity value, and the set of Hamming weight classes, where S-boxes have the same confusion coefficient variance value. The inherent values of these two properties ensure resistance to cryptographic attacks; however, if the value of one property increases, it will imply a decrease in the value of the other property. In view of the aforementioned fact, attaining a trade-off becomes a complex undertaking. The impetus for this research stems from the following hypothesis: if an initial S-box already exhibits a trade-off, it would be advantageous to employ a method that generates new S-boxes while preserving the balance. A thorough review of the extant literature reveals the absence of any methodology that encompasses the aforementioned elements. The present paper proposes a novel methodology for generating an affine-shifted subset of S-boxes, ensuring that the resulting subset possesses the same confusion coefficient variance value. We provide insights on the optimal search strategy to optimize non-linearity and confusion coefficient variance. The proposed methodology guarantees the preservation of constant values on the designated. It is possible to incorporate these properties into a comprehensive design scheme, in which case the remaining S-box properties are to be examined. We also demonstrate that, despite the fact that this subset contains S-boxes with the theoretical resistance to side channel attacks under the Hamming weight model, the S-boxes are in different Hamming weight classes. |
| format | Article |
| id | doaj-art-2999dfb7cf0d495d9e5810c0c11e13a6 |
| institution | Kabale University |
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| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
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| series | Cryptography |
| spelling | doaj-art-2999dfb7cf0d495d9e5810c0c11e13a62025-08-20T03:27:01ZengMDPI AGCryptography2410-387X2025-06-01924510.3390/cryptography9020045Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box SpaceIsmel Martínez-Díaz0Carlos Miguel Legón-Pérez1Guillermo Sosa-Gómez2Department of Mathematics, University of Lleida, Jaume II, 69, 25001 Lleida, SpainInstituto Superior Tecnológico Internacional San Luis (ITSAL), Canonigo Ramos y Avenida La Prensa, Riobamba 060101, EcuadorFacultad de Ciencias Económicas y Empresariales, Universidad Panamericana, Álvaro del Portillo 49, Zapopan 45010, MexicoAmong the multiple important properties that characterize strong S-boxes for symmetric cryptography and are used in their designs, this study focuses on two: the non-linearity property, a classical security metric, and the confusion coefficient variance property, a statistical proxy for side channel resistance under the Hamming weight leakage model. Given an S-box, two sets can be created: the set of affine-shifted S-boxes, where S-boxes have the same non-linearity value, and the set of Hamming weight classes, where S-boxes have the same confusion coefficient variance value. The inherent values of these two properties ensure resistance to cryptographic attacks; however, if the value of one property increases, it will imply a decrease in the value of the other property. In view of the aforementioned fact, attaining a trade-off becomes a complex undertaking. The impetus for this research stems from the following hypothesis: if an initial S-box already exhibits a trade-off, it would be advantageous to employ a method that generates new S-boxes while preserving the balance. A thorough review of the extant literature reveals the absence of any methodology that encompasses the aforementioned elements. The present paper proposes a novel methodology for generating an affine-shifted subset of S-boxes, ensuring that the resulting subset possesses the same confusion coefficient variance value. We provide insights on the optimal search strategy to optimize non-linearity and confusion coefficient variance. The proposed methodology guarantees the preservation of constant values on the designated. It is possible to incorporate these properties into a comprehensive design scheme, in which case the remaining S-box properties are to be examined. We also demonstrate that, despite the fact that this subset contains S-boxes with the theoretical resistance to side channel attacks under the Hamming weight model, the S-boxes are in different Hamming weight classes.https://www.mdpi.com/2410-387X/9/2/45S-boxnon-linearityconfusion coefficient varianceHamming weight class |
| spellingShingle | Ismel Martínez-Díaz Carlos Miguel Legón-Pérez Guillermo Sosa-Gómez Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space Cryptography S-box non-linearity confusion coefficient variance Hamming weight class |
| title | Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space |
| title_full | Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space |
| title_fullStr | Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space |
| title_full_unstemmed | Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space |
| title_short | Generation of Affine-Shifted S-Boxes with Constant Confusion Coefficient Variance and Application in the Partitioning of the S-Box Space |
| title_sort | generation of affine shifted s boxes with constant confusion coefficient variance and application in the partitioning of the s box space |
| topic | S-box non-linearity confusion coefficient variance Hamming weight class |
| url | https://www.mdpi.com/2410-387X/9/2/45 |
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