NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS
Further development of cryptographic algorithms based on the principles of many-valued logic requires more accurate research of non-binary cryptographic primitives – S-boxes. One of the most promising constructions for the synthesis of S-boxes is the Nyberg construction, which ensures high quality o...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Belarusian National Technical University
2017-11-01
|
| Series: | Sistemnyj Analiz i Prikladnaâ Informatika |
| Subjects: | |
| Online Access: | https://sapi.bntu.by/jour/article/view/177 |
| _version_ | 1797873760206848000 |
|---|---|
| author | A. V. Sokolov O. N. Zhdanov |
| author_facet | A. V. Sokolov O. N. Zhdanov |
| author_sort | A. V. Sokolov |
| collection | DOAJ |
| description | Further development of cryptographic algorithms based on the principles of many-valued logic requires more accurate research of non-binary cryptographic primitives – S-boxes. One of the most promising constructions for the synthesis of S-boxes is the Nyberg construction, which ensures high quality of the designed S-boxes in the binary case. The disadvantage of the Nyberg construction is the small cardinality of the classes of the constructed S-boxes. Nevertheless, this disadvantage can be overcome by considering all the isomorphic representations of the main field, substantially expanding the choice of available high-quality S-boxes. The research carried out in this paper has shown that the advantages of the Nyberg construction can be easily transferred to a many-valued case. Thus, we construct complete sets of S-boxes of the Nyberg construction over all isomorphic representations of fields GF(pᵏ), р = 3,5, and research their nonlinear characteristics. As a criterion of nonlinearity, we measure the distances from the component many-valued functions to the set of Vilenkin–Chrestenson functions that are considered to be the most linear. The correlation coefficients of the output and input vectors of the obtained S-boxes are calculated. The researches performed have shown the high quality of the constructed cryptographic primitives and allow recommendation of them for use in cryptoalgorithms based on the principles of many-valued logic. |
| first_indexed | 2024-04-10T01:20:14Z |
| format | Article |
| id | doaj.art-03d08ed662894b6d8896c7baf45740a1 |
| institution | Directory Open Access Journal |
| issn | 2309-4923 2414-0481 |
| language | English |
| last_indexed | 2024-04-10T01:20:14Z |
| publishDate | 2017-11-01 |
| publisher | Belarusian National Technical University |
| record_format | Article |
| series | Sistemnyj Analiz i Prikladnaâ Informatika |
| spelling | doaj.art-03d08ed662894b6d8896c7baf45740a12023-03-13T09:47:40ZengBelarusian National Technical UniversitySistemnyj Analiz i Prikladnaâ Informatika2309-49232414-04812017-11-0103596710.21122/2309-4923-2017-3-59-67137NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOISA. V. Sokolov0O. N. Zhdanov1Одесский национальный политехнический университетСибирский государственный аэрокосмический университет им. академика М. Ф. РешетневаFurther development of cryptographic algorithms based on the principles of many-valued logic requires more accurate research of non-binary cryptographic primitives – S-boxes. One of the most promising constructions for the synthesis of S-boxes is the Nyberg construction, which ensures high quality of the designed S-boxes in the binary case. The disadvantage of the Nyberg construction is the small cardinality of the classes of the constructed S-boxes. Nevertheless, this disadvantage can be overcome by considering all the isomorphic representations of the main field, substantially expanding the choice of available high-quality S-boxes. The research carried out in this paper has shown that the advantages of the Nyberg construction can be easily transferred to a many-valued case. Thus, we construct complete sets of S-boxes of the Nyberg construction over all isomorphic representations of fields GF(pᵏ), р = 3,5, and research their nonlinear characteristics. As a criterion of nonlinearity, we measure the distances from the component many-valued functions to the set of Vilenkin–Chrestenson functions that are considered to be the most linear. The correlation coefficients of the output and input vectors of the obtained S-boxes are calculated. The researches performed have shown the high quality of the constructed cryptographic primitives and allow recommendation of them for use in cryptoalgorithms based on the principles of many-valued logic.https://sapi.bntu.by/jour/article/view/177s-блокконструкция нибергмногозначная логика |
| spellingShingle | A. V. Sokolov O. N. Zhdanov NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS Sistemnyj Analiz i Prikladnaâ Informatika s-блок конструкция ниберг многозначная логика |
| title | NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS |
| title_full | NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS |
| title_fullStr | NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS |
| title_full_unstemmed | NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS |
| title_short | NONLINEAR NYBERG CONSTRUCTION TRANSFORMS OVER ISOMORPHIC REPRESENTATIONS OF FIELDS GALOIS |
| title_sort | nonlinear nyberg construction transforms over isomorphic representations of fields galois |
| topic | s-блок конструкция ниберг многозначная логика |
| url | https://sapi.bntu.by/jour/article/view/177 |
| work_keys_str_mv | AT avsokolov nonlinearnybergconstructiontransformsoverisomorphicrepresentationsoffieldsgalois AT onzhdanov nonlinearnybergconstructiontransformsoverisomorphicrepresentationsoffieldsgalois |