Secret sharing in a special linear group
Objectives. The problem of developing the mathematical foundations of modular secret sharing in a special linear group over the ring of integers is being solved.The relevance of the problem is reduced to the fact that a large number of requirements are imposed on secret sharing schemes. These includ...
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| Format: | Article |
| Language: | Russian |
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National Academy of Sciences of Belarus, the United Institute of Informatics Problems
2024-09-01
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| Series: | Informatika |
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| Online Access: | https://inf.grid.by/jour/article/view/1293 |
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| _version_ | 1832543388288679936 |
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| author | V. I. Yanchevskiĭ I. A. Havarushka G. V. Matveev |
| author_facet | V. I. Yanchevskiĭ I. A. Havarushka G. V. Matveev |
| author_sort | V. I. Yanchevskiĭ |
| collection | DOAJ |
| description | Objectives. The problem of developing the mathematical foundations of modular secret sharing in a special linear group over the ring of integers is being solved.The relevance of the problem is reduced to the fact that a large number of requirements are imposed on secret sharing schemes. These include the ideality of the scheme, the possibility of verification, changing the threshold without the participation of the dealer, the implementation of a non-threshold access structure and some others. Every secret sharing scheme developed to date does not fully satisfy all these requirements. It only has a certain configuration of these properties. The development of a scheme on a new mathematical basis is intended to expand the list of these configurations, which creates more opportunities for the user in choosing the optimal option.Methods. Group theory, modular arithmetic and theory of secret sharing schemes are used.Results. A fundamental domain with respect to the action of the main congruence subgroup by right shifts in the special linear group of second-order matrices over the ring of integers is constructed. On this basis, methods for modular secret sharing and its threshold restoration are proposed.Conclusion. A rigorous mathematical justification is given for the correctness of the algorithms for generating partial secrets and restoring the main secret in the special linear group over the ring of integers. These results will be used to study the configuration of secret sharing properties in this group. |
| format | Article |
| id | doaj-art-cd33ad97d2e04d41a9b76920d61f50e4 |
| institution | Kabale University |
| issn | 1816-0301 |
| language | Russian |
| publishDate | 2024-09-01 |
| publisher | National Academy of Sciences of Belarus, the United Institute of Informatics Problems |
| record_format | Article |
| series | Informatika |
| spelling | doaj-art-cd33ad97d2e04d41a9b76920d61f50e42025-02-03T11:46:36ZrusNational Academy of Sciences of Belarus, the United Institute of Informatics ProblemsInformatika1816-03012024-09-01213394710.37661/1816-0301-2024-21-3-39-471069Secret sharing in a special linear groupV. I. Yanchevskiĭ0I. A. Havarushka1G. V. Matveev2Institute of Mathematics of the National Academy of Sciences of BelarusInstitute of Mathematics of the National Academy of Sciences of BelarusBelarusian State UniversityObjectives. The problem of developing the mathematical foundations of modular secret sharing in a special linear group over the ring of integers is being solved.The relevance of the problem is reduced to the fact that a large number of requirements are imposed on secret sharing schemes. These include the ideality of the scheme, the possibility of verification, changing the threshold without the participation of the dealer, the implementation of a non-threshold access structure and some others. Every secret sharing scheme developed to date does not fully satisfy all these requirements. It only has a certain configuration of these properties. The development of a scheme on a new mathematical basis is intended to expand the list of these configurations, which creates more opportunities for the user in choosing the optimal option.Methods. Group theory, modular arithmetic and theory of secret sharing schemes are used.Results. A fundamental domain with respect to the action of the main congruence subgroup by right shifts in the special linear group of second-order matrices over the ring of integers is constructed. On this basis, methods for modular secret sharing and its threshold restoration are proposed.Conclusion. A rigorous mathematical justification is given for the correctness of the algorithms for generating partial secrets and restoring the main secret in the special linear group over the ring of integers. These results will be used to study the configuration of secret sharing properties in this group.https://inf.grid.by/jour/article/view/1293special linear groupcongruence subgroupfundamental domainmodular secret sharingthreshold access structure |
| spellingShingle | V. I. Yanchevskiĭ I. A. Havarushka G. V. Matveev Secret sharing in a special linear group Informatika special linear group congruence subgroup fundamental domain modular secret sharing threshold access structure |
| title | Secret sharing in a special linear group |
| title_full | Secret sharing in a special linear group |
| title_fullStr | Secret sharing in a special linear group |
| title_full_unstemmed | Secret sharing in a special linear group |
| title_short | Secret sharing in a special linear group |
| title_sort | secret sharing in a special linear group |
| topic | special linear group congruence subgroup fundamental domain modular secret sharing threshold access structure |
| url | https://inf.grid.by/jour/article/view/1293 |
| work_keys_str_mv | AT viyanchevskii secretsharinginaspeciallineargroup AT iahavarushka secretsharinginaspeciallineargroup AT gvmatveev secretsharinginaspeciallineargroup |