Maximality of affine group, and hidden graph cryptosystems
We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as e...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/922 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543172968054784 |
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| author | Ustimenko, A. A. |
| author_facet | Ustimenko, A. A. |
| author_sort | Ustimenko, A. A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T07:18:38Z |
| description | We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as encryption process. To hide such encryption (graph and walk on it) we will use two affine transformation. Like in Imai - Matsumoto encryption the public rule is just a direct polynomial map from the plaintext to the ciphertext.The knowledge about graph and chosen walk on them (the key) allow to decrypt a ciphertext fast. We hope that the system is secure even in the case when the graph is Public but the walk is hidden. In case of "public" graph we can use same encryption as private key algorithm with the resistance to attacks when adversary knows several pairs:(plaintext, ciphertext).We shall discuss the general idea of combining affine transformations and chosen polynomial map of \({\rm deg} \ge 2\) in case of prime field \(F_p\). As it follows from the maximality of affine group each bijection on \({F_p}^n\) can be obtained by such combining. |
| first_indexed | 2026-02-08T07:58:11Z |
| format | Article |
| id | admjournalluguniveduua-article-922 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:11Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9222018-03-21T07:18:38Z Maximality of affine group, and hidden graph cryptosystems Ustimenko, A. A. Data and communication security, e-commerce, Public Key Cryptography, Private Key Encryption We describe a new algebraic-combinatorial method of public key encryption with a certain similarity to the well known Imai-Matsumoto. We use the general idea to treat vertices of a linguistic graph (see [21] and further references) as messages and use the iterative process to walk on such graph as encryption process. To hide such encryption (graph and walk on it) we will use two affine transformation. Like in Imai - Matsumoto encryption the public rule is just a direct polynomial map from the plaintext to the ciphertext.The knowledge about graph and chosen walk on them (the key) allow to decrypt a ciphertext fast. We hope that the system is secure even in the case when the graph is Public but the walk is hidden. In case of "public" graph we can use same encryption as private key algorithm with the resistance to attacks when adversary knows several pairs:(plaintext, ciphertext).We shall discuss the general idea of combining affine transformations and chosen polynomial map of \({\rm deg} \ge 2\) in case of prime field \(F_p\). As it follows from the maximality of affine group each bijection on \({F_p}^n\) can be obtained by such combining. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/922 Algebra and Discrete Mathematics; Vol 4, No 1 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/922/451 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Data and communication security e-commerce Public Key Cryptography Private Key Encryption Ustimenko, A. A. Maximality of affine group, and hidden graph cryptosystems |
| title | Maximality of affine group, and hidden graph cryptosystems |
| title_full | Maximality of affine group, and hidden graph cryptosystems |
| title_fullStr | Maximality of affine group, and hidden graph cryptosystems |
| title_full_unstemmed | Maximality of affine group, and hidden graph cryptosystems |
| title_short | Maximality of affine group, and hidden graph cryptosystems |
| title_sort | maximality of affine group, and hidden graph cryptosystems |
| topic | Data and communication security e-commerce Public Key Cryptography Private Key Encryption |
| topic_facet | Data and communication security e-commerce Public Key Cryptography Private Key Encryption |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/922 |
| work_keys_str_mv | AT ustimenkoaa maximalityofaffinegroupandhiddengraphcryptosystems |