On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups, and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups de...
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| Видавець: | Lugansk National Taras Shevchenko University |
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| Дата: | 2023 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2023
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Algebra and Discrete Mathematics| id |
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oai:ojs.admjournal.luguniv.edu.ua:article-15232023-10-30T03:23:29Z On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups Ustimenko, V. Klisowski, M. multivariate cryptography, stable transformation groups and semigroups, decomposition problem of nonlinear multivariate map into given generators, tame homomorphisms, key exchange protocols, cryptosystems, algebraic graphs 11T71, 14G50 Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups, and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative rings. Efficiently computed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and their inverse versions. The implementation scheme with the sequence of subgroups of affine Cremona group that defines the projective limit was already suggested. We present the implementation of another scheme that uses two projective limits which define two different infinite groups and the homomorphism between them. The security of the corresponding algorithm is based on complexity of the decomposition problem for an element of affine Cremona semigroup into a product of given generators. These algorithms may be used in postquantum technologies. Lugansk National Taras Shevchenko University 2023-10-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1523 10.12958/adm1523 Algebra and Discrete Mathematics; Vol 35, No 2 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1523/pdf Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
multivariate cryptography stable transformation groups and semigroups decomposition problem of nonlinear multivariate map into given generators tame homomorphisms key exchange protocols cryptosystems algebraic graphs 11T71 14G50 |
| spellingShingle |
multivariate cryptography stable transformation groups and semigroups decomposition problem of nonlinear multivariate map into given generators tame homomorphisms key exchange protocols cryptosystems algebraic graphs 11T71 14G50 Ustimenko, V. Klisowski, M. On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| topic_facet |
multivariate cryptography stable transformation groups and semigroups decomposition problem of nonlinear multivariate map into given generators tame homomorphisms key exchange protocols cryptosystems algebraic graphs 11T71 14G50 |
| format |
Article |
| author |
Ustimenko, V. Klisowski, M. |
| author_facet |
Ustimenko, V. Klisowski, M. |
| author_sort |
Ustimenko, V. |
| title |
On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| title_short |
On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| title_full |
On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| title_fullStr |
On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| title_full_unstemmed |
On new protocols of Noncommutative Cryptography in terms of homomorphism of stable multivariate transformation groups |
| title_sort |
on new protocols of noncommutative cryptography in terms of homomorphism of stable multivariate transformation groups |
| description |
Noncommutative cryptography is based on applications of algebraic structures like noncommutative groups, semigroups, and noncommutative rings. Its intersection with Multivariate cryptography contains studies of cryptographic applications of subsemigroups and subgroups of affine Cremona semigroups defined over finite commutative rings. Efficiently computed homomorphisms between stable subsemigroups of affine Cremona semigroups can be used in tame homomorphisms protocols schemes and their inverse versions. The implementation scheme with the sequence of subgroups of affine Cremona group that defines the projective limit was already suggested. We present the implementation of another scheme that uses two projective limits which define two different infinite groups and the homomorphism between them. The security of the corresponding algorithm is based on complexity of the decomposition problem for an element of affine Cremona semigroup into a product of given generators. These algorithms may be used in postquantum technologies. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1523 |
| work_keys_str_mv |
AT ustimenkov onnewprotocolsofnoncommutativecryptographyintermsofhomomorphismofstablemultivariatetransformationgroups AT klisowskim onnewprotocolsofnoncommutativecryptographyintermsofhomomorphismofstablemultivariatetransformationgroups |
| first_indexed |
2024-04-12T06:13:52Z |
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2024-04-12T06:13:52Z |
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