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...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2005 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/156606 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Maximality of affine group, and hidden graph cryptosystems / A.A. Ustimenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 133–150. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862683416117379072 |
|---|---|
| author | Ustimenko, A.A. |
| author_facet | Ustimenko, A.A. |
| citation_txt | Maximality of affine group, and hidden graph cryptosystems / A.A. Ustimenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 133–150. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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 deg ≥ 2 in case of prime
field Fp. As it follows from the maximality of affine group each
bijection on Fp
n
can be obtained by such combining.
|
| first_indexed | 2025-12-07T15:55:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-156606 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T15:55:57Z |
| publishDate | 2005 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ustimenko, A.A. 2019-06-18T17:48:33Z 2019-06-18T17:48:33Z 2005 Maximality of affine group, and hidden graph cryptosystems / A.A. Ustimenko // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 133–150. — Бібліогр.: 25 назв. — англ. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/156606 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 deg ≥ 2 in case of prime
 field Fp. As it follows from the maximality of affine group each
 bijection on Fp
 n
 can be obtained by such combining. Dedicated to Yu.A. Drozd on the occasion of his 60th birthday en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Maximality of affine group, and hidden graph cryptosystems Article published earlier |
| spellingShingle | Maximality of affine group, and hidden graph cryptosystems Ustimenko, A.A. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/156606 |
| work_keys_str_mv | AT ustimenkoaa maximalityofaffinegroupandhiddengraphcryptosystems |