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 a...
Збережено в:
| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2005 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/156606 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-156606 |
|---|---|
| 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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Maximality of affine group, and hidden graph cryptosystems |
| spellingShingle |
Maximality of affine group, and hidden graph cryptosystems Ustimenko, A.A. |
| title_short |
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_sort |
maximality of affine group, and hidden graph cryptosystems |
| author |
Ustimenko, A.A. |
| author_facet |
Ustimenko, A.A. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156606 |
| 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. |
| work_keys_str_mv |
AT ustimenkoaa maximalityofaffinegroupandhiddengraphcryptosystems |
| first_indexed |
2025-12-07T15:55:57Z |
| last_indexed |
2025-12-07T15:55:57Z |
| _version_ |
1850865570733359104 |