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...

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Опубліковано в: :Algebra and Discrete Mathematics
Дата:2005
Автор: Ustimenko, A.A.
Формат: Стаття
Мова:English
Опубліковано: Інститут прикладної математики і механіки НАН України 2005
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/156606
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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.

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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.
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