Maximality of affine group, and hidden graph cryptosystems

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

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.