Some methods are given for cryptanalysis of encryption schemes and key establishment protocols based on a group (loop) algebra or on a graded algebra with multiplicative base and proposed by Rososhek; Mihalev et. al.; Mahalanobis, etc. These cryptosystems have a common feature that all of them (except the scheme of Mihalev) use automorphisms. Also, a cryptanalysis of the key exchange protocol proposed by Megre-leshvili and Djindjihadze is given. An original approach is described to find a secret message or a shared key based on usual tools of linear algebra assuming that platform can be chosen as a finite dimensional algebra, e. g., a matrix algebra over a field. The approach does not suppose to find the secret automorphism used in protocol. A theoretical foundation of this approach and a series of attacks on some cryptosystems based on different generalizations of discrete logarithm and Diffie — Hellman's ideas to noncommutative groups are described by the author earlier. Here the approach is developed by presenting its new applications in cryptanalysis of different schemes and protocols.
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- Title Cryptanalysis of some schemes applying automorphisms
- Headline Cryptanalysis of some schemes applying automorphisms
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Tomsk State University - Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 3(21)
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Keywords
automorphism, El Gamal protocol, Diffie — Hellman scheme, generalized discrete logarithm, discrete logarithm, graded algebra, matrix algebra, loop algebra, group algebra, cryptographic scheme, автоморфизм, протокол ЭльГамаля, схема Диффи — Хеллмана, обобщения дискретного логарифма, дискретный логарифм, градуированная алгебра, матричная алгебра, луповая алгебра, групповая алгебра, схема шифрованияAuthors
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Cryptanalysis of some schemes applying automorphisms | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2013. № 3(21).
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