Cryptanalysis of a diffie - hellman's scheme analogue using conjugation and exponentiation on matrix platform | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).

It is proved that the mixed generalized version of the Diffie - Hellman's protocol using matrix platform with the conjugation and exponentiation in a generic case admits computing the shared key in a polynomial time under assumption that the corresponding multiple discrete logarithm problem can be solved in a polynomial time. The computing algorithm uses the original method of linear decomposition and the approach by Menezes and others reducing the computation of the matrix exponent to the multiple discrete logarithm problem. The combination of these two approaches cannot be directly applied because the exponentiation is not automorphism. The proof of the main result is based on the analysis of belonging a monomial matrices to cosets of a matrix group by elementwise permutable subgroups. Thus, a similar question for the symmetric groups has to be studied. Fortunately, a number of results in this sphere is known
Download file
Counter downloads: 261
  • Title Cryptanalysis of a diffie - hellman's scheme analogue using conjugation and exponentiation on matrix platform
  • Headline Cryptanalysis of a diffie - hellman's scheme analogue using conjugation and exponentiation on matrix platform
  • Publesher Tomask State UniversityTomsk State University
  • Issue Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics 7 (Приложение)
  • Date:
  • DOI
Keywords
Diffie - Hellman's protocol, conjugation, search problem, cryptanalysis, протокол Диффи - Хеллмана, сопряжение, проблема поиска, криптоанализ
Authors
References
Kahrobaei D. and Khan B. A non-commutative generalization of ElGamal key exchange using polycyclic groups // Global Telecommun. Conf. 2006. GL0BEC0M'06, IEEE. P. 1-5.
Романьков В. А. Алгебраическая криптография. Омск: ОмГУ, 2013. 135 с.
Романьков В. А. Криптографический анализ некоторых схем шифрования, использующих автоморфизмы // Прикладная дискретная математика. 2013. №3. С. 36-51.
Ko K. H., Lee S. J., Cheon J. H., et al. New public-key cryptosystem using braid groups // Advances in Cryptology-CRYPT0'2000. LNCS. 2000. V. 1880. P. 166-183.
Menezes A. J. and Wu Y.-H. The discrete logarithm problem in GL(n, q) // Ars Combinatoria. 1997. V. 47. P. 23-32.
Menezes A. J. and Vanstone S. A note on cyclic groups, finite fields, and the discrete logarithm problem // Applic. Alg. Eng. Commun. Comput. 1992. No. 3. P. 67-74.
 Cryptanalysis of a diffie - hellman's scheme analogue using conjugation and exponentiation on matrix platform | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).
Cryptanalysis of a diffie - hellman's scheme analogue using conjugation and exponentiation on matrix platform | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2014. № 7 (Приложение).
Download full-text version
Counter downloads: 1917