Matrix representation of cryptographic functions
نویسندگان
چکیده
The Discrete Logarithm and the Diffie-Hellman are two hard computational problems, closely related to cryptography and its applications. The computational equivalence of these problems has been proved only for some special cases. In this study, using LU-decomposition to Vandermonde matrices, we are able to transform the two problems in terms of matrices, thus giving a new perspective to their equivalence. A first study on matrix expressions for the Double and Multiple Discrete Logarithms is also presented. 1 A.T.E.I. of Epirus, P.O.110, GR-47100 Arta, Greece, University of Patras Artificial Intelligence Research Center, University of Patras, GR-26110 Patras, Greece, e-mail: [email protected] 2 Computational Intelligence Laboratory, Department of Mathematics, Univeristy of Patras, GR-26110 Patras, Greece, e-mail: [email protected] 3 Computational Intelligence Laboratory, Department of Mathematics, Univeristy of Patras, GR-26110 Patras, Greece, e-mail: [email protected] 4 Computational Intelligence Laboratory, Department of Mathematics, Univeristy of Patras, GR-26110 Patras, Greece, Computational Intelligence Laboratory, Department of Mathematics, Univeristy of Patras, GR-26110 Patras, Greece, e-mail: [email protected] Article Info: Received : November 1, 2012. Revised : January 30, 2013 Published online : March 30, 2013 206 Matrix representation of cryptographic functions Mathematics Subject Classification: 94A60, 11T71, 12Y05, 15A24
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