Transformations of two cryptographic problems in terms of matrices

Authors:
E. C. Laskari;G. C. Meletiou;D. K. Tasoulis;M. N. Vrahatis
Affiliations:
University of Patras, Patras, Greece;A.T.E.I. of Epirus, Arta, Greece and University of Patras, Patras, Greece;University of Patras, Patras, Greece;University of Patras, Patras, Greece
Venue:
ACM SIGSAM Bulletin
Year:
2005

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Abstract

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 transformations for the Double and Multiple Discrete Logarithms is also presented.