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Communication Complexity and Fourier Coefficients of the Diffie–Hellman Key

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LATIN 2000: Theoretical Informatics (LATIN 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1776))

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Abstract

Let p be a prime and let g be a primitive root of the field \(\mathbb{F}_p\) of p elements. In the paper we show that the communication complexity of the last bit of the Diffie-Hellman key g xy, is at least n/24 + o(n) where x and y are n-bit integers where n is defined by the inequalities 2n ≤ p ≤ 2n + 1 − 1. We also obtain a nontrivial upper bound on the Fourier coefficients of the last bit of g xy. The results are based on some new bounds of exponential sums with g xy.

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Author information

Authors and Affiliations

  1. Department of Computing, Macquarie University, Sydney, NSW 2109, Australia

    Igor E. Shparlinski

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  1. Igor E. Shparlinski
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Editors and Affiliations

  1. ETH Zurich, Institute of Computational Science, CH-8092 Zurich and, Swiss Institute of Bioinformatics, Switzerland

    Gaston H. Gonnet

  2. Pedeciba Informática, Casilla de Correo 16120, Distrito 6, Montevideo, Uruguay

    Alfredo Viola

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© 2000 Springer-Verlag Berlin Heidelberg

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Shparlinski, I.E. (2000). Communication Complexity and Fourier Coefficients of the Diffie–Hellman Key. In: Gonnet, G.H., Viola, A. (eds) LATIN 2000: Theoretical Informatics. LATIN 2000. Lecture Notes in Computer Science, vol 1776. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719839_27

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  • DOI: https://doi.org/10.1007/10719839_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67306-4

  • Online ISBN: 978-3-540-46415-0

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