Spectral Modular Arithmetic for Cryptography

  • G÷kay Saldamli
  • Çetin Kaya Koç


Most public-key cryptosystems require resource-intensive arithmetic calculations in certain mathematical structures such as finite fields, groups, and rings. The efficient realizations of the these operations, including modular multiplication, inversion, and exponentiation are at the center of research activities in cryptographic engineering. Note that, being modular, these operations involve sequential reduction steps.

Spectral techniques for integer multiplication have been known for over a quarter of a century. Using the spectral integer multiplication of Schönhage and Strassen [1], large to extremely large sizes of numbers can be multiplied efficiently. Such computations are needed when computing \(\pi\)


Discrete Fourier Transform Modular Multiplication Discrete Logarithm Problem Fermat Ring Evaluation Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Eczacibaşi Embedded Design CenterUSA
  2. 2.City University of Istanbul & University of California Santa BarbaraSanta Barbara

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