We estimate character sums over points on elliptic curves over a finite field 
of q
elements. Pseudorandom sequences can be constructed by taking linear combinations with small
coefficients (for example, from the set {−1, 0, 1}) of a fixed vector of points, which forms the seed
of the generator. We consider several particular cases of this general approach which are of special
practical interest and have occurred in the literature. For each of them we show that the resulting
sequence has good uniformity of distribution properties.
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Journal of Mathematical Cryptology
Managing Editor: Magliveras, Spyros S. / Steinwandt, Rainer / Trung, Tran
Editorial Board: Blackburn, Simon R. / Blundo, Carlo / Burmester, Mike / Cramer, Ronald / Dawson, Ed / Gilman, Robert / Gonzalez Vasco, Maria Isabel / Grosek, Otokar / Helleseth, Tor / Kim, Kwangjo / Koblitz, Neal / Kurosawa, Kaoru / Lauter, Kristin / Lange, Tanja / Menezes, Alfred / Nguyen, Phong Q. / Pieprzyk, Josef / Rötteler, Martin / Safavi-Naini, Rei / Shparlinski, Igor E. / Stinson, Doug / Takagi, Tsuyoshi / Williams, Hugh C. / Yung, Moti
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- Online
- ISSN
- 1862-2984
Distribution of some sequences of points on elliptic curves
Tanja Lange / Igor E. Shparlinski
Published Online: 2007-03-29 | DOI: https://doi.org/10.1515/JMC.2007.001
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Get Access to Full TextKey Words: Public key cryptography,; elliptic curves,; Koblitz curves,; character sums,; pseudorandomness
About the article
Published Online: 2007-03-29
Published in Print: 2007-01-01
Citation Information: Mathematical Cryptology JMC, Volume 1, Issue 1, Pages 1–11, ISSN (Online) 1862-2984, ISSN (Print) 1862-2976, DOI: https://doi.org/10.1515/JMC.2007.001.
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