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POLYNOMIAL REPRESENTATIONS FOR n-TH ROOTS IN FINITE FIELDS

  • Chang, Seunghwan (Institute of Mathematical Sciences Ewha Womans University) ;
  • Kim, Bihtnara (Department of Mathematics Ewha Womans University) ;
  • Lee, Hyang-Sook (Department of Mathematics Ewha Womans University)
  • Received : 2014.05.30
  • Published : 2015.01.01

Abstract

Computing square, cube and n-th roots in general, in finite fields, are important computational problems with significant applications to cryptography. One interesting approach to computational problems is by using polynomial representations. Agou, Del$\acute{e}$eglise and Nicolas proved results concerning the lower bounds for the length of polynomials representing square roots modulo a prime p. We generalize the results by considering n-th roots over finite fields for arbitrary n > 2.

Keywords

cube roots;n-th roots;finite fields

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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