Improved Computation of Square Roots in Specific Finite Fields

@article{Han2009ImprovedCO,
  title={Improved Computation of Square Roots in Specific Finite Fields},
  author={Dong-Guk Han and Dooho Choi and Howon Kim},
  journal={IEEE Transactions on Computers},
  year={2009},
  volume={58},
  pages={188-196}
}
In this paper, we study exponentiation in the specific finite fields F, with very special exponents such as those that occur in algorithms for computing square roots. Here, q is a prime power, q = pk, where k > 1, and k is odd. Our algorithmic approach improves the corresponding exponentiation resulted from the better rewritten exponent. To the best of our knowledge, it is the first major improvement to the Tonelli-Shanks algorithm, for example, the number of multiplications can be reduced to… CONTINUE READING
Highly Cited
This paper has 23 citations. REVIEW CITATIONS

Citations

Publications citing this paper.
Showing 1-10 of 12 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 16 references

An Analysis of Shanks’s Algorithm for Computing Square Roots in Finite Fields

  • S. Lindhurst
  • CRM Proc. and Lecture Notes, vol. 19, pp. 231-242…
  • 1999
Highly Influential
3 Excerpts

Probabilistic Primality Testing, summary by F

  • A.O.L. Atkin
  • Morain, Research Report 1779,
  • 1992
Highly Influential
3 Excerpts

Computation in Optimal Extension Fields

  • D. V. Bailey
  • master thesis, http://www.wpi.edu/Pubs/ETD…
  • 2008
1 Excerpt

A Method for Distinguishing the Two Candidate Elliptic Curves in the Complex Multiplication Method

  • Y. Nogami, M. Obara, Y. Morikawa
  • ETRI J., vol. 28, no. 6, pp. 745-760, Dec. 2006.
  • 2006
1 Excerpt

On the Computation of Square Roots in Finite Fields

  • S. Müller
  • J. Design, Codes and Cryptography, vol. 31, pp…
  • 2004
3 Excerpts

A Scalable Structure for a Multiplier and an Inversion Unit in GF ð2Þ

  • C. Lee, J. Lee
  • ETRI J., vol. 25, no. 5, pp. 315-320, Oct. 2003.
  • 2003
1 Excerpt

Similar Papers

Loading similar papers…