Finite Fields and Quadratic Residues

  • Neal Koblitz
Part of the Graduate Texts in Mathematics book series (GTM, volume 114)


In this chapter we shall assume familiarity with the basic definitions and properties of a field. We now briefly recall what we need.


Nonzero Element Finite Field Irreducible Polynomial Splitting Field Quadratic Residue 
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  1. 1.
    L. Adleman, K. Manders, and G. Miller, “On taking roots in finite fields,” Proc. 20th Annual Symposium on the Foundations of Computer Science (1979), 175–178.Google Scholar
  2. 2.
    E. R. Berlekamp, “Factoring polynomials over large finite fields,” Math. comp., 24 (1970), 713–735.MathSciNetCrossRefGoogle Scholar
  3. 3.
    I. Blake, X. Gao, A. Menezes, R. Mullen, S. Vanstone, and T. Yaghoobi-an, Applications of Finite Fields, Kluwer Acad. Publ., 1992.Google Scholar
  4. 4.
    C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966.Google Scholar
  5. 5.
    E. Grosswald, Topics from the Theory of Numbers, 2nd ed., Birkhauser, 1984.Google Scholar
  6. 6.
    I. N. Herstein, Topics in Algebra, 2nd ed., Wiley, 1975.Google Scholar
  7. 7.
    K. Ireland and M. I. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1990.Google Scholar
  8. 8.
    S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.Google Scholar
  9. 9.
    R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge Univ. Press, 1986.Google Scholar
  10. 10.
    V. Pless, Introduction to the Theory of Error-Correcting Codes, Wiley, 1982.Google Scholar
  11. 11.
    D. Shanks, Solved and Unsolved Problems in Number Theory, 3rd ed., Chelsea Publ. Co., 1985.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Neal Koblitz
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA

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