Skip to main content

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 114))

  • 4651 Accesses

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 64.95
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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. E. R. Berlekamp, “Factoring polynomials over large finite fields,” Math. comp., 24 (1970), 713–735.

    Article  MathSciNet  Google Scholar 

  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. C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966.

    Google Scholar 

  5. E. Grosswald, Topics from the Theory of Numbers, 2nd ed., Birkhauser, 1984.

    Google Scholar 

  6. I. N. Herstein, Topics in Algebra, 2nd ed., Wiley, 1975.

    Google Scholar 

  7. K. Ireland and M. I. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1990.

    Google Scholar 

  8. S. Lang, Algebra, 2nd ed., Addison-Wesley, 1984.

    Google Scholar 

  9. R. Lidl and H. Niederreiter, Introduction to Finite Fields and Their Applications, Cambridge Univ. Press, 1986.

    Google Scholar 

  10. V. Pless, Introduction to the Theory of Error-Correcting Codes, Wiley, 1982.

    Google Scholar 

  11. D. Shanks, Solved and Unsolved Problems in Number Theory, 3rd ed., Chelsea Publ. Co., 1985.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Koblitz, N. (1994). Finite Fields and Quadratic Residues. In: A Course in Number Theory and Cryptography. Graduate Texts in Mathematics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8592-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-8592-7_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6442-2

  • Online ISBN: 978-1-4419-8592-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics