Public Key Cryptography

  • Chapter
  • First Online:
Cryptography for Secure Encryption

Part of the book series: Universitext ((UTX))

Abstract

As we have seen, a cryptosystem is a system of the form

$$\displaystyle \langle {\mathcal M},{\mathcal C},e,d,{\mathcal K}_e,{\mathcal K}_d\rangle , $$

where \({\mathcal M}\) is the message space, \({\mathcal C}\) is the space of all possible cryptograms, e is the encryption transformation, d is the decryption transformation, \({\mathcal K}_e\) is the encryption keyspace, and \({\mathcal K}_d\) is the decryption keyspace.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Germany)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 42.79
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 53.49
Price includes VAT (Germany)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. E.R. Canfield, P. Erdős, C. Pomerance, On a problem of Oppenheim concerning “factorisatio numerorum. J. Num. Theory 17(1), 1–28 (1983)

    Google Scholar 

  2. J. Hoffstein, J. Pipher, J.H. Silverman, An Introduction to Mathematical Cryptography. Undergraduate Texts in Mathematics Book Series (Springer, New York, 2008)

    Google Scholar 

  3. N. Koblitz, A Course in Number Theory and Cryptography. Graduate Text in Mathematics, vol. 114 (Springer, New York, 1987)

    Google Scholar 

  4. J.M. Pollard, Theorems on factorizations and primality testing. Proc. Cambridge. Phil. Soc. 76, 521–528 (1974)

    Article  MathSciNet  Google Scholar 

  5. J.M. Pollard, A Monte Carlo method for factorization. Nor. Tid. Inform 15, 331–334 (1975)

    MathSciNet  MATH  Google Scholar 

  6. C. Pomerance, A tale of two sieves. Not. Am. Math. Soc. 43(12), 1473–1485 (1996)

    MathSciNet  MATH  Google Scholar 

  7. K. Rosen, Elementary Number Theory and Its Applications, 6th edn. (Addison-Wesley, Boston, 2011)

    Google Scholar 

  8. N.P. Smart, Cryptography Made Simple (Springer, Cham, 2016)

    Book  Google Scholar 

  9. J.T. Talbot, D. Welsh, Complexity and Cryptography: An Introduction (Cambridge University Press, Cambridge, 2006)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Underwood, R.G. (2022). Public Key Cryptography. In: Cryptography for Secure Encryption. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-030-97902-7_9

Download citation

Publish with us

Policies and ethics

Navigation