Skip to main content

Primality Tests and Use of Primes in Public Key Systems

  • Chapter
  • First Online:
Book cover Lectures on Data Security (EEF School 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1561))

Included in the following conference series:

  • 866 Accesses

Abstract

In the first part of this discussion, we first briefly discuss various prime generation methods, starting with the Rabin-Miller test, and then moving on to a very simple new deterministic test. After that we discuss various ways of constructing so-called strong primes, and why this better be avoided.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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. G.L. Miller, Riemann’s hypothesis and test for primality, Journal of Computer and System Sciences 13 (1976), 300–317.

    MATH  MathSciNet  Google Scholar 

  2. M.O. Rabin, Probabilistic algorithm for testing primality, Journal of Number Theory 12 (1980), 128–138.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Comba, Exponentiation Cryptosystems on the IBM PC, IBM Systems Journal, vol. 29, 4, 1990.

    Article  Google Scholar 

  4. I. Damgaard and P. Landrock: Improved bounds for the Rabin Primality Test, Proceedings of the IMA Conference on Cryptography and Coding III, 1991, Oxford University Press, ed. by M.J. Ganley.

    Google Scholar 

  5. I. Damgaard, P. Landrock and C. Pomerance: Average Case Error estimates for the Strong Probable Prime Test, Math. Computations 61 (1993), 177–194.

    Article  Google Scholar 

  6. S.-H. Kim and C. Pomerance, The probability that a random probable prime is a composite, Math. Computations 86 (1986), 259–279.

    Google Scholar 

  7. P. Beauchemin, G. Brassard, C. Crépeau, C. Goutier and C. Pomerance, (1988), The Generation of random Numbers that are Probably Prime, J. Cryptology vol. 1 (1988), 53–64.

    MATH  Google Scholar 

  8. G.H. Hardy and E.M. Wright, An Introduction to the Theory Numbers, Oxford University Press, fifth ed. (1978).

    Google Scholar 

  9. U. Maurer, Fast generation of secure RSA-moduli with almost maximal diversity, Advances in Cryptology-EUROCRYPT’89, LNCS 547 (1991), 458–471.

    Google Scholar 

  10. J. Brandt, I. Damgaard and P. Landrock, Speeding up Prime Number Generation, Proc. of Asiacrypt’91, Springer LNCS, vol. 739.

    Google Scholar 

  11. J. Gordon, Strong RSA keys, Electronic Letters 20 (June 7, 1984), 514–516.

    Google Scholar 

  12. Mike Ganley Electronic Letters 1990

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Landrock, P. (1999). Primality Tests and Use of Primes in Public Key Systems. In: Damgård, I.B. (eds) Lectures on Data Security. EEF School 1998. Lecture Notes in Computer Science, vol 1561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48969-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-48969-X_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65757-6

  • Online ISBN: 978-3-540-48969-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics