Skip to main content

Abstract

Public-key cryptography ensures both secrecy and authenticity of communication using public-key encryption schemes and digital signatures, respectively. Following a brief introduction to the public-key setting (and a comparison with the classical symmetric-key setting), we present rigorous definitions of security for public-key encryption and digital signature schemes, introduce some number-theoretic primitives used in their construction, and describe various practical instantiations.

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 349.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 449.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 599.99
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. J. Katz, Y. Lindell: Introduction to Modern Cryptography (Chapman & Hall/CRS Press, Boca Raton, FL, USA 2007)

    Google Scholar 

  2. R.L. Rivest, A. Shamir, L.M. Adleman: A method for obtaining digital signature and public-key cryptosystems, Commun. ACM, 21(2), 120–126 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. T. El Gamal: A public key cryptosystem and a signature scheme based on discrete logarithms, Trans. Inf. Theory 31, 469–472 (1985)

    Article  MATH  Google Scholar 

  4. PKCS #1 version 1.5: RSA cryptography standard (RSA Data Security, Inc., 1991), available at http://www.rsa.com/rsalabs

  5. D. Bleichenbacher: Chosen ciphertext attacks against protocols based on the RSA encryption standard PKCS #1. In: Advances in Cryptology – Crypto ’98, Lecture Notes in Computer Science, Vol. 1462, ed. by H. Krawczyk (Springer, Heidelberg, Germany 1998) pp. 1–12

    Google Scholar 

  6. PKCS #1 version 2.1: RSA cryptography standard (RSA Data Security, Inc., 1998), available at http://www.rsa.com/rsalabs

  7. M. Bellare, P. Rogaway: Optimal asymmetric encryption. In: Advances in Cryptology – Eurocrypt ’94, Lecture Notes in Computer Science, Vol. 950, ed. by A. De Santis (Springer, Heidelberg, Germany 1994) pp. 92–111

    Chapter  Google Scholar 

  8. E. Fujisaki, T. Okamoto, D. Pointcheval, J. Stern: RSA-OAEP is secure under the RSA assumption, J. Cryptol. 17(2), 81–104 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  9. M. Bellare, P. Rogaway: Random oracles are practical: A paradigm for designing efficient protocols, 1st ACM Conference on Computer and Communications Security (ACM Press, 1993) pp. 62–73

    Google Scholar 

  10. R. Cramer, V. Shoup: Design and analysis of practical public-key encryption schemes secure against adaptive chosen ciphertext attack, SIAM J. Comput. 33(1), 167–226 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Digital signature standard (dss). National Institute of Standards and Technology (NIST), FIPS PUB #186-2, Department of Commerce, 2000

    Google Scholar 

  12. M. Bellare, P. Rogaway: The exact security of digital signatures: How to sign with RSA and Rabin. In: Advances in Cryptology – Eurocrypt ’96, Lecture Notes in Computer Science, Vol. 1070, ed. by U.M. Maurer (Springer, Heidelberg, Germany 1996) pp. 399–416

    Google Scholar 

  13. O. Goldreich: Foundations of Cryptography, Vol. 1: Basic Tools (Cambridge University Press, Cambridge, UK 2001)

    Google Scholar 

  14. O. Goldreich: Foundations of Cryptography, Vol. 2: Basic Applications (Cambridge University Press, Cambridge, UK 2004)

    Google Scholar 

  15. D.R. Stinson: Cryptography: Theory and Practice, 3rd edn. (Chapman & Hall/CRC Press, Boca Raton, FL, USA 2005)

    Google Scholar 

  16. M. Bellare, P. Rogaway: Introduction to modern cryptography: Lecture notes (2003), available at http://www.cs.ucsd.edu/users/mihir/cse207/classnotes.html

  17. B. Schneier: Applied Cryptography, 2nd edn. (Wiley, New York, NY, USA 1996)

    Google Scholar 

  18. A.J. Menezes, P.C. van Oorschot, S.A. Vanstone: Handbook of Applied Cryptography (CRC Press, Boca Raton, FL, USA 1996)

    Google Scholar 

  19. W. Diffie, M.E. Hellman: New directions in cryptography, IEEE Trans. Inf. Theory 22(6), 644–654 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  20. M.O. Rabin: Digital signatures and public key functions as intractable as factorization. Technical Report MIT/LCS/TR-212 (Massachusetts Institute of Technology, January 1979)

    Google Scholar 

  21. S. Goldwasser, S. Micali: Probabilistic encryption, J. Comput. Syst. Sci. 28(2), 270–299 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  22. M. Naor, M. Yung: Public-key cryptosystems provably secure against chosen ciphertext attacks, 22nd Annual ACM Symposium on Theory of Computing (ACM Press, 1990)

    Google Scholar 

  23. C. Rackoff, D.R. Simon: Non-interactive zero-knowledge proof of knowledge and chosen ciphertext attack. In: Advances in Cryptology – Crypto ’91, Lecture Notes in Computer Science, Vol. 576, ed. by J. Feigenbaum (Springer, Heidelberg, Germany 1992) pp. 433–444

    Google Scholar 

  24. M. Blum, S. Goldwasser: An efficient probabilistic public-key encryption scheme which hides all partial information. In: Advances in Cryptology – Crypto ’84, Lecture Notes in Computer Science, Vol. 196, ed. by G.R. Blakley, D. Chaum (Springer, Heidelberg, Germany 1985) pp. 289–302

    Chapter  Google Scholar 

  25. S. Goldwasser, S. Micali, R.L. Rivest: A digital signature scheme secure against adaptive chosen-message attacks, SIAM J. Comput. 17(2), 281–308 (1988)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Katz, J. (2010). Public-Key Cryptography. In: Stavroulakis, P., Stamp, M. (eds) Handbook of Information and Communication Security. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04117-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04117-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04116-7

  • Online ISBN: 978-3-642-04117-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics