Skip to main content
SpringerLink
Log in

The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES

  • Conference paper
  • First Online:
Topics in Cryptology — CT-RSA 2001 (CT-RSA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2020))

Included in the following conference series:

Abstract

This paper provides security analysis for the public-key encryption scheme DHIES (formerly named DHES and DHAES), which was proposed in [7] and is now in several draft standards. DHIES is a Diffie-Hellman based scheme that combines a symmetric encryption method, a message authentication code, and a hash function, in addition to number-theoretic operations, in a way which is intended to provide security against chosen-ciphertext attacks. In this paper we find natural assumptions under which DHIES achieves security under chosen-ciphertext attack. The assumptions we make about the Diffie-Hellman problem are interesting variants of the customary ones, and we investigate relationships among them, and provide security lower bounds. Our proofs are in the standard model; no random-oracle assumption is required.

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

Access this chapter

Log in via an institution
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. M. Abdalla, M. Bellare, and P. Rogaway. DHIES: An Encryption Scheme Based on the Diffie-Hellman Problem. Full version of current paper, available from authors’ web pages.

    Google Scholar 

  2. American National Standards Institute (ANSI) X9.F1 subcommittee, ANSI X9.63 Public key cryptography for the Financial Services Industry: Elliptic curve key agreement and key transport schemes, Working draft, January 8, 1999.

    Google Scholar 

  3. M. Bellare, R. Canetti, and H. Krawczyk. Keying hash functions for message authentication. Advances in Cryptology ‐ CRYPTO’ 96, Lecture Notes in Computer Science Vol. 1109, N. Koblitz ed., Springer-Verlag, 1996.

    Chapter  Google Scholar 

  4. M. Bellare, A. Desai, D. Pointcheval and P. Rogaway, Relations among notions of security for public-key encryption schemes. Advances in Cryptology ‐ CRYPTO’ 98, Lecture Notes in Computer Science Vol. 1462, H. Krawczyk ed., Springer-Verlag, 1998.

    Google Scholar 

  5. M. Bellare, A. Desai, E. Jokipii and P. Rogaway, A concrete security treatment of symmetric encryption: Analysis of the DES modes of operation. Current version available at URL of first author. Preliminary version in Proc. of the 38th IEEE FOCS, IEEE, 1997.

    Google Scholar 

  6. M. Bellare, J. Kilian and P. Rogaway, The security of cipher block chaining. Advances in Cryptology — CRYPTO’ 94, Lecture Notes in Computer Science Vol. 839, Y. Desmedt ed., Springer-Verlag, 1994.

    Google Scholar 

  7. M. Bellare and P. Rogaway, Minimizing the use of random oracles in authenticated encryption schemes. Information and Communications Security, Lecture Notes in Computer Science, vol. 1334, Springer-Verlag, 1997, pp. 1–16.

    Chapter  Google Scholar 

  8. M. Bellare and P. Rogaway, Optimal asymmetric encryption‐ How to encrypt with RSA. Current version available at URL of either author. Preliminary version in Advances in Cryptology— EUROCRYPT’ 94, Lecture Notes in Computer Science Vol. 950, A. De Santis ed., Springer-Verlag, 1994.

    Google Scholar 

  9. M. Bellare and P. Rogaway, The exact security of digital signatures‐ How to sign with RSA and Rabin. Current version available at URL of either author. Preliminary version in Advances in Cryptology— EUROCRYPT’ 96, Lecture Notes in Computer Science Vol. 1070, U. Maurer ed., Springer-Verlag, 1996.

    Google Scholar 

  10. D. Boneh, The decision Diffie-Hellman problem. Invited paper for the Third Algorithmic Number Theory Symposium (ANTS), Lecture Notes in Computer Science Vol. 1423, Springer-Verlag, 1998.

    Google Scholar 

  11. D. Boneh and R. Venkatesan, Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes. Advances in Cryptology— CRYPTO’ 96, Lecture Notes in Computer Science Vol. 1109, N. Koblitz ed., Springer-Verlag, 1996.

    Google Scholar 

  12. Certicom Research, Standards for Efficient Crpytography Group (SECG) —SEC 1: Elliptic Curve Cryptography. Version 1.0, September 20, 2000. See http://www.secg.org/secg docs.htm.

  13. R. Cramer and V. Shoup, A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. Advances in Cryptology— CRYPTO’ 98, Lecture Notes in Computer Science Vol. 1462, H. Krawczyk ed., Springer-Verlag, 1998.

    Google Scholar 

  14. W. Diffie and M. Hellman, New directions in cryptography. IEEE Transactions on Information Theory, 22, pp. 644–654, 1976.

    Google Scholar 

  15. D. Dolev, C. Dwork and M. Naor. Non-malleable cryptography. Proc. of the 23rd ACM STOC, ACM, 1991.

    Google Scholar 

  16. D. Dolev, C. Dwork and M. Naor. Non-malleable cryptography. Manuscript, March 1998.

    Google Scholar 

  17. T. ElGamal. A public key cryptosystem and signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, vol 31, pp. 469–472, 1985.

    Google Scholar 

  18. E. Fujisaki and T. Okamoto Secure Integration of Asymmetric and Symmetric Encryption Schemes. Advances in Cryptology— CRYPTO’ 99, Lecture Notes in Computer Science Vol. 1666, M. Wiener ed., Springer-Verlag, 1999.

    Google Scholar 

  19. O. Goldreich, A uniform complexity treatment of encryption and zero-knowledge. Journal of Cryptology, vol. 6, 1993, pp. 21–53.

    Article  MATH  MathSciNet  Google Scholar 

  20. S. Goldwasser and S. Micali, Probabilistic encryption. Journal of Computer and System Sciences, vol. 28, 270–299, April 1984.

    MATH  MathSciNet  Google Scholar 

  21. S. Hada and T. Tanaka, On the Existence of 3-Round Zero-Knowledge Protocols. Advances in Cryptology— CRYPTO’ 98, Lecture Notes in Computer Science Vol. 1462, H. Krawczyk ed., Springer-Verlag, 1998.

    Chapter  Google Scholar 

  22. IEEE P1363a Committee, IEEE P1363a, Version D6, November 9, 2000. Standard specifications for public-key cryptography. See http://www.manta.ieee.org/groups/1363/P1363a/draft.html

  23. D. Johnson, S. Matyas, M. Peyravian, Encryption of long blocks using a short-block encryption procedure. November 1996. Available in http://stdsbbs.ieee.org/groups/1363/index.html.

  24. C. Lim and P. Lee, Another method for attaining security against adaptively chosen ciphertext attacks. Advances in Cryptology— CRYPTO’ 93, Lecture Notes in Computer Science Vol. 773, D. Stinson ed., Springer-Verlag, 1993.

    Google Scholar 

  25. S. Micali, C. Rackoff and B. Sloan, The notion of security for probabilistic cryptosystems. SIAM J. of Computing, April 1988.

    Google Scholar 

  26. M. Naor and O. Reingold, Number-Theoretic Constructions of Efficient Pseudo-Random Functions. Proc. of the 38th IEEE FOCS, IEEE, 1997.

    Google Scholar 

  27. M. Naor and M. Yung, Public-key cryptosystems provably secure against chosen ciphertext attacks. Proc. of the 22nd ACM STOC, ACM, 1990.

    Google Scholar 

  28. C. Rackoff and D. Simon. Non-Interactive Zero-Knowledge Proof of Knowledge and Chosen Ciphertext Attack. Advances in Cryptology— CRYPTO’ 91, Lecture Notes in Computer Science Vol. 576, J. Feigenbaum ed., Springer-Verlag, 1991.

    Google Scholar 

  29. V. Shoup, Lower bounds for Discrete Logarithms and Related Problems. Advances in Cryptology— EUROCRYPT’ 97, Lecture Notes in Computer Science Vol. 1233, W. Fumy ed., Springer-Verlag, 1997.

    Google Scholar 

  30. V. Shoup, Personal Communication.

    Google Scholar 

  31. V. Shoup, Using Hash Functions as a Hedge against Chosen Ciphertext Attack. Advances in Cryptology— EUROCRYPT’ 00, Lecture Notes in Computer Science Vol. 1807, B. Preneel ed., Springer-Verlag, 2000.

    Google Scholar 

  32. Y. Zheng, Public key authenticated encryption schemes using universal hashing. ContributiontoP1363. ftp://stdsbbs.ieee.org/pub/p1363/contributions/aes-uhf.ps

  33. Y. Zheng and J. Seberry, Immunizing public key cryptosystems against chosen ciphertext attack. IEEE Journal on Selected Areas in Communications, vol. 11, no. 5, 715–724 (1993).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, University of California at San Diego, La Jolla, California, 92093, USA

    Michel Abdalla & Mihir Bellare

  2. Department of Computer Science, University of California at Davis, Davis, California, 95616, USA

    Phillip Rogaway

Authors
  1. Michel Abdalla
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mihir Bellare
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Phillip Rogaway
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Gemplus Card International, 34 rue Guynemer, 92447, Issy les Moulineaux, France

    David Naccache

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Abdalla, M., Bellare, M., Rogaway, P. (2001). The Oracle Diffie-Hellman Assumptions and an Analysis of DHIES. In: Naccache, D. (eds) Topics in Cryptology — CT-RSA 2001. CT-RSA 2001. Lecture Notes in Computer Science, vol 2020. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45353-9_12

Download citation

  • DOI: https://doi.org/10.1007/3-540-45353-9_12

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41898-6

  • Online ISBN: 978-3-540-45353-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation