Skip to main content
SpringerLink
Log in

The Decision Diffie-Hellman problem

  • Conference paper
  • First Online:
Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

Included in the following conference series:

Abstract

The Decision Diffie-Hellman assumption (ddh) is a gold mine. It enables one to construct efficient cryptographic systems with strong security properties. In this paper we survey the recent applications of DDH as well as known results regarding its security. We describe some open problems in this area.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Beilare, S. Goldwasser, “New paradigms for digital signatures and message authentication based on non-interactive zero-knowledge proofs” Crypto '89, pp. 194–211.

    Google Scholar 

  2. M. Bellare, S. Micali, “Non-interactive oblivious transfer and applications”, Crypto '89, pp. 547–557.

    Google Scholar 

  3. D. Boneh, R. Lipton, “Black box fields and their application to cryptography”, Proc. of Crypto '96, pp. 283–297.

    Google Scholar 

  4. D. Boneh, R. Venkatesan, “Hardness of computing most significant bits in secret keys of Diffie-Hellman and related schemes”, Proc. of Crypto '96, pp. 129–142.

    Google Scholar 

  5. S. Brands, “An efficient off-line electronic cash system based on the representation problem”, CWI Technical report, CS-R9323, 1993.

    Google Scholar 

  6. R. Canetti, “Towards realizing random oracles: hash functions that hide all partial information”, Proc. Crypto '97, pp. 455–469.

    Google Scholar 

  7. R. Canetti, J. Friedlander, I. Shparlinski, “On certain exponential sums and the distribution of Diffie-Hellman triples”, Manuscript.

    Google Scholar 

  8. D. Chaum, H. van Antwerpen, “Undeniable signatures”, Proc. Crypto '89, pp. 212–216.

    Google Scholar 

  9. H. Cohen, “A course in computational number theory”, Springer-Verlag.

    Google Scholar 

  10. D. Coppersmith, “Finding a Small Root of a Bivariate Integer Equation; Factoring with high bits known”, Proc. Eurocrypt '96, 1996.

    Google Scholar 

  11. R. Cramer, V. Shoup, “A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack”, manuscript.

    Google Scholar 

  12. W. Diffie, M. Hellman, “New directions in cryptography”, IEEE Transactions on Information Theory, vol. 22, no. 6, pp. 644–654, 1976.

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Dolev, C. Dwork, M. Naor, “Non-malleable cryptography”, Proc. STOC' 91, pp. 542–552.

    Google Scholar 

  14. O. Goldreich, S. Goldwasser, S. Micali, “On the cryptographic applications of random functions”, Crypto' 84, pp. 276–288.

    Google Scholar 

  15. O. Goldreich, S. Goldwasser, S. Micali, “How to construct random functions”, J. ACM, Vol. 33, 1986, pp. 792–807.

    Article  MathSciNet  Google Scholar 

  16. O. Goldreich, L.A. Levin, “Hard core bits based on any one way function”, Proc. STOC '89.

    Google Scholar 

  17. S. Goldwasser, S. Micali, “Probabilistic encryption”, J. Computer and Syst. Sciences, Vol. 28, 1984, pp. 270–299.

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Hastad, R. Impaglizzo, L. Levin, M. Luby, “Construction of pseudo random generators from one-way functions”, SIAM J. of Computing, to appear. Also see preliminary version in STOC 89.

    Google Scholar 

  19. A. Lenstra, H. Lenstra, L. Lovasz, “Factoring polynomial with rational coefficients”, Mathematiche Annalen, 261:515–534, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  20. U. Maurer, “Towards proving the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms”, Proc. of Crypto '94, pp. 271–281.

    Google Scholar 

  21. U. Maurer, S. Wolf, “Diffie-Hellman oracles”, Proc. of Crypto '96, pp. 268–282.

    Google Scholar 

  22. M. Naor, O. Reingold, “Synthesizers and their application to the parallel construction of pseudo-random functions”, Proc. FOCS '95, pp. 170–181.

    Google Scholar 

  23. M. Naor, O. Reingold, “Number theoretic constructions of efficient pseudo random functions”, Proc. FOCS '97. pp. 458–467.

    Google Scholar 

  24. M. Naor, M. Yung, “Public key cryptosystems provable secure against chosen ciphertext attacks”, STOC '90, pp. 427–437

    Google Scholar 

  25. V. Nechaev, “Complexity of a determinate algorithm for the discrete logarithm”, Mathematical Notes, Vol. 55 (2), 1994, pp. 165–172.

    Article  MATH  MathSciNet  Google Scholar 

  26. C. Rackoff, D. Simon, “Non-interactive zero knowledge proof of knowledge and chosen ciphertext attack”, Crypto' 91, pp. 433–444.

    Google Scholar 

  27. C. Schnorr, “A hierarchy of polynomial time lattice basis reduction algorithms”, Theoretical Computer Science, Vol. 53, 1987, pp. 201–224.

    Article  MATH  MathSciNet  Google Scholar 

  28. J. Schwartz, “Fast probabilistic algorithms for verification of polynomial identities”, J. ACM, Vol. 27 (4), 1980, pp. 701–717.

    Article  MATH  Google Scholar 

  29. V. Shoup, “Lower bounds for discrete logarithms and related problems”, Proc. Eurocrypt '97, pp. 256–266.

    Google Scholar 

  30. M. Stadler, “Publicly verifiable secret sharing”, Proc. Eurocrypt '96, pp. 190–199.

    Google Scholar 

  31. M. Steiner, G. Tsudik, M. Waidner, “Diffie-Hellman key distribution extended to group communication”, Proc. 3rd ACM Conference on Communications Security, 1996, pp. 31–37.

    Google Scholar 

  32. Y. Zheng, J. Seberry, “Practical approaches to attaining security against adaptively chosen ciphertext attacks”, Crypto '92, pp. 292–304.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Department, Stanford University, 94305-9045, Stanford, CA

    Dan Boneh

Authors
  1. Dan Boneh
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Joe P. Buhler

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Boneh, D. (1998). The Decision Diffie-Hellman problem. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054851

Download citation

  • DOI: https://doi.org/10.1007/BFb0054851

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation