Skip to main content

Bilinear Cryptography Using Groups of Nilpotency Class 2

  • Conference paper
  • First Online:
Book cover Cryptography and Coding (IMACC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10655))

Included in the following conference series:

Abstract

In this paper, we develop a novel idea of a bilinear cryptosystem using the discrete logarithm problem in matrices. These matrices come from a linear representation of a group of nilpotency class 2. We discuss an example at the end.

This research was supported by a NBHM and a SERB research grant.

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 EPUB and 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

References

  1. Balasubramanian, R., Koblitz, N.: The improbability than an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm. J. Cryptology 11(2), 141–145 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barua, R., Dutta, R., Sarkar, P.: Extending Joux’s protocol to multi party key agreement. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 205–217. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-24582-7_15

    Chapter  Google Scholar 

  3. Boneh, D., Shacham, H., Lynn, B.: Short signatures from the Weil pairing. J. Cryptology 17(4), 297–319 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chatterjee, S., Sarkar, P.: Identity-Based Encryption. Springer, Boston (2011)

    Book  MATH  Google Scholar 

  5. Chebolu, S., Minác̆, J., Reis, C.: Reciprocity laws for representations of finite groups. Ann. Math. Québec 34(1), 37–61 (2010)

    MathSciNet  MATH  Google Scholar 

  6. Dutta, R., Barua, R., Sarkar, P.: Pairing based cryptographic protocols: A survey. http://eprint.iacr.org/2004/064

  7. Gorenstein, D.: Finite Groups. AMS Chelsea Publishing (1980)

    Google Scholar 

  8. Joux, A.: A one round protocol for Diffie-Hellman. In: Proceedings of the 4th International Symposium on Algorithmic Number Theory, pp. 385–394 (2000)

    Google Scholar 

  9. Kobayashi, Y.: On the structure of exponent semigroups. J. Algebra 78, 1–19 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  10. Menezes, A., Okamoto, T., Vanstone, S.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. Inf. Theor. 39(5), 1639–1646 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Moravec, P.: Schur multipliers and power endomorphisms of groups. J. Algebra 308(1), 12–25 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Rotman, J.J.: An Introduction to the Theory of Groups, 4th edn. Springer, New York (1994)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ayan Mahalanobis .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mahalanobis, A., Shinde, P. (2017). Bilinear Cryptography Using Groups of Nilpotency Class 2. In: O'Neill, M. (eds) Cryptography and Coding. IMACC 2017. Lecture Notes in Computer Science(), vol 10655. Springer, Cham. https://doi.org/10.1007/978-3-319-71045-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-71045-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-71044-0

  • Online ISBN: 978-3-319-71045-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics