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Cryptographers’ Track at the RSA Conference

CT-RSA 2001: Topics in Cryptology — CT-RSA 2001 pp 13–27Cite as

New Key Agreement Protocols in Braid Group Cryptography

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

Abstract

Key agreement protocols are presented whose security is based on the difficulty of inverting one-way functions derived from hard problems for braid groups. Efficient/low cost algorithms for key transfer /extraction are presented. Attacks/security parameters are discussed.

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References

  1. Anshel, I., Anshel, M.: From the Post-Markov Theorem through Decision Problems to Public-Key Cryptography, American Mathematical Monthly Vol. 100, No. 9 (November 1993) 835–845

    Article  MATH  MathSciNet  Google Scholar 

  2. Anshel, I., Anshel, M., and Goldfeld D.: An Algebraic Method for Public-Key Cryptography, Mathematical Research Letters 6 (1999) 1–5

    Google Scholar 

  3. Birman, J.: Braids, Links and Mapping Class Groups, Annals of Mathematical Studies, Study 82 Princeton University Press (1974)

    Google Scholar 

  4. Birman, J., Ko, K. H., Lee, S. J.: A new solution to the word and conjugacy problems in the braid groups, Advances in Mathematics 139 (1998), 322–353

    Article  MATH  MathSciNet  Google Scholar 

  5. Boneh, D.: Twenty Years of Attacks on the RSA Cryptosystem, Notices of the American Mathematical Society, Vol 46, No. 2 (1999) 203–213.

    MATH  MathSciNet  Google Scholar 

  6. Dehornoy, P.: A fast method for comparing braids, Advances in Mathematics 123 (1997), 205–235

    MathSciNet  Google Scholar 

  7. Garzon, M., Zalcstein, Y.: The complexity of Grigorchuk groups with applications to cryptography, Theoretical Computer Science 88:1 (1991) 83–98 (additional discussion may be found in M. Garzon, “Models of Massive Parallelism” Springer-Verlag (1995))

    Article  MathSciNet  Google Scholar 

  8. Hansen, V. L.: Braids and Coverings: Selected topics, LMS, Student Texts 18 Cambridge University Press (1989)

    Google Scholar 

  9. Johnson, D. L.: Presentations of Groups: Second Edition, Cambridge University Press (1997)

    Google Scholar 

  10. Kawauchi, A.: A Survey of Knot Theory, Birhauser Verlag (1996)

    Google Scholar 

  11. Ko, K. H., Lee, S. J., Cheon, J. H., Han, J. W., Kang, J. S., Park, C.: New Public-Key Cryptosystem Using Braid Groups, to appear in Crypto 2000

    Google Scholar 

  12. Koblitz, N.: Algebraic Aspects of Cryptography, Springer-Verlag (1998)

    Google Scholar 

  13. Morton, H. R.: The Multivariable Alexander Polynomial for a Closed Braid, Contemporary Mathematics 233 AMS (1999), 167–172

    Google Scholar 

  14. Sidel’nikov, V. M., Cherepenev, M. A., Yashichenko, V. V.: Systems of open distribution of keys on the basis of noncommutative semigroups, Russian. Acad. Sci. Dokl. Math. Vol. 48 No.2 (1994) 384–386

    Google Scholar 

  15. Wagner, N. R., Magyarik, M. R.: A public key cryptosystem based on the word problem, Advances in Cryptology: Proceedings of Crypto 84, ed. G. R. Blakely and D. Chaum, LNCS 196, Springer Verlag (1985) 19–36

    Google Scholar 

  16. Welsch, D. J. A.: Complexity: Knots, Colourings and Counting, LMS, Lecture Notes Series 186 Cambridge University Press (1993)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Arithmetica Inc., 31 Peter Lynas Ct, Tenafly, NJ, 07670, USA

    Iris Anshel

  2. City College of New York, New York, NY, USA

    Michael Anshel

  3. Boston College,, Chestnut Hill, MA, 02167, USA

    Benji Fisher

  4. Columbia University, NY, USA

    Dorian Goldfeld

Authors
  1. Iris Anshel
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  2. Michael Anshel
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  3. Benji Fisher
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  4. Dorian Goldfeld
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Editor information

Editors and Affiliations

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

    David Naccache

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© 2001 Springer-Verlag Berlin Heidelberg

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Cite this paper

Anshel, I., Anshel, M., Fisher, B., Goldfeld, D. (2001). New Key Agreement Protocols in Braid Group Cryptography. 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_2

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  • DOI: https://doi.org/10.1007/3-540-45353-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41898-6

  • Online ISBN: 978-3-540-45353-6

  • eBook Packages: Springer Book Archive

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