Skip to main content
SpringerLink
Log in

Transitive Signatures from Braid Groups

  • Conference paper
Book cover Progress in Cryptology – INDOCRYPT 2007 (INDOCRYPT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4859))

Included in the following conference series:

Abstract

Transitive signature is an interesting primitive due to Micali and Rivest. During the past years, many constructions of transitive signatures have been proposed based on various assumptions. In this paper, we provide the first construction of transitive signature schemes by using braid groups. In the random oracle model, our proposals are proved to be transitively unforgeable against adaptively chosen message attack under the assumption of the intractability of one-more matching conjugate problem (OM-MCP) over braid groups. Moreover, the proposed schemes are invulnerable to currently known quantum attacks.

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. Anshel, I., Anshel, M., Fisher, B., Goldfeld, D.: New Key Agreement Protocols in Braid Group Cryptography. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 13–27. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Anshel, I., Anshel, M., Goldfeld, D.: An algebraic method for public-key cryptography. Math. Research Letters 6, 287–291 (1999)

    MATH  MathSciNet  Google Scholar 

  3. Anshel, M.: Braid Group Cryptography and Quantum Cryptoanalysis. In: 8th International Wigner Symposium, May 27-30, 2003, GSUC-CUNY 365 Fifth Avenue, NY, NY 10016, USA (2003)

    Google Scholar 

  4. Bellare, M., Neven, G.: Transitive signaures based on factoring and RSA. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 397–414. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Bellare, M., Neven, G.: Transitive signatures: New schemes and proofs. IEEE Transactions on Information Theory 51(6), 2133–2151 (2005)

    Article  MathSciNet  Google Scholar 

  6. Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The One-More-RSA-Inversion Problems and the Security of Chaum’s Blind Signature Scheme. Journal of Cryptology 16(3), 185–215 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cha, J.C., Ko, K.H., Lee, S.J., Han, J.W., Cheon, J.H., et al.: An efficient implementation of braid groups. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 144–156. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  8. Cheon, J.H., Jun, B.: A Polynomial Time Algorithm for the Braid Diffie-Hellman Conjugacy Problem. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 212–225. Springer, Heidelberg (2003)

    Google Scholar 

  9. Dehornoy, P.: Braid-based cryptography. Contemp. Math., Amer. Math. Soc. 360, 5–33 (2004)

    MathSciNet  Google Scholar 

  10. Elrifai, E., Morton, H.R.: Algorithms for positive braids. Quart. J. Math. Oxford Ser. 45(2), 479–497 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  11. Franco, N., Gonzales-Menses, J.: Conjugacy problem for braid groups and garside groups. Journal of Algebra 266, 112–132 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gebhardt, V.: A new approach to the conjugacy problem in garside groups. Journal of Algebra 292, 282–302 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. Gonzales-Meneses, J.: Improving an algorithm to solve the multiple simultaneous conjugacy problems in braid groups, Preprint, math.GT/0212150 (2002)

    Google Scholar 

  14. Huang, Z.-J., Hao, Y.-H., Wang, Y.-M., Chen, K.-F.: Efficient directed transitive signature scheme. Acta Electronica Sinica 33(8), 1497–1501 (2005)

    Google Scholar 

  15. Hughes, J.: The left SSS attack on Ko-Lee-Cheon-Han-Kang-Park key agreement scheme in B45, Rump session Crypto (2000)

    Google Scholar 

  16. Hughes, J.: A linear algebraic attack on the AAFG1 braid group cryptosystem. In: Batten, L.M., Seberry, J. (eds.) ACISP 2002. LNCS, vol. 2384, pp. 176–189. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  17. Kitaev, A.: Quantum measurements and the abelian stabilizer problem. Preprint, quant-ph/9511026 (1995)

    Google Scholar 

  18. Ko, K.H., Choi, D.H., Cho, M.S., Lee, J.W.: New signature scheme using conjugacy problem (preprint 2002), http://eprint.iacr.org/2002/168

  19. Ko, K.H., Lee, S.J., Cheon, J.H., Han, J.W.: New public-key cryptosystem using braid groups. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 166–183. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  20. Ko, K.H., Lee, J.W., Thomas, T.: Towards generating secure keys for braid cryptography, Designs, Codes and Cryptography (to appear, 2007)

    Google Scholar 

  21. Kuwakado, H., Tanaka, H.: Transitive Signature Scheme for Directed Trees. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E86-A(5), 1120–1126 (2003)

    Google Scholar 

  22. Lee, E.: Braig groups in cryptography. IEICE Trans. Fundamentals E87-A(5), 986–992 (2004)

    Google Scholar 

  23. Lee, E., Lee, S.-J., Hahn, S.-G.: Pseudorandomness from Braid Groups. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 486–502. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  24. Magliveras, S., Stinson, D., van Trung, T.: New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups. Journal of Cryptography 15, 285–297 (2002)

    Article  MATH  Google Scholar 

  25. Micali, S., Rivest, R.L.: Transitive signaure schemes. In: Preneel, B. (ed.) CT-RSA 2002. LNCS, vol. 2271, pp. 236–243. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  26. Myasnikov, A., Shpilrain, V., Ushakov, A., Practical, A.: Attack on a Braid Group Based Cryptographic Protocol. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 86–96. Springer, Heidelberg (2005)

    Google Scholar 

  27. Proos, J., Zalka, C.: Shors discrete logarithm quantum algorithm for elliptic curves. Quantum Information and Computation 3, 317–344 (2003)

    MathSciNet  Google Scholar 

  28. Shahandashti, S.F., Salmasizadeh, M., Mohajeri, J.: A provably secure short transitive signature scheme from bilinear group Pairs. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 60–76. Springer, Heidelberg (2005)

    Google Scholar 

  29. Shor, P.: Polynomail-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 5, 1484–1509 (1997)

    Article  MathSciNet  Google Scholar 

  30. Wang, L.: PhD. Disseration. Shanghai Jiao Tong University (June 2007)

    Google Scholar 

  31. Wang, L., Cao, Z., Zeng, P., Li, X.: One-more matching conjugate problem and security of braid-based signatures. In: ASIACCS 2007, pp. 295–301. ACM, New York (2007)

    Google Scholar 

  32. Warren Jr., Henry, S.: A modification of Warshall’s algorithm for the transitive closure of binary relations. Communications of the ACM 18(4), 218–220 (1975)

    Article  Google Scholar 

  33. Yi, X.: Directed transitive signature scheme. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 129–144. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  34. Yi, X., Tan, C.-H., Okamoto, E.: Security of Kuwakado-Tanaka transitive signature scheme for directed trees. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E87-A(4), 955–957 (2004)

    Google Scholar 

  35. Zhu, H.: Model for undirected transitive signatures. IEE Proceedings: Communications 151(4), 312–315 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Security Center, State Key Laboratory of Networking and Switching, Technology, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China

    Licheng Wang, Shihui Zheng, Xiaofang Huang & Yixian Yang

  2. Dept. Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R. China

    Zhenfu Cao

Authors
  1. Licheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhenfu Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shihui Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaofang Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yixian Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

K. Srinathan C. Pandu Rangan Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wang, L., Cao, Z., Zheng, S., Huang, X., Yang, Y. (2007). Transitive Signatures from Braid Groups. In: Srinathan, K., Rangan, C.P., Yung, M. (eds) Progress in Cryptology – INDOCRYPT 2007. INDOCRYPT 2007. Lecture Notes in Computer Science, vol 4859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77026-8_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-77026-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77025-1

  • Online ISBN: 978-3-540-77026-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation