Transitive signatures from braid groups

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4859 LNCS, Issue , 2007, Pages 183-196

  Wang, Licheng ^a   Cao, Zhenfu ^b   Zheng, Shihui ^a   Huang, Xiaofang ^a   Yang, Yixian ^a  

^a BEIJING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Braid group; One more matching conjugate problem; Provable security; Random oracle model; Transitive signature

Indexed keywords

MATHEMATICAL MODELS; MESSAGE PASSING; PROBLEM SOLVING; RANDOM PROCESSES;

BRAID GROUP; ONE-MORE MATCHING CONJUGATE PROBLEMS; PROVABLE SECURITY; RANDOM ORACLE MODELS; TRANSITIVE SIGNATURE;

ELECTRONIC DOCUMENT IDENTIFICATION SYSTEMS;

EID: 38349062457     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-77026-8_14     Document Type: Conference Paper

References (35)

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)
2. Anshel, I., Anshel, M., Goldfeld, D.: An algebraic method for public-key cryptography. Math. Research Letters 6, 287-291 (1999)
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)
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)
5. Bellare, M., Neven, G.: Transitive signatures: New schemes and proofs. IEEE Transactions on Information Theory 51(6), 2133-2151 (2005)
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)
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)
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)
9. Dehornoy, P.: Braid-based cryptography. Contemp. Math., Amer. Math. Soc. 360, 5-33 (2004)
10. Elrifai, E., Morton, H.R.: Algorithms for positive braids. Quart. J. Math. Oxford Ser. 45(2), 479-497 (1994)
11. Franco, N., Gonzales-Menses, J.: Conjugacy problem for braid groups and garside groups. Journal of Algebra 266, 112-132 (2003)
12. Gebhardt, V.: A new approach to the conjugacy problem in garside groups. Journal of Algebra 292, 282-302 (2005)
13. Gonzales-Meneses, J.: Improving an algorithm to solve the multiple simultaneous conjugacy problems in braid groups, Preprint, math.GT/0212150 (2002)
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)
15. Hughes, J.: The left SSS attack on Ko-Lee-Cheon-Han-Kang-Park key agreement scheme in B45, Rump session Crypto (2000)
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)
17. Kitaev, A.: Quantum measurements and the abelian stabilizer problem. Preprint, quant-ph/9511026 (1995)
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)
20. Ko, K.H., Lee, J.W., Thomas, T.: Towards generating secure keys for braid cryptography, Designs, Codes and Cryptography (to appear, 2007)
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)
22. Lee, E.: Braig groups in cryptography. IEICE Trans. Fundamentals E87-A(5), 986-992 (2004)
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)
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)
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)
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)
27. Proos, J., Zalka, C.: Shors discrete logarithm quantum algorithm for elliptic curves. Quantum Information and Computation 3, 317-344 (2003)
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)
29. Shor, P.: Polynomail-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 5, 1484-1509 (1997)
30. Wang, L.: PhD. Disseration. Shanghai Jiao Tong University (June 2007)
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)
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)
33. Yi, X.: Directed transitive signature scheme. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 129-144. Springer, Heidelberg (2006)
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)
35. Zhu, H.: Model for undirected transitive signatures. IEE Proceedings: Communications 151(4), 312-315 (2004)