---
title: "Bibliography"
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chapter: "Braid Groups"
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# Bibliography

<a id="cite-algebraic-public-key"></a>
- **[AAG99]** Iris Anshel, Michael Anshel, and Dorian Goldfeld. An algebraic method for public-key cryptography. *Math. Res. Lett.*, 6(3-4):287–291, 1999.
<a id="cite-artin-braid-groups"></a>
- **[Art47]** E. Artin. Theory of braids. *Ann. of Math. (2)*, 48:101–126, 1947.
<a id="cite-braid-word-problem"></a>
- **[BKL98]** Joan Birman, Ki Hyoung Ko, and Sang Jin Lee. A new approach to the word and conjugacy problems in the braid groups. *Adv. Math.*, 139(2):322–353, 1998.
<a id="cite-braid-garside-groups"></a>
- **[Deh02]** Patrick Dehornoy. Groupes de Garside. *Ann. Sci. École Norm. Sup. (4)*, 35(2):267–306, 2002.
<a id="cite-braid-elrifai-morton"></a>
- **[ERM94]** Elsayed A. El-Rifai and H. R. Morton. Algorithms for positive braids. *Quart. J. Math. Oxford Ser. (2)*, 45(180):479–497, 1994.
<a id="cite-epsteinetal"></a>
- **[ECH+92]** David B. A. Epstein, James W. Cannon, Derek F. Holt, Silvio V. F. Levy, Michael S. Paterson, and William P. Thurston. *Word processing in groups*. Jones and Bartlett Publishers, Boston, MA, 1992. ISBN 0-86720-244-0.
<a id="cite-braid-conjugacy"></a>
- **[FGM03]** Nuno Franco and Juan González-Meneses. Conjugacy problem for braid groups and Garside groups. *J. Algebra*, 266(1):112–132, 2003.
<a id="cite-braid-attack-garber"></a>
- **[GKT+02]** D. Garber, S. Kaplan, M. Teicher, B. Tsaban, and U. Vishne. Length-based conjugacy search in the braid group. Preprint; available at http://www.arxiv.org/math.GR/0209267, 2002.
<a id="cite-braid-garside-alg"></a>
- **[Gar69]** F. A. Garside. The braid group and other groups. *Quart. J. Math. Oxford Ser. (2)*, 20:235–254, 1969.
<a id="cite-braid-ultrasummit"></a>
- **[Geb03]** Volker Gebhardt. A new approach to the conjugacy problem in Garside groups. Preprint; available at http://www.arxiv.org/math.GT/0306199, 2003.
<a id="cite-braid-conjugacy-simultaneous"></a>
- **[GM02]** Juan González-Meneses. Improving an algorithm to solve Multiple Simultaneous Conjugacy Problems in braid groups. Preprint; available at http://www.arxiv.org/math.GT/0212150, 2002.
<a id="cite-braid-attack-hofheinz"></a>
- **[HS03]** D. Hofheinz and R. Steinwandt. A practical attack on some braid group based cryptographic primitives. In *Public Key Cryptography, 6th International Workshop on Practice and Theory in Public Key Cryptography, PKC 2003*, volume 2567 of LNCS, pages 187–198. Springer, 2003.
<a id="cite-braid-attack-hughes-la"></a>
- **[Hug02]** J. Hughes. A linear algebraic attack on the AAFG1 braid group cryptosystem. In *The 7th Australasian Conference on Information Security and Privacy, ACISP 2002*, volume 2384 of LNCS, pages 176–189. Springer, 2002.
<a id="cite-braid-cryptosystem"></a>
- **[KLC+00]** Ki Hyoung Ko, Sang Jin Lee, Jung Hee Cheon, Jae Woo Han, Ju-sung Kang, and Choonsik Park. New public-key cryptosystem using braid groups. In *Advances in cryptology—CRYPTO 2000*, pages 166–183. Springer, Berlin, 2000.
<a id="cite-braid-attack-lee-park"></a>
- **[LP03]** E. Lee and J. H. Park. Cryptanalysis of the public key encryption based on braid groups. In *Advances in Cryptology—EuroCrypt 2003*, volume 2656 of LNCS, pages 477–490. Springer, 2003.
<a id="cite-braid-attack-lee-lee"></a>
- **[LL02]** Sang Jin Lee and Eonkyung Lee. Potential Weakness of the Commutator Key Agreement Protocol Based on Braid Groups. In *Advances in Cryptology—EuroCrypt 2002*, volume 2332 of LNCS, pages 14–28. Springer, 2002.