Abstract
We implement various computations in the braid groups via practically efficient and theoretically optimized algorithms whose pseudo-codes are provided. The performance of an actual implementation under various choices of parameters is listed.
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References
J. S. Birman, K. H. Ko and S. J. Lee, A new approach to the word and conjugacy problem in the braid groups, Advances in Mathematics 139 (1998), 322–353.
E. A. Elrifai and H. R. Morton, Algorithms for positive braids, Quart. J. Math. Oxford 45 (1994), 479–497.
D. Epstein, J. Cannon, D. Holt, S. Levy, M. Paterson and W. Thurston, Word processing in groups, Jones & Bartlett, 1992.
F. A. Garside, The braid group and other groups, Quart. J. Math. Oxford 20 (1969), no. 78, 235–254.
K. H. Ko, S. J. Lee, J. H. Cheon, J. H. Han, J. S. Kang and C. Park, New public key cryptosystem using braid groups, Advances in Cryptology, Proceedings of Crypto 2000, Lecture Notes in Computer Science 1880, ed. M. Bellare, Springer-Verlag (2000), 166–183.
E. Lee, S. J. Lee and S. G. Hahn, Pseudorandomness from braid groups, Advances in Cryptology, Proceedings of Crypto 2001, Lecture notes in Computer Science 2139, ed. J. Kilian, Springer-Verlag (2001), 486–502.
K. H. Ko, et al., Mathematical security analysis of braid cryptosystems, preprint.
R. P. Stanley, Enumerative combinatorics, Wadsworth and Brooks/Cole, 1986.
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© 2001 Springer-Verlag Berlin Heidelberg
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Cha, J.C., Ko, K.H., Lee, S.J., Han, J.W., Cheon, J.H. (2001). An Efficient Implementation of Braid Groups. In: Boyd, C. (eds) Advances in Cryptology — ASIACRYPT 2001. ASIACRYPT 2001. Lecture Notes in Computer Science, vol 2248. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45682-1_9
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DOI: https://doi.org/10.1007/3-540-45682-1_9
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