Cryptosystems using subgroup distortion

Delaram Kahrobaei, Indira Chatterji, Ni Yen Lu


In this paper we propose cryptosystems based on subgroup distortion in hyperbolic groups. We also include concrete examples of hyperbolic groups as possible platforms.

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A. Myasnikov, V. Shpilrain, and A. Ushakov, Non-commutative Cryptography and Complexity of Group-theoretic Problems, American Mathematical Society, 2011, DOI: 10.1090/surv/177

A. Myasnikov, V. Romanov, A. Ushakov, and A. Vershik, The word and geodesic problems in free solvable groups, Transactions of the American Mathematical Society, 362(9):4655-4682, 2010, DOI: 10.1090/s0002-9947-10-04959-7

D. B. A. Epstein, M. S. Paterson, J. W. Cannon, D. F. Holt, S. V. Levy, and W. P. Thurston, Word Processing in Groups, A. K. Peters, Ltd., Natick, MA, USA, 1992.

M. Elder, A linear-time algorithm to compute geodesics in solvable Baumslag–Solitar groups, Illinois J. Math., 54(1):109-128, 2010, DOI: 10.1214/10-AAP256

M. Elder and A. Rechnitzer, Some geodesic problems in groups, Groups - Complexity - Cryptology, 2(2), 2010, DOI: 10.1515/gcc.2010.014

M. R. Bridson and A. Haefliger, Non-positive curvature and group theory, In Grundlehren der mathematischen Wissenschaften, pages 438-518. Springer Berlin Heidelberg, 1999, DOI: 10.1007/978-3-662-12494-9_22

V. Shpilrain and G. Zapata, Using the subgroup membership search problem in public key cryptography, 2006, DOI: 10.1090/conm/418/07955

M. Mitra, Coarse extrinsic geometry: a survey, In The Epstein Birthday Schrift. Mathematical Sciences Publishers, 1998, DOI: 10.2140/gtm.1998.1.341

T. Mecham and A. Mukherjee, Hyperbolic groups which fiber in infinitely many ways, Algebraic & Geometric Topology, 9(4):2101-2120, 2009, DOI: 10.2140/agt.2009.9.2101

R. C. Lyndon and P. E. Schupp, Combinatorial group theory. Reprint of the 1977 edition. Classics in Mathematics, 2001.

J. Barnard, N. Brady, and P. Dani, Super-exponential distortion of subgroups of CAT(-1) groups, Algebraic & Geometric Topology, 7(1):301-308, 2007, DOI: 10.2140/agt.2007.7.301



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Copyright (c) 2018 Indira Chatterji, Delaram Kahrobaei, Ni Yen Lu

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ISSN: 1896-5334 (print), 2300-889X (online)

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