Cryptosystems using subgroup distortion

• Autorzy: Chatterji I. , Kahrobaei D. , Lu N. Y.

Identyfikatory

DOI

10.20904/291-2014

• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

hyberbolic groups; symmetric key; distortion

PL

grupy hiperboliczne; klucz symetryczny; zniekształcenie

• Wydawca: Instytut Informatyki Teoretycznej i Stosowanej Polskiej Akademii Nauk
• Czasopismo: Theoretical and Applied Informatics
• Rocznik: 2017
• Tom: Vol. 29, No. 1-2
• Strony: 14--24
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Chatterji I.

• Laboratoire J.A. Dieudonné de l'Université de Nice, France

autor

Kahrobaei D.

• CUNY Graduate Center, PhD Program in Computer Science

autor

Lu N. Y.

• CUNY Graduate Center, City University of New York

Bibliografia

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• [2] A. Myasnikov, V. Roman'kov, 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.
• [3] 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.
• [4] 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.
• [5] M. Elder and A. Rechnitzer. Some geodesic problems in groups. Groups - Complexity -Cryptology, 2(2), 2010. DOI: 10.1515/gcc.2010.014.
• [6] 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.
• [7] V. Shpilrain and G. Zapata. Using the subgroup membership search problem in public key cryptography, 2006. DOI: 10.1090/conm/418/07955.
• [8] M. Mitra. Coarse extrinsic geometry: a survey. In The Epstein Birthday Schrift. Mathematical Sciences Publishers, 1998. DOI: 10.2140/gtm.1998.1.341.
• [9] 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.
• [10] R. C. Lyndon and P. E. Schupp. Combinatorial group theory. Reprint of the 1977 edition. Classics in Mathematics, 2001.
• [11] 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.

Uwagi

PL

Opracowanie w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).