1 |
L. Wang, L. Wang, Z. Cao, E. Okamoto, and J. Shao, "New constructions of public-key encryption schemes from conjugacy search problems," in Information Security and Cryptology, 2010, pp. 1-17, doi: 10.1007/978-3-642-21518-6_1.
DOI
|
2 |
M. Dehn, "Over infinite discontinuous groups," Math. Ann., vol. 71, no. 1, pp. 116-144, 1911.
DOI
|
3 |
S. H. Paeng, K. C. Ha, J. H. Kim, S. Chee, and C. Park, "New public key cryptosystem using finite non Abelian groups," 2001, pp. 470-485, doi: 10.1007/3-540-44647-8_28.
DOI
|
4 |
I. S. Lee, W. H. Kim, D. Kwon, S. Nahm, N. S. Kwak, and Y. J. Baek, "On the security of MOR public key cryptosystem," 2004, pp. 387-400.
|
5 |
S. H. Paeng, "On the security of cryptosystem using automorphism groups," Inf. Process. Lett., vol. 88, no. 6, pp. 293-298, 2003, doi: 10.1016/j.ipl.2003.09.001.
DOI
|
6 |
J. Birman, "Braids, links, and mapping class groups, volume 82 of Annals of Math," Stud. Princet. Univ. Press, 1974, doi: 10.1515/9781400881420.
|
7 |
P. Dehornoy, "Braid-based cryptography," Contemp Math, vol. 360, pp. 5-33, 2004, doi: 10.1090/conm/360/06566.
DOI
|
8 |
A. Mahalanobis, "A simple generalization of the ElGamal cryptosystem to non-abelian groups," Commun. Algebr., vol. 36, no. 10, pp. 3878-3889, 2008, doi: 10.1080/00927870802160883.
DOI
|
9 |
A. Mahalanobis, "A note on using finite non-abelian pgroups in the MOR cryptosystem," ArXiv Prepr. Cs0702095, 2007.
|
10 |
W. Magnus, A. Karrass, and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations. Courier Corporation, 2004.
|
11 |
R. Alvarez, L. Tortosa, J. Vicent, and A. Zamora, "A nonabelian group based on block upper triangular matrices with cryptographic applications," 2009, pp. 117-126, doi: 10.1007/978-3-642-02181-7_13.
DOI
|
12 |
J. J. Climent, E. Gorla, and J. Rosenthal, "Cryptanalysis of the CFVZ cryptosystem," Adv. Math. Commun., vol. 01, no. 01, pp. 1-11, 2007, doi: 10.3934/amc.2007.1.1.
DOI
|
13 |
A. J. Menezes and Y. H. Wu, "The discrete logarithm problem in GL (n, q)," Ars Comb., vol. 47, pp. 23-32, 1997.
|
14 |
R. Alvarez, F. M. Martinez, J. F. Vicent, and A. Zamora, "A new public key cryptosystem based on matrices," WSEAS Inf. Secur. Priv., vol. 3639, 2007.
|
15 |
D. Grigoriev and I. Ponomarenko, "Constructions in public-key cryptography over matrix groups," ArXiv Prepr. Math0506180, 2005, doi: 10.1090/conm/418/07949.
|
16 |
A. Mahalanobis, "The Diffie-Hellman key exchange protocol and non-abelian nilpotent groups," Isr. J. Math., vol. 165, no. 1, pp. 161-187, 2008, doi: 10.1007/s11856-008-1008-z.
DOI
|
17 |
L. Gu and S. Zheng, "Conjugacy systems based on nonabelian factorization problems and their applications in cryptography," J. Appl. Math., vol. 2014, 2014, doi: 10.1155/2014/630607.
DOI
|
18 |
A. Mahalanobis, "A simple generalization of the ElGamal cryptosystem to non-abelian groups II," Commun. Algebra, vol. 40, no. 9, pp. 3583-3596, 2012, doi: 10.1080/00927872.2011.602998.
DOI
|
19 |
G. Baumslag, Topics in combinatorial group theory. Birkhauser, 2012.
|
20 |
M. Cohen, S. Flannery, and D. Flannery, "In Code: A Mathematical Journey, by Sarah Flannery and David Flannery," Am. Math. Mon., vol. 109, no. 10, p. 929, 2002, doi: 10.2307/3072480.
DOI
|
21 |
C. Tobias, "Security analysis of the MOR cryptosystem," 2003, pp. 175-186.
|
22 |
L. Gu, L. Wang, K. Ota, M. Dong, Z. Cao, and Y. Yang, "New public key cryptosystems based on non-Abelian factorization problems," Secur. Commun. Netw., vol. 6, no. 7, pp. 912-922, 2013, doi: 10.1002/sec.710.
DOI
|
23 |
E. Stickel, "A new public-key cryptosystem in non abelian groups," 2004, pp. 70-80.
|
24 |
V. Shpilrain, "Cryptanalysis of Stickel's key exchange scheme," in Computer Science - Theory and Applications, 2008, pp. 283-288, doi: 10.1007/978-3-540-79709-8_29.
DOI
|
25 |
S. Baba, S. Kotyad, and R. Teja, "A non-Abelian factorization problem and an associated cryptosystem.," IACR Cryptol EPrint Arch, vol. 2011, p. 48, 2011.
|
26 |
V. Roman'kov, "Two general schemes of algebraic cryptography," Groups Complex. Cryptol., vol. 10, no. 2, pp. 83-98, 2018, doi: 10.1515/gcc-2018-0009.
DOI
|
27 |
N. R. Wagner and M. R. Magyarik, "A public-key cryptosystem based on the word problem," 1984, pp. 19-36, doi: 10.1007/3-540-39568-7_3.
DOI
|
28 |
T. Van Trung, Magliveras, and Stinson, "New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups," J. Cryptol., vol. 15, no. 4, pp. 285-297, 2002, doi: 10.1007/s00145-001-0018-3.
DOI
|
29 |
G. H. J. Lanel, H. K. Pallage, J. K. Ratnayake, S. Thevasha, and B. A. K. Welihinda, "A survey on Hamiltonicity in Cayley graphs and digraphs on different groups," Discrete Math. Algorithms Appl., vol. 11, no. 05, p. 1930002, 2019, doi: 10.1142/s1793830919300029.
DOI
|
30 |
G. H. J. Lanel, T. M. K. K. Jinasena, and B. A. K. Welihinda, "Hamiltonian Cycles in Cayley Graphs of Semidirect Products of Finite Groups," Eur. Mod. Stud. J., vol. 04, no. 03, pp. 1-19, 2020.
|
31 |
H. Hong, J. Shao, L. Wang, H. Ahmad, and Y. Yang, "Public Key Encryption in Non-Abelian Groups," ArXiv Prepr. ArXiv160506608, 2016.
|
32 |
V. Shpilrain and G. Zapata, "Using the subgroup membership search problem in public key cryptography," Contemp. Math., vol. 418, p. 169, 2006, doi: 10.1090/conm/418/07955.
DOI
|
33 |
M. Garzon and Y. Zalcstein, "The complexity of Grigorchuk groups with application to cryptography," Theor. Comput. Sci., vol. 88, no. 1, pp. 83-98, 1991, doi: 10.1016/0304-3975(91)90074-c.
DOI
|
34 |
I. Anshel, M. Anshel, and D. Goldfeld, "Non-abelian key agreement protocols," Discrete Appl. Math., vol. 130, no. 1, pp. 3-12, 2003, doi: 10.1016/s0166-218x(02)00585-1.
DOI
|
35 |
R. Cramer and V. Shoup, "Signature schemes based on the strong RSA assumption," ACM Trans. Inf. Syst. Secur. TISSEC, vol. 3, no. 3, pp. 161-185, 2000, doi: 10.1145/357830.357847.
DOI
|
36 |
I. Ilic, "The Discrete Logarithm Problem in Non-abelian Groups," Computing, vol. 1, p. 1, 2010.
DOI
|
37 |
I. Anshel, M. Anshel, B. Fisher, and D. Goldfeld, "New key agreement protocols in braid group cryptography," 2001, pp. 13-27, doi: 10.1007/3-540-45353-9_2.
DOI
|
38 |
I. Ilic and S. S. Magliveras, "Weak discrete logarithms in non-abelian groups," J. Comb. Math. Comb. Comput., vol. 74, p. 3, 2010.
|
39 |
B. Fine, M. Habeeb, D. Kahrobaei, and G. Rosenberger, "Aspects of nonabelian group based cryptography: a survey and open problems," JP J. Algebra Number Theory Appl., 2011.
|
40 |
A. I. S. Moldenhauer and G. Rosenberger, "Cryptosystems using automorphisms of finitely generated free groups," ArXiv Prepr. ArXiv160302328, 2016.
|
41 |
W. Lempken, T. Van Tran, S. S. Magliveras, and W. Wei, "A public key cryptosystem based on non-abelian finite groups," J. Cryptol., vol. 22, no. 1, pp. 62-74, 2009, doi: 10.1007/s00145-008-9033-y.
DOI
|
42 |
C. Bates, N. Meyer, and T. Pulickal, "Cryptographic applications of nonabelian groups," Math Ariz. Edu Asp2008crypto Pdf, 2008.
|
43 |
J. C. Birget, S. S. Magliveras, and W. Wei, "Trap doors from subgroup chains and recombinant bilateral transversals," Proc. RECSI, vol. 7, pp. 31-48, 2002.
|
44 |
R. I. Grigorchuk, "Degrees of growth of finitely generated groups, and the theory of invariant means," Izv. Ross. Akad. Nauk Seriya Mat., vol. 48, no. 5, pp. 939-985, 1984, doi: 10.1070/im1985v025n02abeh001281.
DOI
|
45 |
L. C. Klingler, S. S. Magliveras, F. Richman, and M. Sramka, "Discrete logarithms for finite groups," Computing, vol. 85, no. 1-2, p. 3, 2009, doi: 10.1007/s00607-009-0032-0.
DOI
|
46 |
I. Anshel, M. Anshel, and D. Goldfeld, "An algebraic method for public-key cryptography," Math. Res. Lett., vol. 6, no. 3, pp. 287-291, 1999, doi: 10.4310/mrl.1999.v6.n3.a3.
DOI
|
47 |
K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. S. Kang, and C. Park, "New public-key cryptosystem using braid groups," 2000, pp. 166-183, doi: 10.1007/3-540-44598-6_10.
DOI
|
48 |
V. Shpilrain and G. Zapata, "Combinatorial group theory and public key cryptography," Appl. Algebra Eng. Commun. Comput., vol. 17, no. 3-4, pp. 291-302, 2006, doi: 10.1007/s00200-006-0006-9.
DOI
|
49 |
M. I. G. Vasco, D. Hofheinz, C. Martinez, and R. Steinwandt, "On the security of two public key cryptosystems using non-abelian groups," Des. Codes Cryptogr., vol. 32, no. 1, pp. 207-216, 2004, doi: 10.1023/b:desi.0000029223.76665.7e.
DOI
|
50 |
T. C. Lin, "A study of non-abelian public key cryptography," Int. J. Netw. Secur., vol. 20, no. 2, pp. 278-290, 2018.
|
51 |
D. Kahrobaei and M. Anshel, "Decision and search in nonabelian Cramer-Shoup public key cryptosystem," Groups Complex. Cryptol., vol. 1, no. 2, pp. 217-225, 2009, doi: 10.1515/gcc.2009.217.
DOI
|
52 |
H. K. Pathak and M. Sanghi, "Public key cryptosystem and a key exchange protocol using tools of non-abelian group," IJCSE Int. J. Comput. Sci. Eng., vol. 2, no. 04, pp. 1029-1033, 2010.
|
53 |
R. Alvarez, L. Tortosa, J. F. Vicent, and A. Zamora, "Analysis and design of a secure key exchange scheme," Inf. Sci., vol. 179, no. 12, pp. 2014-2021, 2009, doi: 10.1016/j.ins.2009.02.008.
DOI
|