|
[1]
|
I. J. Aalbersberg and H. J. Hoogeboom, Characterizations of the decidability of some problems for regular trace languages, Mathematical Systems Theory, 22 (1989), 1-19.
doi: 10.1007/BF02088289.
|
|
[2]
|
I. Anshel, M. Anshel and D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett., 6 (1999), 287-291.
doi: 10.4310/MRL.1999.v6.n3.a3.
|
|
[3]
|
L. Bartholdi and P. V. Silva, Rational subsets of groups, Handbook of Automata Theory, Automata in Mathematics and Selected Applications, 2 (2021), 841-869.
doi: 10.4171/Automata-1/23.
|
|
[4]
|
J. Berstel, Transductions and Context-free Languages, Leitfäden der Angewandten Mathematik und Mechanik, 38. B. G. Teubner, Stuttgart, 1979.
doi: 10.1007/978-3-663-09367-1.
|
|
[5]
|
O. Bogopolski, A. Martino, O. Maslakova and E. Ventura, The conjugacy problem is solvable in free-by-cyclic groups, Bull. London Math. Soc., 38 (2006), 787-794.
doi: 10.1112/S0024609306018674.
|
|
[6]
|
O. Bogopolski, A. Martino and E. Ventura, Orbit decidability and the conjugacy problem for some extensions of groups, Trans. Amer. Math. Soc., 362 (2010), 2003-2036.
doi: 10.1090/S0002-9947-09-04817-X.
|
|
[7]
|
P. Brinkmann, Detecting automorphic orbits in free groups, J. Algebra, 324 (2010), 1083-1097.
doi: 10.1016/j.jalgebra.2010.05.032.
|
|
[8]
|
A. Carvalho, On generalized conjugacy and some related problems, Comm. Algebra, 51 (2022), 3528-3542.
doi: 10.1080/00927872.2023.2186132.
|
|
[9]
|
A. Carvalho, Algebraic and context-free subsets of subgroups, Theor. Comput. Sci., 980 (2023), 114229, 10 pp.
doi: 10.1016/j.tcs.2023.114229.
|
|
[10]
|
A. Carvalho, On the dynamics of endomorphisms of the direct product of two free groups, (2023), arXiv: 2307.13875.
doi: 10.1515/jgth-2021-0197.
|
|
[11]
|
A. Carvalho, Quantifying Brinkmann's problem: $\varphi$-order and $\varphi$-spectrum, (2023), arXiv: 2306.12563.
|
|
[12]
|
A. Carvalho and J. Delgado, Decidability of the Brinkmann problems for endomorphisms of the free group, Arch. Math., to appear.
|
|
[13]
|
M. Casals-Ruiz and I. V. Kazachkov, Two remarks on first-order theories of Baumslag-Solitar groups, Sib. Math. J., 53 (2012), 805-809.
doi: 10.1134/S0037446612050060.
|
|
[14]
|
D. Collins, Baumslag-Solitar Group, Encyclopedia of Mathematics, Kluwer Academic Publishers, 2001.
|
|
[15]
|
R. Gilman, Formal languages and infinite groups, Geometric and Computational Perspectives on Infinite Groups, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Amer. Math. Soc., Providence, RI, 25 (1995), 27-51.
doi: 10.1090/dimacs/025/03.
|
|
[16]
|
M. Habeeb, D. Kahrobaei, C. Koupparis and V. Shpilrain, Public key exchange using semidirect product of (semi)groups, Applied Cryptography and Network Security ACNS 2013, (2013), 475-486.
doi: 10.1007/978-3-642-38980-1_30.
|
|
[17]
|
T. Herbst, On a subclass of context-free groups, RAIRO Inform. Théor. Appl., 25 (1991), 255-272.
doi: 10.1051/ita/1991250302551.
|
|
[18]
|
D. Kahrobaei, R. Flores and M. Noce, Group-based cryptography in the quantum era, Notices Amer. Math. Soc., 70 (2023), 752-763.
doi: 10.1090/noti2684.
|
|
[19]
|
D. Kahrobaei, R. Flores, M. Noce, M. E. Habeeb and C. Battarbee, Applications of Group Theory in Cryptography: Post-quantum Group-based Cryptography, Mathematical Surveys and Monographs, 278. American Mathematical Society, Providence, RI, 2024.
doi: 10.1090/surv/278.
|
|
[20]
|
R. Kannan and R. Lipton, Polynomial-time algorithm for the orbit problem, J. Assoc. Comput. Mach., 33 (1986), 808-821.
doi: 10.1145/6490.6496.
|
|
[21]
|
K. H. Ko, S. J. Lee, J. H. Cheon, J. W. Han, J. Kang and C. Park, New public-key cryptosystem using braid groups, Advances in Cryptology - CRYPTO 2000 (Santa Barbara, CA), Lecture Notes in Comput. Sci., Springer, Berlin, 1880 (2000), 166-183.
doi: 10.1007/3-540-44598-6_10.
|
|
[22]
|
Y. Kurt, A new key exchange primitive based on the triple decomposition problem, IACR Cryptology ePrint Archive, 378 (2006).
|
|
[23]
|
M. Ladra and P. V. Silva, The generalized conjugacy problem for virtually free groups, Forum Math., 23 (2011), 447-482.
doi: 10.1515/form.2011.015.
|
|
[24]
|
S. Lal and A. Chaturvedi, Authentication schemes using braid groups, (2005), arXiv: cs/0507066.
|
|
[25]
|
J. C. Lennox, On soluble groups in which centralizers are finitely generated, Rend. Sem. Mat. Univ. Padova, 96 (1996), 131-135.
|
|
[26]
|
A. D. Logan, The conjugacy problem for ascending HNN-extensions of free groups, (2022), preprint, arXiv: 2209.04357.
|
|
[27]
|
M. Lohrey, The rational subset membership problem for groups: A survey, Groups St Andrews 2013, London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 422 (2015), 368-389.
doi: 10.1017/CBO9781316227343.024.
|
|
[28]
|
M. Lohrey and B. Steinberg, The submonoid and rational subset membership problems for graph groups, J. Algebra, 320 (2008), 728-755.
doi: 10.1016/j.jalgebra.2007.08.025.
|
|
[29]
|
F. Matucci, Cryptanalysis of the Shpilrain-Ushakov protocol in Thompson's group, J. Cryptology, 21 (2008), 458-468.
doi: 10.1007/s00145-007-9016-4.
|
|
[30]
|
A. Myasnikov, V. Shpilrain and A. Ushakov, Group-Based Cryptography, Advanced Courses in Mathematics, CRM Barcelona, Birkhäuser Verlag, Basel, 2008.
|
|
[31]
|
A. V. Rozhkov, Centralizers of elements in a group of tree automorphisms, Izv. Math., 43 (1994), 471-492.
doi: 10.1070/IM1994v043n03ABEH001639.
|
|
[32]
|
D. Ruinskiy, A. Shamir and B. Tsaban, Cryptanalysis of group-based key agreement protocols using subgroup distance functions, Public Key Cryptography – PKC 2007, Lecture Notes in Comput. Sci., 4450 (2007), 61-75.
doi: 10.1007/978-3-540-71677-8_5.
|
|
[33]
|
A. P. Sánchez and M. Shapiro, Growth in higher Baumslag-Solitar groups, Geom. Dedicata, 195 (2017), 79-99.
doi: 10.1007/s10711-017-0277-2.
|
|
[34]
|
V. Shpilrain, Search and witness problems in group theory, Groups, Complexity, Cryptology, 2 (2010), 231-246.
doi: 10.1515/gcc.2010.015.
|
|
[35]
|
V. Shpilrain, Problems in group theory motivated by cryptography, (2018), arXiv: 1802.07300.
|
|
[36]
|
V. Shpilrain and A. Ushakov, Thompson's group and public key cryptography, Applied Cryptography and Network Security – ACNS 2005, Lecture Notes in Computer Science, 3531 (2005), 151-164.
doi: 10.1007/11496137_11.
|
|
[37]
|
V. Shpilrain and A. Ushakov, A new key exchange protocol based on the decomposition problem, Algebraic Methods in Cryptography, Contemporary Mathematics, American Mathematical Society, 418 (2006), 161-167.
doi: 10.1090/conm/418/07954.
|
|
[38]
|
V. Shpilrain and A. Ushakov, An authentication scheme based on the twisted conjugacy problem, Applied Cryptography and Network Security – ACNS 2008, Lecture Notes in Computer Science, 5037 (2008), 366-372.
doi: 10.1007/978-3-540-68914-0_22.
|
|
[39]
|
V. Shpilrain and G. Zapata, Using the subgroup membership search problem in public key cryptography, Algebraic Methods in Cryptography, Contemp. Math., Amer. Math. Soc., Providence, RI, 418 (2006), 169-178.
doi: 10.1090/conm/418/07955.
|
|
[40]
|
P. V. Silva, On the rational subsets of the monogenic free inverse monoid, J. Algebra, 618 (2023), 214-240.
doi: 10.1016/j.jalgebra.2022.12.006.
|
|
[41]
|
P. V. Silva and P. Weil, Automorphic orbits in free groups: Words versus subgroups, Internat. J. Algebra Comput., 20 (2010), 561-5900.
doi: 10.1142/S0218196710005790.
|
|
[42]
|
M. Valiunas, Negligibity of elliptic elements in ascending HNN-extensions of $\mathbb{Z}^m$, Comm. Algebra, 47 (2019), 5101-5120.
doi: 10.1080/00927872.2019.1612417.
|
|
[43]
|
E. Ventura, Group-theoretic orbit decidability, Groups Complex. Cryptol., 6 (2014), 133-148.
doi: 10.1515/gcc-2014-0012.
|
{{journal.titleEn}} 
DownLoad: