[1]

Anshel I., Anshel M. and Goldfeld D.,
An algebraic method for public-key cryptography,
Math. Res. Lett. 6 (1999), 287–291.

[2]

Baumslag G., Cannonito F. B., Robinson D. J. S. and Segal D.,
The algorithmic theory of polycyclic-by-finite groups,
J. Algebra 142 (1991), 118–149.

[3]

Ben-Zvi A., Kalka A. and Tsaban B.,
Cryptanalysis via algebraic spans,
preprint 2014, https://eprint.iacr.org/2014/041.

[4]

Bosma W., Cannon J. and Playoust C.,
The MAGMA algebra system I: The user language,
J. Symbolic Comput. 24 (1997), 235–265.

[5]

Cavallo B. and Kahrobaei D.,
A family of polycyclic groups over which the conjugacy problem is NP-complete,
preprint 2014, https://arxiv.org/abs/1403.4153v2.

[6]

Cheon J. and Jun B.,
A polynomial time algorithm for the braid Diffie–Hellman conjugacy problem,
Advances in Cryptology (CRYPTO 2003),
Lecture Notes in Comput. Sci. 2729,
Springer, Berlin (2003), 212–225.

[7]

Ding J., Miasnikov A. D. and Ushakov A.,
A linear attack on a key exchange protocol using extensions of matrix semigroups,
preprint 2015, https://eprint.iacr.org/2015/018.

[8]

Eick B. and Kahrobaei D.,
Polycyclic groups: A new platform for cryptology?,
preprint 2004, https://arxiv.org/abs/math/0411077.

[9]

Eick B. and Ostheimer G.,
On the orbit-stabilizer problem for integral matrix actions of polycyclic groups,
Math. Comp. 72 (2003), 1511–1529.

[10]

Garber D., Kahrobaei D. and Lam H. T.,
Analysing the length-based attack on polycyclic groups,
preprint 2013, https://arxiv.org/abs/1305.0548v1.

[11]

Garber D., Kaplan S., Teicher M., Tsaban B. and Vishne U.,
Probabilistic solutions of equations in the braid group,
Adv. Appl. Math. 35 (2005), 323–334.

[12]

Garber D., Kaplan S., Teicher M., Tsaban B. and Vishne U.,
Length-based conjugacy search in the braid group,
Algebraic Methods in Cryptography (Mainz/Bochum 2005),
Contemp. Math. 418,
American Mathematical Society, Providence (2006), 75–87.

[13]

Habeeb M., Kahrobaei D., Koupparis C. and Shpilrain V.,
Public key exchange using semidirect product of (semi)groups,
preprint 2013, https://arxiv.org/abs/1304.6572v1.

[14]

Hall P.,
Edmonton Notes on Nilpotent Groups,
Queen Mary College Math. Notes,
Queen Mary College, London, 1969.

[15]

Hughes J. and Tannenbaum A.,
Length-based attacks for certain group-based encryption rewriting systems,
Workshop SECI02 Securite de la Communication sur Internet 2002.

[16]

Janusz G. J.,
Faithful representations of *p*-groups at characteristic *p*,
J. Algebra 15 (1970), 335–351.

[17]

Kahrobaei D. and Anshel M.,
Decision and search in non-abelian Cramer–Shoup public key cryptosystem,
Groups Complex. Cryptol. 1 (2009), 217–225.

[18]

Kahrobaei D. and Khan B.,
A non-commutative generalization of ElGamal key exchange using polycyclic groups,
Global Telecommunications Conference 2006 (GLOBECOM ’06),
IEEE Press, Piscataway (2006), DOI 10.1109/GLOCOM.2006.290.

[19]

Kahrobaei D. and Koupparis C.,
Non-commutative digital structures using non-commutative groups,
Groups Complex. Cryptol. 4 (2012), 377–384.

[20]

Kahrobaei D., Koupparis C. and Shpilrain V.,
Key exchange using semidirect product of (semi)groups,
Applied Cryptography and Network Security (ACNS 2013),
Lecture Notes in Comput. Sci. 7954,
Springer, Berlin (2013), 475–486.

[21]

Kahrobaei D., Lam H. and Shpilrain V.,
Public key exchange using extensions by endomorphisms and matrices over a Galois field,
preprint, http://www.sci.ccny.cuny.edu/~shpil/res.html.

[22]

Kahrobaei D. and Shpilrain V.,
Using semidirect product of (semi)groups in public key cryptography,
preprint 2016, https://arxiv.org/abs/1604.05542v1.

[23]

Ko K. H., Lee S. J., Cheon J. H., Han J. W., Kang J. and Park C.,
New public-key cryptosystem using braid groups,
Advances in Cryptology (CRYPTO 2000),
Lecture Notes in Comput. Sci. 1880,
Springer, Berlin (2000), 166–183.

[24]

Kreuzer M., Myasnikov A. D. and Ushakov A.,
A linear algebra attack to group-ring-based key exchange protocols,
Applied Cryptography and Network Security (ACNS 2014),
Lecture Notes in Comput. Sci. 8479,
Springer, Berlin (2014), 37–43;
https://eprint.iacr.org/2015/018.pdf.

[25]

Leedham-Green C. and Soicher L.,
Symbolic collection from the left and other strategies,
J. Symbolic Comput. 9 (1990), 665–675.

[26]

Lennox J. C. and Robinson D. J. S.,
The Theory of Infinite Soluble Groups,
Oxford Mathematical Monographs,
Clarendon Press, Oxford, 2004.

[27]

Mahalanobis A.,
The Diffie–Hellman key exchange protocol and non-abelian nilpotent groups,
Israel J. Math. 165 (2008), 161–87.

[28]

Miasnikov A. G., Shpilrain V. and Ushakov A.,
Random subgroups of braid groups: An approach to cryptanalysis of a braid group based cryptographic protocol,
Public Key Cryptography (PKC 2006),
Lecture Notes in Comput. Sci. 3958,
Springer, Berlin (2006), 302–314.

[29]

Miasnikov A. G. and Ushakov A.,
Random subgroups and analysis of the length-based and quotient attacks,
J. Math. Cryptol. 2 (2008), 29–61.

[30]

Myasnikov A. G. and Roman’kov V. A.,
A linear decomposition attack,
Groups Complex. Cryptol. 7 (2015), 81–94;
see also https://arxiv.org/abs/1412.6401v1.

[31]

Myasnikov A., Shpilrain V. and Ushakov A.,
Group-Based Cryptography,
Adv. Courses Math. CRM Barcelona,
Birkhäuser, Basel, 2008.

[32]

Myasnikov A., Shpilrain V. and Ushakov A.,
Non-Commutative Cryptography and Complexity of Group-theoretic Problems. With appendix by Natalia Mosina,
Math. Surveys Monogr. 177,
American Mathematical Society, Providence, 2011.

[33]

Myasnikov A. D. and Ushakov A.,
Length based attack and braid groups: Cryptanalysis of Anshel–Anshel–Godlfeld key exchange protocol,
Public Key Cryptography (PKC 2007),
Lecture Notes in Comput. Sci. 4450,
Springer, Berlin (2007), 76–88.

[34]

Roman’kov V. A.,
Equations over groups,
Groups Complex. Cryptol. 4 (2012), no. 2, 191–239.

[35]

Roman’kov V. A.,
Algebraic Cryptography (in Russian),
Omsk, Omsk State University, 2013.

[36]

Roman’kov V. A.,
Cryptanalysis of some schemes applying automorphisms (in Russian),
Appl. Discrete Math. 3 (2013), 35–51.

[37]

Roman’kov V. A.,
A polynomial time algorithm for the braid double shielded public key cryptosystems,
preprint 2014, https://arxiv.org/abs/1412.5277v1.

[38]

Roman’kov V. A.,
Linear decomposition attack on public key exchange protocols using semidirect products of (semi)groups,
preprint 2015, https://arxiv.org/abs/1501.01152v1.

[39]

Roman’kov V. A. and Menshov A.,
Cryptanalysis of Andrecut’s public key cryptosystem,
preprint 2015, https://arxiv.org/abs/1507.01496v1.

[40]

Segal D.,
Polycyclic Groups,
Cambridge Tracts in Math. 82,
Cambridge University Press, Cambridge, 2005.

[41]

Shpilrain V. and Zapata G.,
Using the subgroup membership search problem in public key cryptography,
Algebraic Methods in Cryptography (Mainz/Bochum 2005),
Contemp. Math. 418,
American Mathematical Society, Providence (2006), 169–181.

[42]

Sims C. C.,
Computation with Finitely Presented Groups,
Encyclopedia Math. Appl. 48,
Cambridge University Press, Cambridge, 1994.

[43]

Tsaban B.,
Practical polynomial time solutions of several major problems in noncommutative-algebraic cryptography (preliminary announcement),
preprint 2014, https://eprint.iacr.org/2014/041/20140115:201530.

[44]

Tsaban B.,
Polynomial time solutions of computational problems in noncommutative algebraic cryptography,
J. Cryptology 28 (2015), no. 2, 601–622.

[45]

The GAP group, GAP – Groups, Algorithms and Programming, 2000.

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