A selection of publications by ACC members. For preprints and additional publications consult the Cryptology ePrint Archive, and arXiv.org.
Books
Algorithmic Problems of Group Theory, Their Complexity, and Applications to Cryptography, Delaram Kahrobaei and Vladimir Shpilrain eds., Contemporary Mathematics, 633, American Mathematical Society 2015.
http://dx.doi.org/10.1090/conm/633
Computational and Combinatorial Group Theory and Cryptography, Benjamin Fine, Delaram Kahrobaei and Gerhard Rosenberger eds., Contemporary Mathematics, 582, American Mathematical Society 2012.
http://dx.doi.org/10.1090/conm/582
Non-Commutative Cryptography and Complexity of Group-Theoretic Problems, Alexei Myasnikov, Vladimir Shpilrain and Alexander Ushakov, Mathematical Surveys and Monographs, 177, American Mathematical Society 2011.
http://dx.doi.org/10.1090/surv/177
Public Key Cryptography -- PKC 2011, Dario Catalano, Nelly Fazio, Rosario Gennaro and Antonio Nicolosi, eds., Lecture Notes in Computer Science 6571, Springer 2011.
http://dx.doi.org/10.1007/978-3-642-19379-8
Group-based Cryptography.
Alexei Myasnikov, Vladimir Shpilrain and Alexander Ushakov.
Advanced Courses in Mathematics CRM Barcelona, Birkhäuser 2008.
Articles
2017
Volker Diekert, Alexei G. Myasnikov and Armin Weiß.
Amenability of Schreier graphs and strongly generic algorithms for the conjugacy problem. J. Symbolic Comput. 83 (2017), 147-165.
https://doi.org/10.1016/j.jsc.2016.11.009
Albert Garreta, Alexei G. Miasnikov and Denis Ovchinnikov.
Random nilpotent groups, polycyclic presentations, and Diophantine problems.
Groups Complex. Cryptol. 9 (2017), 99-115.
https://doi.org/10.1515/gcc-2017-0007
Funda Gul, Alexei G. Myasnikov and Mahmood Sohrabi.
Distortion of embeddings of a torsion-free finitely generated nilpotent group into a unitriangular group.
Internat. J. Algebra Comput. 27 (2017), 633-653.
https://doi.org/10.1142/S021819671750031X
Funda Gul, Mahmood Sohrabi and Alexander Ushakov.
Magnus embedding and algorithmic properties of groups F/N^d.
Trans. Amer. Math. Soc. 369 (2017), 6189-6206.
https://doi.org/10.1090/tran/6880
Olga Kharlampovich, Alexei Myasnikov and Mark Sapir.
Algorithmically complex residually finite groups.
Bull. Math. Sci. 7 (2017), 309-352.
https://doi.org/10.1007/s13373-017-0103-z
Andrei Malyutin, Tatiana Nagnibeda and Denis Serbin.
Boundaries of Z^n-free groups.
Groups, graphs and random walks, 355-390, London Math. Soc. Lecture Note Ser., 436, Cambridge Univ. Press, Cambridge, 2017.
Alexei Miasnikov and Paul Schupp.
Computational complexity and the conjugacy problem.
Computability 6 (2017), 307-318.
Alexei Miasnikov and Svetla Vassileva.
Log-space conjugacy problem in the Grigorchuk group.
Groups Complex. Cryptol. 9 (2017), 77-85.
https://doi.org/10.1515/gcc-2017-0005
Alexei Miasnikov, Svetla Vassileva and Armin Weiß.
The conjugacy problem in free solvable groups and wreath products of abelian groups is in TC0.
Computer science—theory and applications, 217-231, Lecture Notes in Comput. Sci., 10304, Springer, 2017.
2016
Laura Ciobanu, Volker Diekert and Murray Elder.
Solution sets for equations over free groups are EDT0L languages.
Internat. J. Algebra Comput. 26 (2016) 843--886.
http://dx.doi.org/10.1142/S0218196716500363
Volker Diekert, Alexei G. Myasnikov, Armin Weiß.
Conjugacy in Baumslag's group, generic case complexity, and division in power circuits.
Algorithmica 74 (2016) 1-28.
http://dx.doi.org/10.1007/s00453-016-0117-z
Elizaveta Frenkel, Andrey Nikolaev and Alexander Ushakov.
Knapsack problems in products of groups.
J. Symbolic Comput. 74 (2016), 96--108.
http://dx.doi.org/10.1016/j.jsc.2015.05.006
Delaram Kahrobaei and Vldimir Shpilrain.
Using semidirect product of (semi)groups in public key cryptography.
CiE 2016. In vol. 9709 of Lecture Notes Comp. Sci. 132--141, Springer, 2016.
http://dx.doi.org/10.1007/978-3-319-40189-8_14
Denis R. Hirschfeldt, Carl G. Jockusch, Timothy H. McNicholl and Paul E. Schupp.
Asymptotic density and the coarse computability bound.
Computability 5 (2016), 13--27.
http://dx.doi.org/10.3233/COM-150035
Alexei Myasnikov, Andrey Nikolaev and Alexander Ushakov.
Non-commutative lattice problems.
J. Group Theory 19 (2016) 455--475.
http://dx.doi.org/10.1515/jgth-2016-0506
Igor Lysenok, Alexei Miasnikov and Alexander Ushakov.
Quadratic equations in the Grigorchuk group.
Groups Geom. Dyn. 10 (2016) 201--239.
http://dx.doi.org/10.4171/GGD/348
Alexei Myasnikov, Andrey Nikolaev and Alexander Ushakov.
Non-commutative lattice problems.
J. Group Theory 19 (2016) 455--475.
http://dx.doi.org/10.1515/jgth-2016-0506
Tullio Ceccherini-Silberstein, Michel Coornaert, Francsca Fiorenzi, Paul E. Schupp and Nicholas W. M. Touikan, Nicholas.
Multipass automata and group word problems.
Theoret. Comput. Sci. 600 (2015), 19--33.
http://dx.doi.org/10.1016/j.tcs.2015.06.054
Volker Diekert, Olga Kharlampovich and Atefeh Mohajeri Moghaddam.
SLP compression for solutions of equations with constraints in free and hyperbolic groups.
Internat. J. Algebra Comput. 25 (2015) 81--111. http://dx.doi.org/10.1142/S0218196715400056
Volker Diekert, Akexei G. Myasnikov and Armin Weiß.
Amenability of Schreier graphs and strongly generic algorithms for the conjugacy problem.
In ISSAC'15—Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, 141--148, ACM, 2015.
http://dx.doi.org/10.1145/2755996.2756644
D. Kahrobaei, C. Koupparis, and V. Shpilrain.
A CCA secure cryptosystem using matrices over group rings.
Contemp. Math., Amer. Math. Soc. 633 (2015), 73-80. http://dx.doi.org/10.1090/conm/633/12652
Matvei Kotov and Alexander Ushakov.
Analysis of a certain polycyclic-group-based cryptosystem.
J. Math. Cryptol. 9 (2015), 161--167.
http://dx.doi.org/10.1515/jmc-2015-0013
Pavel Morar and Alexander Ushakov.
Search problems in groups and branching processes.
Internat. J. Algebra Comput. 25 (2015) 445--480.
http://dx.doi.org/10.1142/S0218196715500058
Volker Diekert, Alexei G. Myasnikov and Armin Weiß.
Conjugacy in Baumslag's group, generic case complexity, and division in power circuits.
Algorithmica (2016), 1--28.
http://dx.doi.org/10.1007/s00453-016-0117-z
Nelly Fazio, Antonio R. Nicolosi and Irippuge Milinda Perera.
Broadcast steganography.
In Topics in Cryptology -- CT-RSA 2014, vol. 8366 of Lecture Notes in Computer Science 64--84 Springer 2014.
http://dx.doi.org/10.1007/978-3-319-04852-9_4
Dima Grigoriev and Vladimir Shpilrain.
Yao's millionaires' problem and decoy-based public key encryption by classical physics.
Journal of Foundations of Computer Science 25 (2014), 409--417.
http://dx.doi.org/10.1142/S0129054114400036 /p>
Martin Kreuzer, Alexei D. Myasnikov and Alexander Ushakov.
A linear algebra attack to group-ring-based key exchange protocols.
Applied cryptography and network security.
In vol. 8479 of Lecture Notes in Computer Science, 37--43, Springer, 2014.
http://dx.doi.org/10.1007/978-3-319-07536-5_3
Alexei Myasnikov, Andrey Nikolaev and Alexander Ushakov.
The Post correspondence problem in groups.
J. Group Theory 17 (2014), 991--1008.
http://dx.doi.org/10.1515/jgth-2014-0022
A. G. Myasnikov and V. N. Remeslennikov.
Generic theories as a method for approximating elementary theories. (Russian).
Algebra Logika 53 (2014), 779--789.
Translation in Algebra and Logic 53 (2014), 512--519.
http://dx.doi.org/10.1007/s10469-015-9314-0
Alexei Myasnikov, and Vitalĭ Roman'kov.
Diophantine cryptography in free metabelian groups: theoretical base.
Groups Complex. Cryptol. 6 (2014) 103--120.
http://dx.doi.org/10.1515/gcc-2014-0011
Alexey D. Myasnikov and Alexander Ushakov.
Cryptanalysis of matrix conjugation schemes.
J. Math. Cryptol. 8 (2014), 95--114.
http://dx.doi.org/10.1515/jmc-2012-0033
Alexey D Myasnikov and Alexander Ushakov.
Quantum algorithm for discrete logarithm problem for matrices over finite group rings.
Groups Complex. Cryptol. 6 (2014) 31--36.
http://dx.doi.org/10.1515/gcc-2014-0003
Georg Neugebauer, Lucas Brutschy, Ulrike Meyer and Susanne Wetzel.
Privacy-preserving multi-party reconciliation secure in the malicious model.
In Data Privacy Management and Autonomous Spontaneous Security,
vol. 8247 of Lect. Notes in Comp. Sci., 178--193, Springer 2014.
http://dx.doi.org/10.1007/978-3-642-54568-9_12
2013
Rodney G. Downey, Carl G. Jockusch, Jr. and Paul E. Schupp.
Asymptotic density and computably enumerable sets.
J. Math. Log. 13 (2013), 1350005, 43 pp.
http://dx.doi.org/10.1142/S0219061313500050
D. Kahrobaei, C. Koupparis, and V. Shpilrain.
Public key exchange using matrices over group rings.
Groups, Complexity, and Cryptology 5 (2013), 97-115.
http://dx.doi.org/10.1515/gcc-2013-0007
Olga Kharlampovich, Alexei Myasnikov and Denis Serbin.
Actions, length functions, and non-Archimedean words.
Internat. J. Algebra Comput. 23 (2013) 325--455.
http://dx.doi.org/10.1142/S0218196713400031
Chunyu Tang, David A. Naumann and Susanne Wetzel.
Analysis of authentication and key establishment in inter-generational mobile telephony.
2013 IEEE 10th International Conference on High Performance Computing and Communications & 2013 IEEE International Conference on Embedded and Ubiquitous Computing.
http://dx.doi.org/10.1109/HPCC.and.EUC.2013.226
2012
Volker Diekert, Jonathan Kausch and Markus Lohrey.
Logspace computations in Coxeter groups and graph groups.
In Computational and combinatorial group theory and cryptography, vol.
582 of Contemp. Math., 77--94. Amer. Math. Soc., Providence, RI,
2012.
http://dx.doi.org/10.1090/conm/582/11553
Dima Grigoriev and Vladimir Shpilrain.
No-leak authentication by the Sherlock Holmes method.
Groups Complex. Cryptol., 4 (2012)(1) 177--189.
http://dx.doi.org/10.1515/gcc-2012-0009
Maggie Habeeb, Delaram Kahrobaei and Vladimir Shpilrain.
A secret sharing scheme based on group presentations and the word problem.
In Computational and combinatorial group theory and cryptography, vol.
582 of Contemp. Math., 143--150. Amer. Math. Soc., Providence, RI,
2012.
http://dx.doi.org/10.1090/conm/582/11557
Carl G. Jockusch, Jr. and Paul E. Schupp.
Generic computability, Turing degrees, and asymptotic density.
J. Lond. Math. Soc. (2), 85 (2012)(2) 472--490.
http://dx.doi.org/10.1112/jlms/jdr051
Delaram Kahrobaei and Elizabeth Vidaurre.
Publicly verifiable secret sharing using non-abelian groups.
In Computational and combinatorial group theory and cryptography, vol.
582 of Contemp. Math., 175--179. Amer. Math. Soc., Providence, RI,
2012.
http://dx.doi.org/10.1090/conm/582/11561
Alexei G. Miasnikov, Alexander Ushakov and Dong Wook Won.
Power circuits, exponential algebra, and time complexity.
Internat. J. Algebra Comput., 22 (2012)(6) 1250047, 51.
http://dx.doi.org/10.1142/S0218196712500476
2011
Gilbert Baumslag, Nelly Fazio, Antonio R. Nicolosi, Vladimir Shpilrain and
William E. Skeith, III.
Generalized learning problems and applications to non-commutative cryptography
(extended abstract).
In Provable security, vol. 6980 of Lecture Notes in Comput. Sci.,
324--339. Springer, Heidelberg, 2011.
http://dx.doi.org/10.1007/978-3-642-24316-5_23
Volker Diekert and Alexei G. Myasnikov.
Solving word problems in group extensions over infinite words.
In Developments in language theory, vol. 6795 of Lecture Notes in
Comput. Sci., 192--203. Springer, Heidelberg, 2011.
http://dx.doi.org/10.1007/978-3-642-22321-1_17
Benjamin Fine, Maggie Habeeb, Delaram Kahrobaei and Gerhard Rosenberger.
Aspects of nonabelian group based cryptography: a survey and open problems.
JP J. Algebra Number Theory Appl., 21 (2011)(1) 1--40.
Robert H. Gilman, Alexei Myasnikov and Vitalii Roman'kov.
Random equations in free groups.
Groups Complex. Cryptol., 3 (2011)(2) 257--284.
http://dx.doi.org/10.1515/gcc.2011.010
I. G. Lysenok and A. G. Myasnikov.
A polynomial bound for solutions of quadratic equations in free groups.
Tr. Mat. Inst. Steklova, 274 (2011)(Algoritmicheskie Voprosy Algebry i
Logiki) 148--190.
http://dx.doi.org/10.1134/S0081543811060101
Natalia Mosina and Alexander Ushakov.
Strong law of large numbers on graphs and groups.
Groups Complex. Cryptol., 3 (2011)(1) 67--103.
http://dx.doi.org/10.1515/GCC.2011.004
Alexei Myasnikov and Alexander Ushakov.
Random van Kampen diagrams and algorithmic problems in groups.
Groups Complex. Cryptol., 3 (2011)(1) 121--185.
http://dx.doi.org/10.1515/GCC.2011.006
Alexei Myasnikov, Alexander Ushakov and Dong Wook Won.
The word problem in the Baumslag group with a non-elementary Dehn function is
polynomial time decidable.
J. Algebra, 345 (2011) 324--342.
http://dx.doi.org/10.1016/j.jalgebra.2011.07.024
Jad Naous, Michael Walfish, Antonio Nicolosi, David Mazières,
Michael Miller and Arun Seehra.
Verifying and enforcing network paths with icing.
In Kenjiro Cho and Mark Crovella, eds., CoNEXT, 30. ACM, 2011.
http://dl.acm.org/citation.cfm?id=2079296
2010
Sean Cleary, Murray Elder, Andrew Rechnitzer and Jennifer Taback.
Random subgroups of Thompson's group F.
Groups Geom. Dyn., 4 (2010)(1) 91--126.
http://dx.doi.org/10.4171/GGD/76
Volker Diekert, Andrew J. Duncan and Alexei G. Myasnikov.
Geodesic rewriting systems and pregroups.
In Combinatorial and geometric group theory, Trends Math., 55--91.
Birkhäuser/Springer Basel AG, Basel, 2010.
http://dx.doi.org/10.1007/978-3-7643-9911-5_3
Murray Elder and Andrew Rechnitzer.
Some geodesic problems in groups.
Groups Complex. Cryptol., 2 (2010)(2) 223--229.
http://dx.doi.org/10.1515/GCC.2010.014
Elizaveta Frenkel, Alexei G. Myasnikov and Vladimir N. Remeslennikov.
Regular sets and counting in free groups.
In Combinatorial and geometric group theory, Trends Math., 93--118.
Birkhäuser/Springer Basel AG, Basel, 2010.
http://dx.doi.org/10.1007/978-3-7643-9911-5_4
Dima Grigoriev and Vladimir Shpilrain.
Authentication schemes from actions on graphs, groups, or rings.
Ann. Pure Appl. Logic, 162 (2010)(3) 194--200.
http://dx.doi.org/10.1016/j.apal.2010.09.004
Delaram Kahrobaei and Michael Anshel.
Applications of group theory in cryptography.
Int. J. Pure Appl. Math., 58 (2010)(1) 21--23.
O. Kharlampovich, I. G. Lysënok, A. G. Myasnikov and N. W. M. Touikan.
The solvability problem for quadratic equations over free groups is
NP-complete.
Theory Comput. Syst., 47 (2010)(1) 250--258.
http://dx.doi.org/10.1007/s00224-008-9153-7
Igor Lysenok, Alexei Myasnikov and Alexander Ushakov.
The conjugacy problem in the Grigorchuk group is polynomial time decidable.
Groups Geom. Dyn., 4 (2010)(4) 813--833.
http://dx.doi.org/10.4171/GGD/108
Natalia Mosina and Alexander Ushakov.
Mean-set attack: cryptanalysis of Sibert et al. authentication protocol.
J. Math. Cryptol., 4 (2010)(2) 149--174.
http://dx.doi.org/10.1515/JMC.2010.006
A. Myasnikov, V. Roman'kov, A. Ushakov and A. Vershik.
The word and geodesic problems in free solvable groups.
Trans. Amer. Math. Soc., 362 (2010)(9) 4655--4682.
Dimitri Bormotov, Robert Gilman and Alexei Myasnikov.
Solving one-variable equations in free groups.
J. Group Theory, 12 (2009)(2) 317--330.
http://dx.doi.org/10.1515/JGT.2008.080
Benjamin Fine, Alexei Myasnikov and Gerhard Rosenberger.
Generic subgroups of group amalgams.
Groups Complex. Cryptol., 1 (2009)(1) 51--61.
http://dx.doi.org/10.1515/GCC.2009.51
Dima Grigoriev and Vladimir Shpilrain.
Authentication from matrix conjugation.
Groups Complex. Cryptol., 1 (2009)(2) 199--205.
http://dx.doi.org/10.1515/GCC.2009.199
Delaram Kahrobaei and Michael Anshel.
Decision and search in non-abelian Cramer--Shoup public key cryptosystem.
Groups Complex. Cryptol., 1 (2009)(2) 217--225.
http://dx.doi.org/10.1515/GCC.2009.217
Ilya Kapovich and Paul E. Schupp.
Random quotients of the modular group are rigid and essentially incompressible.
J. Reine Angew. Math., 628 (2009) 91--119.
http://dx.doi.org/10.1515/CRELLE.2009.019
Jonathan Longrigg and Alexander Ushakov.
A practical attack on a certain braid group based shifted conjugacy
authentication protocol.
Groups Complex. Cryptol., 1 (2009)(2) 275--286.
http://dx.doi.org/10.1515/GCC.2009.275
Alex D. Myasnikov and Alexander Ushakov.
Cryptanalysis of the Anshel-Anshel-Goldfeld-Lemieux key agreement protocol.
Groups Complex. Cryptol., 1 (2009)(1) 63--75.
http://dx.doi.org/10.1515/GCC.2009.63
Arun Seehra, Jad Naous, Michael Walfish, David Mazières, Antonio
Nicolosi and Scott Shenker.
A policy framework for the future internet.
In Lakshminarayanan Subramanian, Will E. Leland and Ratul Mahajan, eds.,
HotNets. ACM SIGCOMM, 2009.
http://conferences.sigcomm.org/hotnets/2009/papers/hotnets2009-final57.pdf
Vladimir Shpilrain and Gabriel Zapata.
Using decision problems in public key cryptography.
Groups Complex. Cryptol., 1 (2009)(1) 33--49.
http://dx.doi.org/10.1515/GCC.2009.33
2008
Michael Batty, Andrea Casaccino, Andrew J. Duncan, Sarah Rees and Simone
Severini.
An application of the Deutsch-Jozsa algorithm to formal languages and the word
problem in groups.
In Theory of quantum computation, communication, and cryptography, vol.
5106 of Lecture Notes in Comput. Sci., 57--69. Springer, Berlin,
2008.
http://dx.doi.org/10.1007/978-3-540-89304-2_6
Murray Elder, Mark Kambites and Gretchen Ostheimer.
On groups and counter automata.
Internat. J. Algebra Comput., 18 (2008)(8) 1345--1364.
http://dx.doi.org/10.1142/S0218196708004901
Ilya Kapovich and Paul Schupp.
On group-theoretic models of randomness and genericity.
Groups Geom. Dyn., 2 (2008)(3) 383--404.
http://dx.doi.org/10.4171/GGD/45
Jonathan Longrigg and Alexander Ushakov.
Cryptanalysis of the shifted conjugacy authentication protocol.
J. Math. Cryptol., 2 (2008)(2) 109--116.
http://dx.doi.org/10.1515/JMC.2008.005
Alexei G. Myasnikov and Alexander N. Rybalov.
Generic complexity of undecidable problems.
J. Symbolic Logic, 73 (2008)(2) 656--673.
http://dx.doi.org/10.2178/jsl/1208359065
Alexei G. Myasnikov and Alexander Ushakov.
Random subgroups and analysis of the length-based and quotient attacks.
J. Math. Cryptol., 2 (2008)(1) 29--61.
http://dx.doi.org/10.1515/JMC.2008.003
2007
Alexandre V. Borovik, Alexei G. Myasnikov and Vladimir N. Remeslennikov.
The conjugacy problem in amalgamated products. i. regular elements and black
holes.
Internat. J. Algebra Comput., 17 (2007)(7) 1299--1333.
http://dx.doi.org/10.1142/S0218196707003652
Alexandre V. Borovik, Alexei G. Myasnikov and Vladimir N. Remeslennikov.
Generic complexity of the conjugacy problem in {HNN}-extensions and algorithmic
stratification of Miller's groups.
Internat. J. Algebra Comput., 17 (2007)(5-6) 963--997.
http://dx.doi.org/10.1142/S0218196707003913
Inna Bumagin, Olga Kharlampovich and Alexei Miasnikov.
The isomorphism problem for finitely generated fully residually free groups.
J. Pure Appl. Algebra, 208 (2007)(3) 961--977.
http://dx.doi.org/10.1016/j.jpaa.2006.03.025
Nelly Fazio, Antonio Nicolosi and Duong Hieu Phan.
Traitor tracing with optimal transmission rate.
In Juan A. Garay, Arjen K. Lenstra, Masahiro, Mambo and Renè, eds.,
ISC, vol. 4779. Springer, 2007.
Michael J. Freedman and Antonio Nicolosi.
Efficient private techniques for verifying social proximity.
In John R. Douceur and Roger Wattenhofer, eds., IPTPS. 2007.
http://www.iptps.org/papers-2007/FreedmanNicolosi.pdf
Ilya Kapovich, Igor Rivin, Paul Schupp and Vladimir Shpilrain.
Densities in free groups and zk, visible points and test
elements.
Math. Res. Lett., 14 (2007)(2) 263--284.
Alex D. Myasnikov and Alexander Ushakov.
Length based attack and braid groups: cryptanalysis of anshel-anshel-goldfeld
key exchange protocol.
In Public key cryptography---PKC 2007, vol. 4450 of Lecture Notes in
Comput. Sci., 76--88. Springer, Berlin, 2007.
http://dx.doi.org/10.1007/978-3-540-71677-8_6
2006
Michael Batty, Andrew J. Duncan and Samuel L. Braunstein.
Extending the promise of the Deutsch-Jozsa-{H}øyer algorithm for finite
groups.
LMS J. Comput. Math., 9 (2006) 40--63 (electronic).
Alexandre V. Borovik and Alexei G. Myasnikov.
Quotient tests and random walks in computational group theory.
In Topological and asymptotic aspects of group theory, vol. 394 of
Contemp. Math., 31--45. Amer. Math. Soc., Providence, RI, 2006.
http://dx.doi.org/10.1090/conm/394/07432
Ivan Damgård, Nelly Fazio and Antonio Nicolosi.
Non-interactive zero-knowledge from homomorphic encryption.
In Shai Halevi and Tal Rabin, eds., TCC, vol. 3876 of Lecture Notes
in Computer Science, 41--59. Springer, 2006.
http://dx.doi.org/10.1007/11681878_3
Ivan Damgård, Nelly Fazio and Antonio Nicolosi.
Non-iterative zero-knowledge from homomorphic encryption.
In Theory of cryptography, vol. 3876 of Lecture Notes in Comput.
Sci., 41--59. Springer, Berlin, 2006.
http://dx.doi.org/10.1007/11681878_3
Joel David Hamkins and Alexei Miasnikov.
The halting problem is decidable on a set of asymptotic probability one.
Notre Dame J. Formal Logic, 47 (2006)(4) 515--524 (electronic).
http://dx.doi.org/10.1305/ndjfl/1168352664
Ilya Kapovich, Paul Schupp and Vladimir Shpilrain.
Generic properties of whitehead's algorithm and isomorphism rigidity of random
one-relator groups.
Pacific J. Math., 223 (2006)(1) 113--140.
http://dx.doi.org/10.2140/pjm.2006.223.113
Martin Kreuzer, Alexei Myasnikov, Gerhard Rosenberger and Alexander
Ushakov.
Quotient tests and Gröbner bases.
In Combinatorial group theory, discrete groups, and number theory, vol.
421 of Contemp. Math., 187--200. Amer. Math. Soc., Providence, RI,
2006.
http://dx.doi.org/10.1090/conm/421/08037
A. D. Myasnikov and R. M. Haralick.
A hybrid search algorithm for the Whitehead minimization problem.
J. Symbolic Comput., 41 (2006)(7) 818--834.
http://dx.doi.org/10.1016/j.jsc.2006.04.001
Alexei Myasnikov, Vladimir Shpilrain and Alexander Ushakov.
Random subgroups of braid groups: an approach to cryptanalysis of a braid group
based cryptographic protocol.
In Public key cryptography---PKC 2006, vol. 3958 of Lecture Notes in
Comput. Sci., 302--314. Springer, Berlin, 2006.
http://dx.doi.org/10.1007/11745853_20
Vladimir Shpilrain.
Hashing with polynomials.
In Information security and cryptology---ICISC 2006, vol. 4296 of
Lecture Notes in Comput. Sci., 22--28. Springer, Berlin, 2006.
http://dx.doi.org/10.1007/11927587_4
Vladimir Shpilrain and Alexander Ushakov.
The conjugacy search problem in public key cryptography: unnecessary and
insufficient.
Appl. Algebra Engrg. Comm. Comput., 17 (2006)(3-4) 285--289.
http://dx.doi.org/10.1007/s00200-006-0009-6
Vladimir Shpilrain and Alexander Ushakov.
A new key exchange protocol based on the decomposition problem.
In Algebraic methods in cryptography, vol. 418 of Contemp. Math.,
161--167. Amer. Math. Soc., Providence, RI, 2006.
http://dx.doi.org/10.1090/conm/418/07954
Vladimir Shpilrain and Gabriel Zapata.
Combinatorial group theory and public key cryptography.
Appl. Algebra Engrg. Comm. Comput., 17 (2006)(3-4) 291--302.
http://dx.doi.org/10.1007/s00200-006-0006-9
Vladimir Shpilrain and Gabriel Zapata.
Using the subgroup membership search problem in public key cryptography.
In Algebraic methods in cryptography, vol. 418 of Contemp. Math.,
169--178. Amer. Math. Soc., Providence, RI, 2006.
http://dx.doi.org/10.1090/conm/418/07955
2005
Ilya Kapovich and Paul Schupp.
Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for
one-relator groups.
Math. Ann., 331 (2005)(1) 1--19.
http://dx.doi.org/10.1007/s00208-004-0570-x
Alexei Myasnikov, Vladimir Shpilrain and Alexander Ushakov.
A practical attack on a braid group based cryptographic protocol.
In Advances in cryptology---CRYPTO 2005, vol. 3621 of Lecture Notes
in Comput. Sci., 86--96. Springer, Berlin, 2005.
http://dx.doi.org/10.1007/11535218_6
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