Curriculum Vitae

Arkadius Georg KalkaSeveringstr. 144328 Dortmund, Germany

E-mail: Arkadius.Kalka@rub.de

Homepage: http://homepage.ruhr-uni-bochum.de/arkadius.kalka/

Academic studies, grants and positions (in reverse order)

• October 2015 - February 2016: Guest at the Bar-Ilan University in Ra-mat Gan. Hosts: Prof. Mina Teicher, Prof. Boaz Tsaban. Also: Localcoordinator for the mathematical exhibition IMAGINARY in Bar-Ilan.

• 22. April 2013 - 30. September 2015: Postdoctoral Researcher at theBar-Ilan University in Ramat Gan. Supervisors: Prof. Mina Teicher,Prof. Boaz Tsaban.

• April 2012-March 2013: Postdoctoral Research Fellow in the School ofMathematics & Physics at The University of Queensland in Brisbane,Australia.

• January 2012-March 2012: Guest at Max-Planck-Institut für Mathe-matik, Bonn, Germany.

• October 2010-December 2011: Researcher at the Bar-Ilan University inRamat Gan. Supervisors: Prof. Mina Teicher, Dr. Boaz Tsaban. (Onleave: October 2010-February 2011)

• October 2007-September 2010: Postdoctoral Research Fellow at theBar-Ilan University in Ramat Gan. Supervisors: Prof. Mina Teicher,Dr. Boaz Tsaban.

• July 6, 2007: Doctoral examination (Magna cum laude), PhD thesis:Representations of braid groups and braid-based cryptography (submit-ted: May 9th 2007), Advisor: Prof. Lothar Gerritzen.

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• June 2003-July 2006: Graduate assistant, Faculty of Mathematics,Ruhr-University Bochum.

• June 2003-May 2006: Scholarship of the Graduate College Methods ofMathematics and Engineering for Secure Data Transmision and Infor-mation Transfer, Speaker: Prof. G. Frey.

• March 28, 2003: Diplom-Mathematiker (Master), Grade: sehr gut (A).Diploma thesis: Zopfgruppen und kryptographische Anwendungen (braidgroups and cryptographic applications), Advisor: Prof. L. Gerritzen.

• November 2002: Studienabschlussstipendium (grant) of the Ruth undGert-Massenberg Stiftung.

• After studies in physics (University Dortmund) and a perennial break,October 2000-March 2003: Studies in mathematics, Ruhr-UniversityBochum.

Fields of researchBraid groups, Garside groups, public key cryptography, complexity theory, ef-�cient algorithms, combinatorial group theory, Artin groups, Coxeter groups,knots, selfdistributive systems.

Further interestsQuantum computation, combinatorics, normal surface theory, 3-manifolds.

Published work, preprints and works in progress

• Arkadius Kalka, Representation attacks on the braid Di�e-Hellmanpublic key encryption, Applicable Algebra in Engineering, Communi-cation and Computing 17 (2006), 257-266.http://www.springerlink.com/content/87245vg6725n8322/

• Arkadius Kalka, Representations of braid groups and braid-based cryp-tography, PhD thesis, submitted: May 9th 2007. Doctoral examination:July 6th 2007 (Magna cum laude). Advisor: Prof. L. Gerritzen.www-brs.ub.ruhr-uni-bochum.de/netahtml/HSS/Diss/KalkaArkadiusG/

• Arkadius Kalka, Mina Teicher, and Boaz Tsaban, Short expressionsof permutations as products and cryptanalysis of the Algebraic Eraser,Advances in Applied Mathematics, Volume 49, issue 1 (July, 2012), p.57-76.Preprint: arxiv.org/abs/0804.0629.

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• Arkadius Kalka, Improved linear time inversion heuristic for the Buraurepresentation, preprint (2008)http://homepage.ruhr-uni-bochum.de/arkadius.kalka/

CompPreimBrShortVersionUsePackageAlg.tex.pdf, to be changed,extended and re-submitted.

• Arkadius Kalka, Eran Liberman, and Mina Teicher, A note on theshifted conjugacy problem in braid groups, Groups � Complexity � Cryp-tology, Volume 1, no. 2 (2009), 227-230.

• Arkadius Kalka, Eran Liberman, and Mina Teicher, Solution to thesubgroup conjugacy problem for Garside subgroups of Garside groups,Groups � Complexity � Cryptology, Volume 2, no. 2 (2010), 157-174.

• Joel Hass, Arkadius Kalka, and Tahl Nowik, Complexity of relations inthe braid group, preprint: arXiv.org/abs/0906.0137

• Arkadius Kalka, Non-associative public-key cryptography,preprint http://arxiv.org/abs/1210.8270, submitted.

• Arkadius Kalka and Mina Teicher, Non-associative key establishmentfor left distributive systems,Groups � Complexity � Cryptology, Volume 5, no. 2 (2013), 169-191.Preprint http://arxiv.org/abs/1305.4401.

• Murray Elder and Arkadius Kalka, Logspace-computations for rigidGarside groups,preprint http://arxiv.org/abs/1310.0933v2, extended version of thefollowing paper.

• Murray Elder and Arkadius Kalka, Logspace-computations for Garsidegroups of spindle type,preprint http://arxiv.org/abs/1310.0933.

• David Garber, Arkadius Kalka, Eran Liberman, Boaz Tsaban and MinaTeicher, Double centralizers for parabolic subgroups of braid groups, sub-mitted,preprint http://arxiv.org/abs/1310.0936.

• Arkadius Kalka and Mina Teicher, Iterated LD-Problem in public-keycryptography, submitted to GCC,preprint http://arxiv.org/abs/1312.6791.

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• Arkadius Kalka and Mina Teicher, Non-associative key establishmentprotocols and their implementation, submitted,preprint http://arxiv.org/abs/1312.6794.

• Arkadius Kalka, Boaz Tsaban and Gary Vinokur, Complete simultane-ous conjugacy invariants in Garside groups,preprint http://arxiv.org/abs/1403.4622.

• Arkadius Kalka, Mina Teicher and Boaz Tsaban, On the Double CosetProblem for parabolic subgroups in braid groups,preprint http://arxiv.org/abs/1402.5541.

• Ben Burton, Murray Elder, Arkadius Kalka and Stephan Tillmann, 2-manifold recognition is in logspace,preprint http://arxiv.org/abs/1412.1188.

• Adi Ben-Zvi, Arkadius Kalka and Boaz Tsaban, Cryptanalysis via al-gebraic spans,preprint https://eprint.iacr.org/2014/041.

• Arkadius Kalka, Power commutator groups, preprint http://arxiv.org/abs/1510.02286.

• Arkadius Kalka, Mina Teicher, and Boaz Tsaban, Approximating short-est braid words is Co-NP-complete, work in progress.

• Arkadius Kalka, On the diameter of the Tits graph of the longest ele-ment in A, B, and D-type Coxeter groups, work in progress.

• Other work in progress.

RefereeingI have refereed or am refereeing papers for the following journals or conferenceproceedings:

• Applicable Algebra in Engineering, Communication and Computing.(4 papers)

• Contemporary Mathematics.

• Groups � Complexity � Cryptology. (3 papers)

• Proceedings of the Conference Combinatorial and Geometric GroupTheory with Applications, University of Dortmund (Germany), August27-31, 2007.

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• International Journal of Algebra and Computation (IJAC) (2 papers)

• Journal of the European Mathematical Society (JEMS).

• Journal of Symbolic Computation.

Visits

• August 16-20, 2010: Visiting Prof. Dror Bar Natan and his researchgroup, in particular Karene Chu, at University of Toronto.

• January 1, 2012 - March 31, 2012: Guest at Max-Planck-Institut fürMathematik, Bonn, Germany.

• May 21-25, 2012: Visiting Stephan Tillman and Murray Elder (fromNewcastle) for collaboration at University of Sydney.

• December 17-21 2013: Visiting Murray Elder (from Newcastle) for col-laboration in Melbourne.

Conference Talks (invited)

• Non-associative public key cryptography, Workshop on "Complexityand Group-based Cryptography", CRM (Centre de recherches mathe-matiques), CRM, Montreal, August 30-September 3, 2010.

• Introduction to Garside calculus, Workshop on knot theory, UniversityZürich and ETH, November 18-29, 2013.

• Simultaneous conjugacy and double coset problem in braid and Garsidegroups, Special session on Applications of Algebra in Cryptography,Second Joint Meeting of the AMS and the IMU, Israel, June 16-19,2014.

Conference Talks (contributed)

• Computing preimage braids for the Burau representation, Workshopon Algebraic Methods in Cryptography, University of Dortmund (Ger-many), March 11-12, 2004.

• Representation attacks in braid group cryptography, Workshop on Alge-braic Methods in Cryptography, Ruhr-University Bochum (Germany),November 17-18, 2005.

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• AAG-like key agreement scheme for magmas and shifted conjugacyin braid-based cryptography, Conference Combinatorial and GeometricGroup Theory with Applications, University of Dortmund (Germany),August 27-31, 2007.

• Improved linear time inversion heuristic for the Burau representation,Conference Braids in Paris, Paris, September 17-20, 2008.

• The shifted conjugacy decision problem in braid groups and its gener-alizations, Conference Geometric and Asymptotic Group Theory withApplications, Hoboken, NJ, March 9-12, 2009.

• Subgroup conjugacy problem for parabolic subgroups of the braid group,Workshop Braids in Pau, Pau (France), October 5-8, 2009.

• Subgroup conjugacy problem for Garside subgroups of Garside group,Conference Singularities, knots, and mapping class groups, in memoryof Bernard Perron, Dijon, September 6-9, 2010.

• Conjugacy in Braid Groups and related Problems, Workshop WinterBraids II, Caen (France), December 12-15, 2011

• Non-associative key establishment protocols and their implementation,emac13: 11th Engineering Mathematics and Applications Conference,Queensland University of Technology (QUT), December 1-4, 2013.

• On some Artin- and Coxeter-like groups, ConferenceGeometric, Asymp-totic and Combinatorial Group Theory and Applications (GAGTA-9),CIRM, Luminy (Marseille), September 14-18, 2015.

Further Conferences

• Workshop on Complexity-theoretical and Algebraic Methods in Cryp-tography, Ruhr-University Bochum, Germany, November 7-8, 2002.

• Joint meeting of AMS, DMV, ÖMG, Mainz, June 16-19, 2005.

• Conference on Representations of Algebras, Groups and Semigroups,Bar-Ilan University, Ramat Gan, December 30, 2007-January 3, 2008.

• HIRZ80, Bar-Ilan University, Ramat Gan, May 18-23, 2008.

• Workshop on Cryptology, Technion, Haifa, May 29, 2008.

• Compression and Combinatorial Algorithms (CCA), Haifa, July 8, 2008.

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• Israel CS Theory day, Raanana (Israel), March 2, 2009.

• Workshop Why Knot? The mathematics of knots, links and braids,Technion, Haifa, September 6-10, 2009.

• Workshop on Algebra and Geometry of Con�guration Spaces and relatedstructures, Centro di Ricerca Matematica Ennio De Giorgi, Pisa, June21-5, 2010.

• Workshop Topics in Algorithmic and Geometric Group and SemigroupTheory, CRM, Montreal, August 23-27, 2010.

• The Fourth Israel CS Theory Day, The Open University in Raanana(Israel), March 24, 2011.

• A Celebration Commemorating 20 Years of the Great Aliya of Immi-grant Scientists from the Former Soviet Union, Bar-Ilan University,Ramat Gan, June 14, 2011.

• The 2011 Meeting of the Israel Mathematical Union, Bar-Ilan Univer-sity, Ramat Gan, June 16, 2011.

• International Conference Trends and Perspectives in Mathematics, Tel-Aviv , November 14-15, 2011.

• International Conference on Geometric, Combinatorial and Dynamicsaspects of Semigroup and Group Theory, Bar-Ilan University, RamatGan (Israel), June 11-14, 2013.

• Summer School on Algebraic and Tropical Geometry, TU Kaiserslautern,Germany, September 7-11, 2015.

Further Presentations

• Presentation of research projects, Review of the Emmy Noether Min-erva Center, Golan meeting room, Hotel Dan Panorama, Tel Aviv, May20, 2011.

Talks in Seminars as postdoc

• Shifted conjugacy in braid-based cryptography and an AAG-like keyagreement scheme for magmas and LD-systems, ENI Seminar, Bar-IlanUniversity, November 21, 2007.

• Cryptanalysis of the Algebraic Eraser, CGC Seminar, Bar-Ilan Univer-sity, January 13, 2008.

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• Improved linear time inversion heuristic for the Burau representation,ENI Seminar, Bar-Ilan University, August 6+13, 2008.

• On the structure sheaf, Algebraic geometry study seminar, Bar-IlanUniversity, September 3, 2008.

• Introduction to the Braid group and cryptography, CGC Seminar, Bar-Ilan University, November 13+20+27, 2008.

• The shifted conjugacy decision problem in braid groups and its general-izations, ENI (joint with CGC) Seminar, Bar-Ilan University, January21, 2009.

• The subgroup conjugacy problem for Bm ≤ Bn, ENI (joint with CGC)Seminar, Bar-Ilan University, February 4, 2009.

• Complexity of relations in the braid group, Bar-Ilan Combinatorics Sem-inar, Bar-Ilan University, November 10, 2009.

• Gaussian and Garside monoids, CGC Seminar (informal meeting), Bar-Ilan University, April 26, 2010.

• Parabolic subgroups and Garside subgroups of a Garside group, ENI(joint with CGC) Seminar, Bar-Ilan University, April 28, 2010.

• The Subword reversing method and its applications, CGC seminar (in-formal meeting), Bar-Ilan University, May 17+31, 2010.

• Reidemeister distance of knot diagrams and complexity of relations inthe braid group, Mathematics Colloquium, University of Toronto, Au-gust 17, 2010.

• Garside subgroups of a Garside group and the subgroup conjugacy prob-lem, Knot Theory Seminar (informal meeting), University of Toronto,August 18, 2010.

• On the diameter of the Tits graph of the longest element in Coxetergroups of classical type, Bar-Ilan Combinatorics Seminar, Bar-Ilan Uni-versity, March 22, 2011.

• Tropical Cryptography, Joint CGC and ENI seminar, Bar-Ilan Univer-sity, April 27, 2011.

• Non-associative Cryptography, CGC colloquium, Bar-Ilan University,July 12, 2011.

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• Non-associative Cryptography II: Anshel-Anshel-Goldfeld KAP for multi-LD-systems, CGC seminar, Bar-Ilan University, July 13, 2011.

• Simultaneous Conjugacy Problem in Garside Groups, Joint ENI Semi-nar and CGC Colloquium, Bar-Ilan Uni, December 21, 2011.

• Conjugacy in Braid Groups and related Problems + Applications innon-commutative Cryptography, Algebra, Geometry and Physics Sem-inar, Max Planck Institute for Mathematics, Bonn, March 20, 2012.

• Conjugacy in braid groups and related problems, Pure Maths Seminar,School of Mathematics and Physics, University of Queensland (UQ),Brisbane, April 17, 2012.

• Conjugacy in braid groups and related problems, with cryptographic ap-plications, Group Actions Seminar, Department of Mathematics, Uni-versity of Sydney, May 22, 2012.

• Unknotting is in NP modulo Extended Riemann Hypothesis, Compu-tational Geometry and Topology Seminar, School of Mathematics andPhysics, University of Queensland (UQ), Brisbane, May 16, 2012.

• Introduction to Quantum Computation I, Computational Geometry andTopology Seminar, School of Mathematics and Physics, University ofQueensland (UQ), Brisbane, August 8, 2012.

• Introduction to Quantum Computation II: Shor's algorithm, Compu-tational Geometry and Topology Seminar, School of Mathematics andPhysics, University of Queensland (UQ), Brisbane, August 22, 2012.

• Graph connectivity in Logspace, Computational Geometry and Topol-ogy Seminar (joint with Sydney and Newcastle), School of Mathematicsand Physics, University of Queensland (UQ), Brisbane, September 14,2012.

• Secure information transmission based on physical principles, CGC col-loquium, Bar-Ilan University, March 6, 2014.

• Conjugacy, centralizers and double cosets in braid groups, Colloquiumin Mathematics and Computer Science, Holon Institute of Technology(HIT), Holon, March 23, 2014.

• Introduction to non-commutative and non-associative public-key cryp-tography, CGC colloquium, Bar-Ilan University, March 27, 2014.

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• No-leak authentication by the Sherlock Holmes method, CGC collo-quium, Bar-Ilan University, May 29, 2014.

Teaching (Mathematics) at Ruhr-Universität Bochum (RUB)

WS 03/04 150301 Seminar über Kryptographie(Seminar on Cryptography).

SS 2004 150103Übungen zu Höhere Mathematik für Ergänzungsstudiengänge(Teaching assistant: Higher mathematics).

WS 04/05 150101 Übungen zu Mathematik I für Maschinenbau-, Bauinge-nieure und UTRM(Teaching assistant: Mathematics I for engineers).150127 Übungen zu Kryptographie I(Teaching assistant: Cryptography I).

WS 05/06 150231 Übungen zu Diskrete Mathematik I(Teaching assistant: Discrete Mathematics I).

WS 06/07 150128 Tutorium: Mathematik für Naturwissenschaftler(Tutorial: Mathematics for scientists).

Lecture Series given at Bar-Ilan University (BIU)

• Introduction to Quantum Computing, Mini-course held inside the CGCColloquium (WS 2009/10).

• Coxeter groups (SS 2010).

Other professional activities

• I helped to organize the workshop on Algebraic Methods in Cryptogra-phy, Ruhr-University Bochum (Germany), November 17-18, 2005.In particular, I maintained the conference webpage:http://www.ruhr-uni-bochum.de/ffm/Lehrstuehle/Lehrstuhl-VI/Workshop05.htm

• Since 2009/10 until Dec 2011, and again March-May 2014, I co-organizedthe BIU Colloquium on Combinatorial Group theory and Cryptography(CGC).http://u.math.biu.ac.il/� kalkaa/CGCColloq.html

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• At BIU I informally co-supervised the Master thesis of Gary Vinokur(supervisors: Boaz Tsaban and David Garber).

• I also informally co-supervise the Master thesis of Adi Ben-Zvi (super-visor: Boaz Tsaban).

• In December 2015/ January 2016 I bring the mathematical exhibitionIMAGINARY from the Weizmann Institute to Bar-Ilan University.

• I am building the website for an upcoming German-Israeli workshop inJanuary 2016. Seehttp://homepage.ruhr-uni-bochum.de/arkadius.kalka/workshopJan2016/

Hobbies

• I play chess (International Master).

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