Lehrstuhl für Mathematik mit Schwerpunkt Symbolic Computation
Wissenschaftliche Arbeiten

Wissenschaftliche Arbeiten

Wichtige Anmerkung

Bei den *.dvi/*.pdf Dateien der folgenden Arbeiten handelt es sich um die unveröffentlichten Vorabversionen. Für die Endversionen wird jeweils auf die gedruckten Exemplare verwiesen.


  • M. Kreuzer, Le Ngoc Long, Characterizations of zero-dimensional complete intersections, Beitr. Algebra Geom. Volume 58, Issue 1, pp 93-129,
    DOI: 10.1007/s13366-016-0311-9

  • M. Kreuzer and Dilip P. Patil, Computational aspects of Burnside rings, Part I: The ring structure, Beitr. Algebra Geom. Volume 58, Issue 3, pp 427-452,
    DOI 10.1007/s13366-016-0324-4

  • M. Kreuzer, Tran N.K. Linh und Le Ngoc Long, Kähler differential algebras for 0-dimensional schemes, J. Algebra (erscheint), verfügbar unter arXiv:1704.02111

  • M. Kreuzer, Tran N.K. Linh und Le Ngoc Long, On the Dedekind different of a Cayley-Bacharach scheme, preprint 2017, verfügbar unter arXiv:1704.03702

  • A. Hashemi, M. Kreuzer und S. Pourkhajouei, Computing all border bases for ideals of points, preprint 2017, verfügbar unter arXiv:1707.02076

  • J. Horácek und M. Kreuzer, On conversions from CNF to ANF, Proc. 2nd Int. Workshop on Satisfiability Checking and Symbolic Computation (SC^2), Kaiserslautern 2017, verfügbar unter ceur-ws.org/Vol-1974/RP1.pdf

  • J. Burchard, M. Gay, A.S. Messeng Ekossono, J. Horácek, B. Becker, T. Schubert, M. Kreuzer und I. Polian: AutoFault: towards automatic construction of algebraic fault attacks. In: Proceedings of Conference on Fault Diagnosis and Tolerance in Cryptography (FDTC 2017), Tapei (2017), IEEE Xplore, verfügbar unter ieeexplore.ieee.org/document/8167712

  • J. Burchard, A.S. Messeng Ekossono, J. Horácek, M. Gay, B. Becker, T. Schubert, M. Kreuzer und I. Polian, Towards mixed structual-functional models for algebraic fault attacks on ciphers, in: IEEE 2nd Int. Verification and Security Workshop (IVSW 2017), Thessaloniki, 2017, IEEE Xplore, verfügbar unter ieeexplore.ieee.org/document/8031537

  • J. Horácek, M. Kreuzer und A.S. Messeng Ekossono, A signature based border basis algorithm, in: Conf. on Algebraic Informatics (CAI), Kalamata, 2017.

  • J. Horácek, J. Burchard, B. Becker und M. Kreuzer, Integrating algebraic and SAT solvers, in: J. Blömer et al (Eds.), Int. Conf. on Math. Aspects of Computer and Inf. Sciences (MACIS 2017), LNCS 10693, Springer Int. Publ., Cham 2017, pp. 147-162.

  • M. Kreuzer, Le Ngoc Long und L. Robbiano, On the Cayley-Bacharach property, preprint 2017.


  • J. Horacek, M. Kreuzer and A.-S. Messeng Ekossono, Computing Boolean border bases, Proc. SC2 2016 - International Workshop on Satisfiability Checking and Symbolic Computation, Timisoara 2016, verfügbar unter
    DOI: 10.1109/SYNASC.2016.076

  • J. Burchard, M. Gay, J. Horacek, A.-S. Messeng Ekossono, T. Schubert, B. Becker, I. Polian and M. Kreuzer, Small scale AES toolbox: Algebraic and propositional formulas, circuit-implementations and fault equations, Proc. Conf. TRUDEVICE 2016, Barcelona.

  • E. Guardo, M. Kreuzer, Tran N.K. Linh und Le Ngoc Long, Kähler differentials for fat point schemes in P^1 x P^1, preprint 2016, verfügbar unter arXiv:1611.09851


  • B. Fine, M. Kreuzer and G. Rosenberger, Free Polynomial Algebras and Magnus's Freiheitssatz, Int. J. Group Theory 4 (2015), pp. 13-19
  • M. Kreuzer, Tran N.K. Linh and Le N. Long, Kähler differentials and Kähler differents for fat point schemes, J. Pure Appl. Algebra (2015), Vol. 219, Issue 10, pp. 4479-4509


  • M. Kreuzer and G. Rosenberger, Growth in Hecke groups, in: M. Izquierdo (ed.), Riemann and Klein Surfaces, Symmetries and Moduli Spaces, Contemp. Math. 629 (2014), pp. 261-281
  • M. Kreuzer, A.D. Myasnikov and A. Ushakov, A linear algebra attack to group-ring-based key exchange protocols, in: I. Boureanu, P. Owesarski and S. Vandenay (eds.), Proc. Conf. ACNS 2014, LNCS 8475, Springer Verlag 2014, pp. 37-43
  • B. Fine, M. Kreuzer and G. Rosenberger, Faithful real representations of cyclically pinched one-relator groups, Int. J. Group Theory 3 (2014), pp. 1-8
  • F. Kiraly, M. Kreuzer and L. Theran, Dual-to-Kernel Learning with Ideals, Preprint 2014 (9 pages), verfügbar unter: arXiv:1402.0099
  • F. Kiraly, M. Kreuzer and L. Theran, Learning with Cross-Kernels and Ideal PCA, Preprint 2014, verfügbar unter: arXiv:1406.2646
  • M. Kreuzer and X. Xiu, Non-commutative Gebauer-Möller criteria, 20 p., Preprint 2014, verfügbar unter: arXiv:1302.3805
  • M. Kreuzer, J. Limbeck and H. Poulisse, Rational approximation of border bases, Preprint 2014


  • M. Beck, H. de Meer, M. Kreuzer and S. Schuster, Estimating photo-voltaic power supply without smart metering infrastructure, in: S. Klingert, X. Hesselbach-Serra, M. Perez Ortega and G. Guliani, Energy Efficient Data Centers: Second Int. Workshop E2DC 2013, LNCS 8343, Springer Verlag, Heidelberg 2013,  pp. 25-39

  • I. Polian and M. Kreuzer, Fault-based attacks on cryptographic hardware, in: Design and Diagnostics of Electronic Circuits & Systems (DDECS), 2013 IEEE 16th International Symposium in Karlyovy Vary, IEEE Xplore, Piscataway, 2013, pp. 12-17,  DOI: 10.1109/DDECS.2013.6549781

  • P. Jovanovic, M. Kreuzer and I. Polian, Multi-stage fault attacks, in: 14th Workshop on RTL and High Level Testing (WRTLT '13), Jiaosi/Taiwan 2013, IEEE Computer Society, 2013

  • A.V. Geramita and M. Kreuzer, On the uniformity of zero-dimensional complete intersections, J. Algebra 391 (2013), pp. 82-92


  • P. Jovanovic, M, Kreuzer and I. Polian, A fault attack on the LED Block Cipher, in: W. Schindler and A. Huss (eds.), Constructive Side-Channel Analysis and Secure Design (COSADE 2012), LNCS 7275, Springer Verlag, Heidelberg 2012, pp. 120-134

  • R. Ali and M. Kreuzer, Weyl Gröbner Basis crypto systems, in: B. Fine, D. Kahrobaei and G. Rosenberger (eds.), Computational and Combinatorial Group Theory and Cryptosystems, Contemp. Math. 582, Amer. Math. Soc., Providence 2012


  • C. Baciu und M. Kreuzer, Algebraisches Erdöl, Mitteilungen der DMV 19 (2011), pp. 142-147
  • M. Kreuzer, La matematica degli scacchi, in: C. Bartocci and P.Odifreddi (eds.), La Matematica, Vol. 3: Snoni, forme, parole, G. Einaudi Editore, Torino 2011, pp. 535-572

  • M. Kreuzer and H. Poulisse, Subideal border bases, Math. Comp. 80 (2011), pp. 1135-1154

  • M. Kreuzer, L. Robbiano, The geometry of border bases, Journal of Pure and Applied Algebra 215 (2011), pp. 2005-2018


  • P. Jovanovic, M. Kreuzer, Algebraic Attacks using SAT-solvers, Groups - Complexity - Cryptology 2 (2010), 247-259


  • M. Kreuzer, Algebraic attacks galore!, Groups - Complexity - Cryptology 1 (2009), 231-259

  • M. Kreuzer, H. Poulisse and L. Robbiano, From oil fields to Hilbert schemes, in: J. Abbott and L. Robbiano (eds.), Approximate Commutative Algebra, Springer, Vienna 2009, pp. 1-54

  • D. Heldt, M. Kreuzer, S. Pokutta and H. Poulisse, Approximate computation of zero-dimensional polynomial ideals, J. Symb. Comput. 44 (2009), pp. 1566-1591


  • M. Kreuzer and L. Robbiano, Deformations of Border Bases, Coll. Math. 59 (2008), pp. 275-297


  • M. Kreuzer, Computing Hilbert-Kunz functions of 1-dimensional graded rings, Univ. Iagellonicae Acta Math. 45 (2007), pp. 81-95
  • H. Bluhm and M. Kreuzer, Computation of two-sided syzygies over non-commutative rings, Contemp. Math. 421 (2007), S. 45-64 < pdf-file>

  • M. Kreuzer, A. Myasnikov, G. Rosenberger and A. Ushakov, Quotient tests and Gröbner bases, Contemp. Math. 421 (2007), S. 187-200  < pdf-file>  < dvi-file>


  • P. Ackermann and M. Kreuzer, Gröbner basis cryptosystems, Appl. Alg. in Eng., Comm. and Comp. 17 (2006), S. 173-194   [MR 2233780; Zbl pre05067384] < pdf-file>  < dvi-file>
  • A. Kehrein and M. Kreuzer, Computing border bases, J. Pure Appl. Alg. 205 (2006), S. 279-295   [MR 2006k:13058; Zbl 1097.13036]   < pdf-file>  < dvi-file>

  • D. Heldt, M. Kreuzer, S. Pokutta and H. Poulisse, Algebraische Modellierung mit Methoden der approximativen Computeralgebra und Anwendungen in der Ölindustrie, OR News 28 (2006), S. 15-18    <pdf-file> 


  • M. Kreuzer and L. Robbiano, Idealization of modules in computer algebra, in: S. Cojocaru, G. Pfister, und V. Ufnarovski (Hrsg.), Computational Non-Commutative and Commutative Algebraic Geometry, Proc. Conf. Chisinau 2004, NATO Science Series III, IOS Press, Amsterdam 2005, S. 226-243   [MR 2006g:13053]   < pdf-file>  < dvi-file>
  • A. Kehrein and M. Kreuzer, Characterizations of border bases, J. Pure Appl. Alg. 196 (2005), S. 251-270   [MR 2006e:13037; Zbl 1081.13011]   < pdf-file>  < dvi-file>

  • J. Abbott, M. Kreuzer and L. Robbiano, Computing zero-dimensional schemes, J. Symb. Comp. 39 (2005), S. 31-49   [MR 2006g:13050]   < pdf-file>  <dvi-file>
  • A. Kehrein, M. Kreuzer and L. Robbiano, An algebraist's view on border bases, in: A. Dickenstein and I. Emiris (Hrsg.), Solving Polynomial Equations: Foundations, Algorithms, and Applications, Proc. CIMPA School (Buenos Aires 2003), Springer Verlag, Heidelberg 2005, S. 169-202   [MR 2161988]   < ps-file>


  •  M. Caboara, M. Kreuzer and L. Robbiano, Efficiently computing minimal sets of critical pairs, J. Symb. Comp. 38 (2004), S. 1169-1190   [MR 2005g:13045]   < pdf-file>  < dvi-file>


  • M. Kreuzer and L. Robbiano, Basic tools for computing in multigraded rings, in: J. Herzog, V. Vuletescu (Hrsg.), Commutative Algebra, Singularities, an Computer Algebra, Proc. Conf. Sinaia 2002, NATO Science Series II, Kluwer Acad. Publ., Dordrecht 2003, S. 197-216   [MR 2005f:13034; Zbl 1048.13019]   < ps-file>


  • M. Caboara, M. Kreuzer and L. Robbiano, Minimal sets of critical pairs, in: A. Cohen, X. Gao und N. Takayama (Hrsg.), Mathematical Software, Proceedings of the First Int. Congress on Math. Software (Beijing 2002), World Scientific, Singapore 2002, S. 390-404   [MR 2003d:00014; Zbl 1057.68136]   <dvi-file>


  • M. Kreuzer, Algorithms for checking uniformity conditions and applications in coding theory, in: A.V. Geramita (ed.), Proceedings of the workshop ``Zero-Dimensional Schemes and Applications'', Naples 2000, Queen's Papers in Pure and Appl. Math. 123, Queen's University, Kingston 2001, S. C1-C9   [MR 2003c:14053: Zbl 1060.14069]   <dvi-file>


  • J. Abbott, A. Bigatti, M. Kreuzer and L. Robbiano, Computing ideals of points, J. Symb. Comp. 30 (2000), S. 341-356   [MR 2001j:13026; Zbl. 977.13011]   <dvi-file>

  • M. Kreuzer, J.C. Migliore, U. Nagel and C. Peterson, Determinantal schemes and Buchsbaum-Rim sheaves, J. Pure Appl. Alg. 150 (2000), S. 155-174   [MR 2001f:14092; Zbl. 999.14014]   <dvi-file>
  • M. Kreuzer, On the canonical ideal of a set of points, Boll. Un. Mat. Ital. (8) 1-B (2000), S. 221-261   [MR 2001g:13026; Zbl. 2001g:13026]   <dvi-file>


  • G. de Dominicis and M. Kreuzer, Kähler differentials for points in P^n, J. Pure Appl. Alg. 141 (1999), 153-173   <dvi-file>   [MR: 2000f:13050; Zbl 943.13019]


  • B. Kreuzer and M. Kreuzer, Extremal zerodimensional subschemes of P^2, J. Pure Appl. Alg. 131 (1998), 159-177   [MR 99g:14061; ZBl 987.14032]   <dvi-file>


  • M. Kreuzer and R. Waldi, On the Castelnuovo-Mumford regularity of a projective system,  Comm. Algebra 25 (1997) , S. 2919-2929   [MR 98e:13016; Zbl 883.13014]  <dvi-file>


  • S. Beck and M. Kreuzer, How to compute the canonical module of a set of points, in: L. Gonzales-Vega und T. Recio (Hrsg.), Algorithms in Algebraic Geometry and Applications, Proc. Conf. MEGA '94, Santander 1994, Progress in Math. 143, Birkhäuser Verlag, Basel 1996, pp. 51-78   [MR 97g:13044; Zbl 894.13003]  <dvi-file>


  • M. Kreuzer and L. Robbiano, On maximal Cayley-Bacharach schemes, Comm. Algebra 23 (1995),  S. 3357-3378   [MR 96g:14008; Zbl 849.14017]    <dvi-file>


  • M. Kreuzer, Some applications of the canonical module of a 0-dimensional scheme, in: F. Orecchia and L. Chiantini (Hrsg.), Zero-Dimensional Schemes, Proc. Conf. Ravello 1992, de Gruyter, Berlin 1994, S. 243-252  [MR 95h:14008; Zbl 826.14031]    <dvi-file>
  • M. Kreuzer, On the canonical module of a 0-dimensional scheme, Can. J. Math. 46 (1994), S. 357-379   [MR 95d:13021; Zbl 826.14030] <dvi-file>


  • A.V. Geramita, M. Kreuzer and L. Robbiano, Cayley-Bacharach schemes and their canonical modules, Trans. Amer. Math. Soc. 339 (1993), S. 163-189   [MR 93k:14065; Zbl 793.14002]  <dvi-file>
  • M. Kreuzer, Vector bundles with good sections, Comm. Algebra 21 (1993), S. 1043-1062   [MR 94d:14018; Zbl 781.14005]   <dvi-file>


  • M. Kreuzer, On 0-dimensional complete intersections, Math. Ann. 292 (1992), S. 43 - 58   [MR 92m:14064; Zbl 741.14030]  <dvi-file>


  • M. Kreuzer, An introduction to a theorem of Strano, in: The Curves Seminar at Queen's, Vol. VIII, Queen's Papers in Pure and Appl. Math. 88, Queen's University, Kingston 1991, S. C1-C23   [MR 93d:14074; Zbl 754.14017]   <dvi-file>


  • M. Kreuzer and E. Kunz, Traces in strict Frobenius algebras and strict complete intersections, J. Reine Angew. Math. 381 (1987), S. 181-204   [MR 89c:14022; Zbl 626.13009]