Scientific Papers

M. Kreuzer und F. Walsh, Computing the binomial part of a polynomial ideal, J. Symbolic Comput. 124 (2024), DOI:10.1016/j.jsc.2024.102298

S. Pircher, J. Geier, J. Danner, D. Mueller-Gritschneder, A. Wachter-Zeh, Key-recovery fault injection attack on the classic McEliece KEM, in: J. C. Deneuville (ed.), Code-Based Cryptography, Proc. Conf. CBCrypto 2022, LNCS 13839, Springer Int. Publ., Cham 2023, pp. 37-61, DOI:10.1007/978-3-031-29689-5_3

M. Kreuzer, Tran N.K. Linh und Le N. Long, Differential theory of zero-dimensional schemes, Preprint 2023, 32 Seiten, verfügbar unter arXiv:2302.11903 [math.AC]

M. Kreuzer, Le N. Long und L. Robbiano, Re-embeddings of affine algebras via Gröbner fans of linear ideals, Preprint 2023, 21 Seiten, verfügbar unter arXiv:2306.08481 [math.AC]

Le N. Long, The Kähler different of a 0-dimensional scheme, J. Algebra Appl. (2023), 26 Seiten, DOI:10.1142/S0219498824500567

M. Kreuzer, A. Miasnikov und F. Walsh, Decomposing finite Z-algebras, Preprint 2023, 31 Seiten, verfügbar unter arXiv:2308.01735[math.RA]

M. Kreuzer und F. Walsh, Efficient Algorithms for finite Z-algebras, Preprint 2023, 19 Seiten, verfügbar unter arXiv:2308.02610[math.AC]

M. Kreuzer, L.N. Long und L. Robbiano, Algorithms for checking zero-dimensional complete intersections, J. Commut. Algebra 14 (2022), S. 61-76, DOI:10.1216/jca.2022.14.61

F. A. Khalafbadam, S. Rahmany, M. Kreuzer und A. Basiri, An algorithm for calculating the order ideals of points and their applications to biological models, J. Adv. Math. Modelling 12 (2022), S. 304-315, DOI:10.22055/jamm.2022.40218.2017

M. Kreuzer, L.N. Long und L. Robbiano, Cotangent spaces and separating re-embeddings, J. Algebra Appl. 21 (2022), DOI:10.1142/S0219498822501882

M. Kreuzer, L.N. Long und L. Robbiano, Restricted Gröbner fans and re-embeddings of affine algebras, São Paulo J. Math. Sci. (2022), 26 Seiten, verfügbar online, DOI:10.1007/s40863-022-00324-w

M. Kreuzer, L.N. Long und L. Robbiano, Optimal re-embeddings of border basis schemes, 49 Seiten, verfügbar unter arXiv:2207.08115[math.AG]

Tran N.K. Linh und Le N. Long, The Dedekind different for a uniform set of points in Pn, Hue University Journal of Science: Natural Science 131 (1B) (2022), S. 81-91, DOI:10.26459/hueunijns.v131i1B.6563

Tran N.K. Linh und Le N. Long, Kähler differential modules and configurations of points in P2, Dalat University Journal of Science 12 (2022), S. 48-60, DOI:10.37569/DalatUniversity.12.2.887(2022)

Nguyen T. Hoa, Tran N.K. Linh, Le N. Long, Phan T.T. Nhan und Nguyen T.P. Nhi, The Kähler different of a set of points in Pm × Pn, Bull. Korean Math. Soc. 59 (2022), S. 929-949, DOI:10.4134/BKMS.b210544

M. Kreuzer, Tran N. K. Linh und Le N. Long, Hilbert polynomials of Kähler differential modules for fat point schemes, Acta Math. Vietnam. 46 (2021), S. 441-455, DOI:10.1007/s40306-021-00432-3

B. Fine, M. Kreuzer und G. Rosenberger, Further potential applications of group theory in information security, Int. J. Comput. Math. Comput. Syst. Theory 6 (2021), S. 375-380, DOI:10.1080/23799927.2021.1931455

E. Guardo, M. Kreuzer, Tran N. K. Linh und Le N. Long, Kähler differentials for fat point schemes in P^1 x P^1, J. Commut. Algebra 13 (2021), S. 179-207, DOI:10.1216/jca.2021.13.179

J. Danner und M. Kreuzer, A fault attack on the family of Enocoro stream ciphers, Cryptography 5 (2021), DOI:10.3390/cryptography5040026

J. Danner und M. Kreuzer, A fault attack on KCipher-2, Int. J. Comput. Math. Comput. Syst. Theory 6 (2021), S. 291-312, DOI:10.1080/23799927.2020.1854863

B. Fine, A. Gaglione, M. Kreuzer, G. Rosenberger und D. Spellman, The axiomatics of free group rings, J. Groups, Complexity, Cryptology 13 (2021),
DOI:10.46298/jgcc.2021.13.2.8796

M. Kreuzer, B. Sipal und Le N. Long, On the regularity of the monomial point of a border basis scheme, Beitr. Algebra Geom. 61 (2020), S. 515-532 DOI:10.1007/s13366-019-00482-7

M. Kreuzer und X. Xiu, Non-commutative Gebauer-Möller criteria, in: P. Baginski et al. (eds.), Elementary Theory of Groups and Group Rings, and Related Topics, de Gruyter, Berlin 2020, S. 149-175, DOI:10.1515/9783110638387-015

M. Kreuzer und G. Rosenberger, On the numbers of the form x² + 11y², in: P. Baginski et al. (eds.), Elementary Theory of Groups and Group Rings, and Related Topics, de Gruyter, Berlin 2020, S. 177-201, DOI:10.1515/9783110638387-016

A. Hashemi, M. Kreuzer und S. Pourkhajouei, Computing coupled border bases, Math. Comput. Sci. 14 (2020), S. 123-140, DOI:10.1007/s11786-020-00452-6

J. Horácek, M. Kreuzer und A. Messeng Ekossono, A signature based border basis algorithm, Math. Comput. Sci. 14 (2020), S. 177-189, DOI:10.1007/s11786-020-00459-z

J. Danner und M. Kreuzer, A fault attack on the Niederreiter cryptosystem using binary irreducible Goppa codes, Journal of Groups, Complexity, Cryptology 12 (2020), S. 2:1-2:20, DOI:10.46298/jgcc.2020.12.1.6074

J. Horácek und M. Kreuzer, On conversions from CNF to ANF, J. Symbolic Comput. 100 (2020), S. 164-186, DOI:10.1016/j.jsc.2019.07.023

M. Kreuzer, Tran N.K. Linh, Le N. Long und Nguyen C. Tu, An application of liaison theory to zero-dimensional schemes, Taiwanese J. Math. 24 (2020), S. 553-573, DOI:10.11650/tjm/190710

M. Kreuzer und D. Patil, Computational aspects of Burnside rings, part II: Important maps, Beitr. Algebra Geom. 62 (2020), S. 475-494, DOI:10.1007/s13366-020-00520-9

M. Kreuzer, Le N. Long und L. Robbiano, Computing subschemes of the border basis scheme, Int. J. Algebra Comput., 30 (2020), S. 1671 - 1716, DOI:10.1142/S0218196720500599

A. Hashemi, M. Kreuzer und S. Pourkhajouei, Computing all border bases for ideals of points, J. Algebra Appl. 18 (2019), DOI:10.1142/S0219498819501020

M. Kreuzer, Le Ngoc Long und L. Robbiano, On the Cayley-Bacharach property, Comm. Algebra 47 (2019), S. 328-354, DOI:10.1080/00927872.2018.1476525

M. Kreuzer, Tran N.K. Linh und Le N. Long, The Dedekind different of a Cayley-Bacharach scheme, J. Algebra Appl. 18 (2019), DOI:10.1142/S0219498819500270

M. Kreuzer, N. Elhamawy, M. Gay, A.-S. Messeng Ekossono und I. Polian, Fault attacks on the elliptic curve ElGamal cryptosystem, Preprint 7/2019, 9 Seiten <pdf-Datei>

M. Kreuzer, N. Elhamawy, M. Gay, A.-S. Messeng Ekossono und I. Polian, Fault attacks on ElGamal-type cryptosystems, Preprint 12/2019, 23 Seiten <pdf-Datei>

M. Kreuzer, Tran N.K. Linh und Le Ngoc Long, Kähler differential algebras for 0-dimensional schemes, J. Algebra 501 (2018), S. 255-284, DOI:10.1016/j.jalgebra.2017.12.023

J. Horácek und M. Kreuzer, 3BA: A border basis solver with a SAT extension, in: J.H. Davenport et al. (Eds.), Mathematical Software -- ICMS 2018, LNCS 10931, Springer Int. Publ., Basel 2018, S. 209-217, DOI:10.1007/978-3-319-96418-8_25
J. Horácek und M. Kreuzer, Refutation of products of linear polynomials, in: Proc. Third Int. Workshop on Satisfiability Checking and Symbolic Computation (SC^2), Oxford 2018, verfügbar unter http://ceur-ws.org/Vol-2189/

M. Kreuzer und Le Ngoc Long, Characterizations of zero-dimensional complete intersections, Beitr. Algebra Geom. 58 (2017), S. 93-129,
DOI:10.1007/s13366-016-0311-9
M. Kreuzer und Dilip P. Patil, Computational aspects of Burnside rings, Part I: The ring structure, Beitr. Algebra Geom. Volume 58 (2017), S. 427-452,
DOI:10.1007/s13366-016-0324-4
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. <pdf-file>
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, S. 147-162, DOI:10.1007/978-3-319-72453-9_11

J. Horácek, M. Kreuzer und A.-S. Messeng Ekossono, Computing Boolean border bases, Proc. SC2 2016 - International Workshop on Satisfiability Checking and Symbolic Computation, Timisoara 2016, DOI:10.1109/SYNASC.2016.076
J. Burchard, M. Gay, J. Horácek, A.-S. Messeng Ekossono, T. Schubert, B. Becker, I. Polian und M. Kreuzer, Small scale AES toolbox: Algebraic and propositional formulas, circuit-implementations and fault equations, Proc. Conf. TRUDEVICE 2016, Barcelona, verfügbar unter upcommons.upc.edu/handle/2117/99210

B. Fine, M. Kreuzer und G. Rosenberger, Free Polynomial Algebras and Magnus's Freiheitssatz, Int. J. Group Theory 4 (2015), 13-19, DOI:10.22108/ijgt.2015.7279

M. Kreuzer, Tran N.K. Linh und Le N. Long, Kähler differentials and Kähler differents for fat point schemes, J. Pure Appl. Algebra 219 (2015), 4479-4509, DOI:10.1016/j.jpaa.2015.02.028

M. Kreuzer, J. Limbeck and H. Poulisse, Rational approximation of border bases, preprint 2014
M. Kreuzer and X. Xiu, Non-commutative Gebauer-Möller criteria, 20 p., preprint 2014
M. Kreuzer and M. Kriegl, Gröbner bases for syzygy modules of border bases, J. Algebra Appl. 13 (2014), 145003 (32 pages)
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
F. Kiraly, M. Kreuzer and L. Theran, Dual-to-Kernel Learning with Ideals, preprint 2014 (9 pages)

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, Springer Verlag, Heidelberg 2013, 15 p. (to appear)
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
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
B. Fine, M. Kreuzer and G. Rosenberger, Free Polynomial Algebras and Magnus's Freiheitssatz, 8 p., preprint 2013

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]

Chair of Symbolic Computation