Publications

Kreuzer, M., Moldenhauer, A., & Rosenberger, G. (2026). SUBGROUPS OF CYCLICALLY AMALGAMATED FREE PRODUCTS. Groups, Complexity, Cryptology, 18(1), 11–115. https://doi.org/10.46298/jgcc.2026.18.1.17174

Andraschko, B., Kreuzer, M., & Long, L. N. (2025). Efficient Checking of Separating Indeterminates. Mathematics in Computer Science, 19(1). https://doi.org/10.1007/s11786-025-00616-2

Kreuzer, M. & Robbiano, L. (2025). Elimination by substitution. Journal of Symbolic Computation, 131. https://doi.org/10.1016/j.jsc.2025.102445

Kreuzer, M. & Robbiano, L. (2025). Reembeddings of special border basis schemes. De Gruyter Proceedings in Mathematics, 353–388. https://doi.org/10.1515/9783110999365-012

Kreuzer, M., Linh, T. N., & Long, L. N. (2025). Differential theory of zero-dimensional schemes. Journal of Pure and Applied Algebra, 229(1). https://doi.org/10.1016/j.jpaa.2024.107815

Kreuzer, M., Miasnikov, A., & Walsh, F. (2025). Decomposing finite Z-algebras. Journal of Algebra, 664, 206–246. https://doi.org/10.1016/j.jalgebra.2024.10.027

Andraschko, B., Danner, J., & Kreuzer, M. (2024). SAT Solving Using XOR-OR-AND Normal Forms. Mathematics in Computer Science, 18(4). https://doi.org/10.1007/s11786-024-00594-x

Diekert, V. & Kreuzer, M. (2024). Finitely presented groups: With applications in post-quantum cryptography and artificial intelligence. Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence, 1–252. https://doi.org/10.1515/9783111473574

Diekert, V. & Kreuzer, M. (2024). Preface. Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence, VII–VIII. https://doi.org/10.1515/9783111473574-201

Kreuzer, M. & Walsh, F. (2024). An algorithmic survey of finite z-algebras. Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence, 115–136. https://doi.org/10.1515/9783111473574-007

Kreuzer, M. & Walsh, F. (2024). COMPUTING THE UNIT GROUP OF A COMMUTATIVE FINITE Z-ALGEBRA. Groups, Complexity, Cryptology, 16(1), 6:1–6:16. https://doi.org/10.46298/jgcc.2024.16.1.13875

Kreuzer, M. & Walsh, F. (2024). Computing the binomial part of a polynomial ideal. Journal of Symbolic Computation, 124. https://doi.org/10.1016/j.jsc.2024.102298

Kreuzer, M. & Walsh, F. (2024). EFFICIENT ALGORITHMS FOR FINITE Z-ALGEBRAS. Groups, Complexity, Cryptology, 15(2). https://doi.org/10.46298/jgcc.2023.15.2.12496

Kreuzer, M. (2024). A brief biography. Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence, 225–238. https://doi.org/10.1515/9783111473574-014

Kreuzer, M., Long, L. N., & Robbiano, L. (2024). Re-embeddings of affine algebras via Gröbner fans of linear ideals. Beitrage zur Algebra und Geometrie, 65(4), 827–851. https://doi.org/10.1007/s13366-024-00733-2

Kreuzer, M., Long, L. N., & Robbiano, L. (2023). Restricted Gröbner fans and re-embeddings of affine algebras. Sao Paulo Journal of Mathematical Sciences, 17(1), 242–267. https://doi.org/10.1007/s40863-022-00324-w

Kreuzer, M., Long, L. N., & Robbiano, L. (2022). ALGORITHMS FOR CHECKING ZERO-DIMENSIONAL COMPLETE INTERSECTIONS. Journal of Commutative Algebra, 14(1), 61–76. https://doi.org/10.1216/jca.2022.14.61

Kreuzer, M., Ngoc Long, L., & Robbiano, L. (2022). Cotangent spaces and separating re-embeddings. Journal of Algebra and its Applications, 21(9). https://doi.org/10.1142/S0219498822501882

Danner, J. & Kreuzer, M. (2021). A fault attack on KCipher-2. International Journal of Computer Mathematics: Computer Systems Theory, 6(4), 291–312. https://doi.org/10.1080/23799927.2020.1854863

Fine, B., Gaglione, A., Kreuzer, M., Rosenberger, G., & Spellman, A. D. (2021). THE AXIOMATICS OF FREE GROUP RINGS. Groups, Complexity, Cryptology, 13(2), 3:1–3:13. https://doi.org/10.46298/jgcc.2021.13.2.8796

Fine, B., Kreuzer, M., & Rosenberger, G. (2021). Further potential applications of group theory in information security. International Journal of Computer Mathematics: Computer Systems Theory, 6(4), 375–380. https://doi.org/10.1080/23799927.2021.1931455

Guardo, E., Kreuzer, M., Linh, T. N. K., & Long, L. N. (2021). KÄHLER DIFFERENTIALS FOR FAT POINT SCHEMES IN (Formula presented) x (Formula presented). Journal of Commutative Algebra, 13(2), 179–207. https://doi.org/10.1216/jca.2021.13.179

Kreuzer, M. & Patil, D. P. (2021). Computational aspects of Burnside rings part II: important maps. Beitrage zur Algebra und Geometrie, 62(2), 475–494. https://doi.org/10.1007/s13366-020-00520-9

Kreuzer, M., Linh, T. N. K., & Long, L. N. (2021). Hilbert Polynomials of Kähler Differential Modules for Fat Point Schemes. Acta Mathematica Vietnamica, 46(3), 441–455. https://doi.org/10.1007/s40306-021-00432-3

Danner, J. & Kreuzer, M. (2020). A FAULT ATTACK ON THE NIEDERREITER CRYPTOSYSTEM USING BINARY IRREDUCIBLE GOPPA CODES. Groups, Complexity, Cryptology, 12(1). https://doi.org/10.46298/jgcc.2020.12.1.6074

Hashemi, A., Kreuzer, M., & Pourkhajouei, S. (2020). Computing Coupled Border Bases. Mathematics in Computer Science, 14(1), 123–140. https://doi.org/10.1007/s11786-020-00452-6

Horáček, J. & Kreuzer, M. (2020). On conversions from CNF to ANF. Journal of Symbolic Computation, 100, 164–186. https://doi.org/10.1016/j.jsc.2019.07.023

Horáček, J., Kreuzer, M., & Messeng Ekossono, A. (2020). A Signature Based Border Basis Algorithm. Mathematics in Computer Science, 14(1), 177–189. https://doi.org/10.1007/s11786-020-00459-z

Kreuzer, M. & Rosenberger, G. (2020). On the numbers of the form x2 + 11y2. De Gruyter Proceedings in Mathematics, 177–201. https://doi.org/10.1515/9783110638387-016

Kreuzer, M. & Xiu, X. (2020). Noncommutative Gebauer–Möller criteria. De Gruyter Proceedings in Mathematics, 149–175. https://doi.org/10.1515/9783110638387-015

Kreuzer, M., Linh, T. N. K., Long, L. N., & Nguyen, T. C. (2020). An application of liaison theory to zero-dimensional schemes. Taiwanese Journal of Mathematics, 24(3), 553–573. https://doi.org/10.11650/tjm/190710

Kreuzer, M., Long, L. N., & Robbiano, L. (2020). Computing subschemes of the border basis scheme. International Journal of Algebra and Computation, 30(8), 1671–1716. https://doi.org/10.1142/S0218196720500599

Kreuzer, M., Sipal, B., & Long, L. N. (2020). On the regularity of the monomial point of a border basis scheme. Beitrage zur Algebra und Geometrie, 61(3), 515–532. https://doi.org/10.1007/s13366-019-00482-7

Hashemi, A., Kreuzer, M., & Pourkhajouei, S. (2019). Computing all border bases for ideals of points. Journal of Algebra and its Applications, 18(6). https://doi.org/10.1142/S0219498819501020

Kreuzer, M., Linh, T. N. K., & Long, L. N. (2019). The Dedekind different of a Cayley-Bacharach scheme. Journal of Algebra and its Applications, 18(2). https://doi.org/10.1142/S0219498819500270

Kreuzer, M., Long, L. N., & Robbiano, L. (2019). On the Cayley-Bacharach Property. Communications in Algebra, 47(1), 328–354. https://doi.org/10.1080/00927872.2018.1476525

Horáček, J. & Kreuzer, M. (2018). 3BA: A Border Bases Solver with a SAT Extension. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10931 LNCS, 209–217. https://doi.org/10.1007/978-3-319-96418-8_25

Horáček, J. & Kreuzer, M. (2018). Refutation of products of linear polynomials. CEUR Workshop Proceedings, 2189, 33–47.

Kreuzer, M., Linh, T. N., & Long, L. N. (2018). Kähler differential algebras for 0-dimensional schemes. Journal of Algebra, 501, 255–284. https://doi.org/10.1016/j.jalgebra.2017.12.023

Burchard, J., Ekossono, A. M., Horáček, J., Gay, M., Becker, B., Schubert, T., Kreuzer, M., & Polian, I. (2017). Towards mixed structural-functional models for algebraic fault attacks on ciphers. 2017 2nd International Verification and Security Workshop, IVSW 2017, 7–12. https://doi.org/10.1109/IVSW.2017.8031537

Burchard, J., Gay, M., Ekossono, A. M., Horacek, J., Becker, B., Schubert, T., Kreuzer, M., & Polian, I. (2017). AutoFault: Towards Automatic Construction of Algebraic Fault Attacks. Proceedings - 2017 Workshop on Fault Diagnosis and Tolerance in Cryptography, FDTC 2017, 2017-January, 65–72. https://doi.org/10.1109/FDTC.2017.13

Horacek, J., Kreuzer, M., & Ekossono, A. S. M. (2017). Computing boolean border bases. Proceedings - 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2016, 465–472. https://doi.org/10.1109/SYNASC.2016.076

Horáček, J. & Kreuzer, M. (2017). On Conversions from CNF to ANF. CEUR Workshop Proceedings, 1974.

Horáček, J., Burchard, J., Becker, B., & Kreuzer, M. (2017). Integrating algebraic and SAT solvers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10693 LNCS, 147–162. https://doi.org/10.1007/978-3-319-72453-9_11

Kreuzer, M. & Long, L. N. (2017). Characterizations of zero-dimensional complete intersections. Beitrage zur Algebra und Geometrie, 58(1), 93–129. https://doi.org/10.1007/s13366-016-0311-9

Kreuzer, M. & Patil, D. P. (2017). Computational aspects of Burnside rings, part I: the ring structure. Beitrage zur Algebra und Geometrie, 58(3), 427–452. https://doi.org/10.1007/s13366-016-0324-4

Kreuzer, M. & Robbiano, L. (2016). Computational linear and commutative algebra. Computational Linear and Commutative Algebra, 1–321. https://doi.org/10.1007/978-3-319-43601-2

Baumslag, G., Fine, B., Kreuzer, M., & Rosenberger, G. (2015). A Course in Mathematical Cryptography. A Course in Mathematical Cryptography, 1–376. https://doi.org/10.1515/9783110372779

Fine, B., Kreuzer, M., & Rosenberger, G. (2015). On Magnus' freiheitssatz and free polynomial algebras. International Journal of Group Theory, 4(1), 13–19.

Kreuzer, M., Tran, N. L., & Le, N. L. (2015). Kähler differentials and Kähler differents for fat point schemes. Journal of Pure and Applied Algebra, 219(10), 4479–4509. https://doi.org/10.1016/j.jpaa.2015.02.028

Beck, M. T., De Meer, H., Schuster, S., & Kreuzer, M. (2014). Estimating photo-voltaic power supply without smart metering infrastructure. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8343 LNCS, 25–39. https://doi.org/10.1007/978-3-642-55149-9_3

Fine, B., Kreuzer, M., & Rosenberger, G. (2014). Faithful real representations of cyclically pinched one-relator groups. International Journal of Group Theory, 3(1), 1–8.

Kreuze, M. & Kriegl, M. (2014). Gr̈obner bases for syzygy modules of border bases. Journal of Algebra and its Applications, 13(6). https://doi.org/10.1142/S0219498814500030

Kreuzer, M., Myasnikov, A., & Ushakov, A. (2014). A linear algebra attack to group-ring-based key exchange protocols. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8479 LNCS, 37–43. https://doi.org/10.1007/978-3-319-07536-5_3

Geramita, A. V. & Kreuzer, M. (2013). On the uniformity of zero-dimensional complete intersections. Journal of Algebra, 391, 82–92. https://doi.org/10.1016/j.jalgebra.2013.05.027

Polian, I. & Kreuzer, M. (2013). Fault-based attacks on cryptographic hardware. Proceedings of the 2013 IEEE 16th International Symposium on Design and Diagnostics of Electronic Circuits and Systems, DDECS 2013, 12–17. https://doi.org/10.1109/DDECS.2013.6549781

Jovanovic, P., Kreuzer, M., & Polian, I. (2012). A fault attack on the LED block cipher. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 7275 LNCS, 120–134. https://doi.org/10.1007/978-3-642-29912-4_10

Kreuzer, M. & Poulisse, H. (2011). Subideal border bases. Mathematics of Computation, 80(274), 1135–1154. https://doi.org/10.1090/S0025-5718-2010-02432-9

Kreuzer, M. & Robbiano, L. (2011). The geometry of border bases. Journal of Pure and Applied Algebra, 215(8), 2005–2018. https://doi.org/10.1016/j.jpaa.2010.11.011

Jovanovic, P. & Kreuzer, M. (2010). Algebraic attacks using SAT-solvers. Groups, Complexity, Cryptology, 2(2), 247–259. https://doi.org/10.1515/GCC.2010.016

Heldt, D., Kreuzer, M., Pokutta, S., & Poulisse, H. (2009). Approximate computation of zero-dimensional polynomial ideals. Journal of Symbolic Computation, 44(11), 1566–1591. https://doi.org/10.1016/j.jsc.2008.11.010

Kreuzer, M. & Kühling, S. (2009). All logical, or what?; [Alles logisch, oder was?]. Informatik-Spektrum, 32(1), 4–7. https://doi.org/10.1007/s00287-008-0305-6

Kreuzer, M. & Poulisse, H. (2009). Algebraic petroleum; [Algebraisches Erdöl]. Informatik-Spektrum, 32(1), 12–17. https://doi.org/10.1007/s00287-008-0306-5

Kreuzer, M. (2009). Algebraic attacks galore!. Groups, Complexity, Cryptology, 1(2), 231–259. https://doi.org/10.1515/GCC.2009.231

Kreuzer, M. & Robbiano, L. (2008). Deformations of border bases. Collectanea Mathematica, 59(3), 275–297. https://doi.org/10.1007/BF03191188

Ackermann, P. & Kreuzer, M. (2006). Gröbner basis cryptosystems. Applicable Algebra in Engineering, Communications and Computing, 17(3-4), 173–194. https://doi.org/10.1007/s00200-006-0002-0

Kehrein, A. & Kreuzer, M. (2006). Computing border bases. Journal of Pure and Applied Algebra, 205(2), 279–295. https://doi.org/10.1016/j.jpaa.2005.07.006

Abbott, J., Kreuzer, M., & Robbiano, L. (2005). Computing zero-dimensional schemes. Journal of Symbolic Computation, 39(1), 31–49. https://doi.org/10.1016/j.jsc.2004.09.001

Kehrein, A. & Kreuzer, M. (2005). Characterizations of border bases. Journal of Pure and Applied Algebra, 196(2-3), 251–270. https://doi.org/10.1016/j.jpaa.2004.08.028

Kreuzer, M. & Robbiano, L. (2005). Computational commutative algebra 2. Computational Commutative Algebra 2, 1–586. https://doi.org/10.1007/3-540-28296-3

Caboara, M., Kreuzer, M., & Robbiano, L. (2004). Efficiently computing minimal sets of critical pairs. Journal of Symbolic Computation, 38(4), 1169–1190. https://doi.org/10.1016/j.jsc.2003.08.009

Abbott, J., Bigatti, A., Kreuzer, M., & Robbiano, L. (2000). Computing ideals of points. Journal of Symbolic Computation, 30(4), 341–356. https://doi.org/10.1006/jsco.2000.0411

Kreuzer, M. (2000). On the Canonical Ideal of a Set of Points. Bollettino della Unione Matematica Italiana B, 3(1), 221–261.

Kreuzer, M., Migliore, J. C., Peterson, C., & Nagel, U. (2000). Determinantal schemes and buchsbaum-rim sheaves. Journal of Pure and Applied Algebra, 150(2), 155–174. https://doi.org/10.1016/S0022-4049(99)00046-8

De Dominicis, G. & Kreuzer, M. (1999). Kähler differentials for points in ℙn. Journal of Pure and Applied Algebra, 141(2), 153–173. https://doi.org/10.1016/S0022-4049(98)00016-4

Kreuzer, B. & Kreuzer, M. (1998). Extremal zero-dimensional subschemes of ℙ2. Journal of Pure and Applied Algebra, 131(2), 159–177. https://doi.org/10.1016/S0022-4049(97)00164-3

Kreuzer, M. & Waldi, R. (1997). On the Castelnuovo-Mumford regularity of a projective system. Communications in Algebra, 25(9), 2919–2929. https://doi.org/10.1080/00927879708826031

Kreuzer, M. (1995). On maximal cayley-bacharach schemes. Communications in Algebra, 23(9), 3357–3378. https://doi.org/10.1080/00927879508825405

Geramita, A. V., Kreuzer, M., & Robbiano, L. (1993). Cayley-Bacharachsc hemes and their canonical modulesgs. Transactions of the American Mathematical Society, 339(1), 163–189. https://doi.org/10.1090/S0002-9947-1993-1102886-5

Kreuzer, M. (1993). Vector Bundles with Good Sections. Communications in Algebra, 21(3), 1043–1062. https://doi.org/10.1080/00927879308824608

Kreuzer, M. (1992). On 0-dimensional complete intersections. Mathematische Annalen, 292(1), 43–58. https://doi.org/10.1007/BF01444608

Kreuzer, M. & Kunz, E. (1987). Traces in strict Frobenius algebras and strict complete intersections. Journal fur die Reine und Angewandte Mathematik, 1987(381), 181–204. https://doi.org/10.1515/crll.1987.381.181

Research projects

1

Re-Embeddings of Affine Varieties

2

Subschemes of the Border Basis Scheme

3

Algebraic Fault Attacks

Books

1

Kreuzer, M., & Robbiano, L. (2000). Computational commutative algebra 2. Berlin, Heidelberg: Springer Berlin Heidelberg.