Jens Zumbrägel's Website
Mathematics and More

Prof. Dr. Jens Zumbrägel

Universität Passau
Innstraße 33
94032 Passau
Germany

Tel. +49 851 509 3133

Research

I am intrigued by algebra and its applications in public-key cryptography and channel coding theory.

Research Interests

  • Discrete Logarithms, Function Field Sieve
  • Simple Semirings: here is an Introduction
  • Semigroup Actions for Public-Key Cryptography
  • Coding Theory over Frobenius Rings
  • Finite-Length Analysis of LDPC Codes

Links

PIDS - Passau Institute of Digital Security

AMC Journal - Advances in Mathematics of Communications

iacr.org - International Association for Cryptologic Research

itsoc.org - IEEE Information Theory Society . IEEE Student Branch Passau

network-coding.eu - COST Action on Random Network Coding and Designs over GF(q)

PI Grant on Public-Key Cryptography Based on Finite Simple Semirings

mathematics and music . Stefan E. Schmidt . Franziska Leonhardi

Publications

Preprints

  • S. Pohmann, M. Stevens, J. Zumbrägel. Lattice Enumeration on GPUs for fplll. 13 pages.  eprint

Journal Articles

  1. R. Granger, T. Kleinjung, A. K. Lenstra, B. Wesolowski, J. Zumbrägel. Computation of a 30750-Bit Binary Field Discrete Logarithm. Math. Comp. (to appear), 22 pages.  arXiv
  2. T. G. Nam, J. Zumbrägel. On Steinberg algebras of Hausdorff ample groupoids over commutative semirings. J. Pure Appl. Algebra 225, no. 4 (2021), 106548 (23 pages).  doi  arXiv
  3. F. M. Schneider, J. Zumbrägel. MacWilliams' extension theorem for infinite rings. Proc. Amer. Math. Soc. 147, no. 3 (2019), pp. 947-961.  doi  arXiv
  4. M. Greferath, Z. Liu, X.-W. Wu, J. Zumbrägel. New results on the pseudoredundancy. Bull. Korean Math. Soc. 56, no. 1 (2019), pp. 111-130.  doi  arXiv
  5. Y. Katsov, T. G. Nam, J. Zumbrägel. On congruence-semisimple semirings and the K0-group characterization of ultramatricial algebras over semifields. J. Algebra 508 (2018), pp. 157-195.  doi  arXiv
  6. R. Granger, T. Kleinjung, J. Zumbrägel. Indiscreet logarithms in finite fields of small characteristic. Adv. Math. Commun. 12, no. 2 (2018), pp. 263-286.  doi  arXiv
  7. R. Granger, T. Kleinjung, J. Zumbrägel. On the discrete logarithm problem in finite fields of fixed characteristic. Trans. Amer. Math. Soc. 370, no. 5 (2018), pp. 3129-3145.  doi  arXiv
  8. F. M. Schneider, J. Zumbrägel. Profinite algebras and affine boundedness. Adv. Math. 305 (2017), pp. 661-681.  doi  arXiv
  9. Y. Katsov, T. G. Nam, J. Zumbrägel. Simpleness of Leavitt path algebras with coefficients in a commutative semiring. Semigroup Forum 94, no. 3 (2017), pp. 481-499.  doi  arXiv
  10. F. M. Schneider, J. Zumbrägel. Every simple compact semiring is finite. Topology Appl. 206 (2016), pp. 305-310.  doi  arXiv
  11. M. Greferath, T. Honold, C. Mc Fadden, J. A. Wood, J. Zumbrägel. MacWilliams' Extension Theorem for bi-invariant weights over finite principal ideal rings. J. Combin. Theory Ser. A 125 (2014), pp. 177-193.  doi  arXiv
  12. Y. Katsov, T. G. Nam, J. Zumbrägel. On simpleness of semirings and complete semirings. J. Algebra Appl. 13, no. 6 (2014), 1450015 (29 pages).  doi  arXiv
  13. A. Kendziorra, J. Zumbrägel. Finite simple additively idempotent semirings. J. Algebra 388 (2013), pp. 43-64.  doi  arXiv
  14. A. Kendziorra, S. E. Schmidt, J. Zumbrägel. Invertible matrices over finite additively idempotent semirings. Semigroup Forum 86, no. 3 (2013), pp. 525-536.  doi  arXiv
  15. E. Byrne, M. Greferath, J. Pernas, J. Zumbrägel. Algebraic decoding of negacyclic codes over Z₄. Des. Codes Cryptogr. 66, no. 1-3 (2013), pp. 3-16.  doi  arXiv
  16. M. Greferath, C. Mc Fadden, J. Zumbrägel. Characteristics of invariant weights related to code equivalence over rings. Des. Codes Cryptogr. 66, no. 1-3 (2013), pp. 145-156.  doi  arXiv
  17. J. Zumbrägel, V. Skachek, M. F. Flanagan. On the pseudocodeword redundancy of binary linear codes. IEEE Trans. Inform. Theory 58, no. 7 (2012), pp. 4848-4861.  doi  arXiv
  18. J. Zumbrägel. Classification of finite congruence-simple semirings with zero. J. Algebra Appl. 7, no. 3 (2008), pp. 363-377.  doi  arXiv

Conference Proceedings

  1. S. Puchinger, J. Renner, A. Wachter-Zeh, J. Zumbrägel. Efficient Decoding of Gabidulin Codes over Galois Rings. Proc. IEEE International Symposium on Information Theory (ISIT 2021), Melbourne, Australia, 6 pages.  arXiv
  2. O. W. Gnilke, M. Greferath, T. Honold, J. A. Wood, J. Zumbrägel. The extension theorem for bi-invariant weights over Frobenius rings and Frobenius bimodules. In: Noncommutative Rings and Their Applications (NCRA V) 2017, Lens, France. Contemp. Math. 727 (2019), pp. 117-129.  doi  arXiv
  3. T. Hanika, J. Zumbrägel. Towards Collaborative Conceptual Exploration. In: 23rd International Conference on Conceptual Structures (ICCS 2018), Edinburgh, UK.  doi  arXiv
  4. R. Granger, T. Kleinjung, J. Zumbrägel. Breaking '128-bit Secure' Supersingular Binary Curves. In: Advances in Cryptology−CRYPTO 2014, Santa Barbara, CA, USA.  doi  eprint
  5. Z. Liu, J. Zumbrägel, M. Greferath, X.-W. Wu. Notes on the Pseudoredundancy. Proc. IEEE International Symposium on Information Theory (ISIT 2014), Honolulu, HI, USA.  doi
  6. M. Greferath, J. Zumbrägel. A Grey-Rankin Bound for Codes over Frobenius Rings. Proc. 21th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, 3 pages.  link
  7. F. Göloğlu, R. Granger, G. McGuire, J. Zumbrägel. Solving a 6120-bit DLP on a Desktop Computer. In: Selected Areas in Cryptography−SAC 2013, Burnaby, BC, Canada.  doi  eprint
  8. F. Göloğlu, R. Granger, G. McGuire, J. Zumbrägel. On the Function Field Sieve and the Impact of Higher Splitting Probabilities. In: Advances in Cryptology−CRYPTO 2013, Santa Barbara, CA, USA.  Best Paper Award.  doi  eprint
  9. M. Greferath, J. Zumbrägel. On the algebraic representation of selected optimal non-linear binary codes. Proc. IEEE International Symposium on Information Theory (ISIT 2012), Cambridge, MA, USA, pp. 3115-3119.  doi  arXiv
  10. C. Mc Fadden, M. Greferath, J. Zumbrägel. Characteristics of invariant weights related to code equivalence over rings. Proc. 7th International Workshop on Coding and Cryptography (WCC 2011), Paris, France, pp. 91-99.
  11. E. Byrne, M. Greferath, J. Pernas, J. Zumbrägel. Algebraic decoding of negacyclic codes over Z4. Proc. 7th International Workshop on Coding and Cryptography (WCC 2011), Paris, France, pp. 101-110.
  12. J. Zumbrägel, M. F. Flanagan, V. Skachek. Exploration of AWGNC and BSC pseudoredundancy. Proc. 19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010), Budapest, Hungary, 7 pages.  arXiv
  13. J. Zumbrägel, M. F. Flanagan, V. Skachek. On the pseudocodeword redundancy. Proc. IEEE International Symposium on Information Theory (ISIT 2010), Austin, TX, USA, pp. 759-763.  doi  arXiv
  14. J. Zumbrägel, G. Maze, J. Rosenthal. Efficient recovering of operation tables of black box groups and rings. Proc. IEEE International Symposium on Information Theory (ISIT 2008), Toronto, ON, Canada, pp. 639-643.  doi  arXiv

Theses

  1. J. Zumbrägel. Public-key cryptography based on simple semirings. Ph. D. dissertation, Universität Zürich, Switzerland, December 2008.  pdf
  2. J. Zumbrägel. Modular-Theorie und die Konstruktion nicht-kommutativer Lp-Räume nach Haagerup. Diploma thesis, Universität Oldenburg, Germany, October 2004.  pdf
  3. J. Zumbrägel. Subharmonic methods in Banach algebra theory. Essay as part of the Part III Examination, University of Cambridge, UK, May 2003.  pdf
© 2015 by Jens Zumbrägel