Tran van Trung's Home Page

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Professor of Mathematics, IEM (Institut für Experimentelle Mathematik), Fakultät für Mathematik, Universität Duisburg-Essen

Education

  • ​Licence-ès-sciences (1970), University of Saigon

  • Dipl.-Math. (1974), Dr. rer.nat. (1976), Habilitation, Venia Legendi (1988),  Ruprecht-Karls-Universität Heidelberg

Research Topics

  • Group Theory
  • Finite Geometry
  • Combinatorial Designs
  • Cryptology, Group-based Cryptography
  • Applications of Discrete Mathematics  to Cryptology and Information Theory

Publications

  •  Tran van Trung.  Resolutions of the designs in two infinite series of 4-designs,  Discrete Math. 347 (2024) 113907
  • Tran van Trung.  Point-missing s-resolvable t-designs: infinite series of 4-designs with constant index, Des. Codes Cryptogr., (2023),https://doi.org/10.1007/s10623-023-01206-8
  • Tran van Trung.  A method of constructing 2-resolvable t-designs for t=3,4,
    Des. Codes Cryptogr.,(2022), https://doi.org/10.1007/s10623-022-01056-w
  • Tran van Trung.  An extending theorem for s-resolvable t-designs,
    Des. Codes Cryptogr.,(2021) 89: 589--597, DOI:10.1007/s10623-029-00835-7
  • Tran van Trung.  On simple 3-designs having 2-resolutions,
    Discrete Math.,(2020) 343 doi.org/10.1016/j.disc.2020.111963.
  •  Tran van Trung.  On t-designs and s-resolvable t-designs from hyperovals,
    J. Combin. Des.,(2020) 28: 261--270, DOI:10.1002/jcd.21693
  • Tran van Trung.  Recursive constructions for s-resolvable t-designs,
    Des. Codes Cryptogr.,(2019) 87: 2835--2845, doi.org/10.1007/s10623-019-00653-6.
  • Tran van Trung. On existence theorems for simple t-designs,
    Des. Codes Cryptogr. (2018) 87:1521--1540, doi.org/10.1007/s10623-018-0550-x.
  • Tran van Trung. Construction of strongly aperiodic logarithmic signatures,
    J. Math. Cryptol., (2018) 12: 23--35.
  • Tran van Trung. A recursive construction for simple t-designs using resolutions,
    Des. Codes Cryptogr., (2018) 86: 1185--1200, DOI 10.1007/s10623-017-0389-6 (2017).
  • Tran van Trung. Simple t-designs: a recursive construction for arbitrary t,
    Des. Codes Cryptogr. 83, 493--502 (2017), DOI 10.1007/s10623-016-0238-z (2016).
  • Tran van Trung. Construction of 3-designs using (1,σ)-resolution,
    Advances in Mathematics of Communications, 10(2016), pp. 511--524 DOI: 10.3934/amc2016022.
  • Chuan Guo, D.R.Stinson, Tran van Trung. On symmetric designs and binary 3-frameproof codes,
    Algebraic Design Theory and Hadamard Matrices, ADTHM Lethbridge, Alberta, Canada, July 2014 Ed. Charles J.~ Colbourn, (2015) pp. 125--136
  • Chuan Guo, D. R. Stinson, Tran van Trung. On tight bounds for binary frameproof codes,
    Des. Codes Cryptogr. 77 (2015), pp. 301--319
  • D.R.Stinson, C.M. Swason, Tran van Trung. A new look at an old construction: Constructing (simple) 3-designs from resolvable 2-designs,
    Discrete Math. 325 (2014), pp. 23--31
  • P.Svaba, Tran van Trung, P. Wolf.  Logarithmic signatures for abelian groups and their factorization,
    Tatra Mt. Math. Publ. 57 (2013), pp. 1--13, DOI: 10.2478/tmmp-2013-0033
  • R. Staszewski, Tran van Trung.  Strongly aperiodic logarithmic signatures,
    J. Math. Cryptol., 7 (2013), pp. 147--179, DOI: 10.1515/jmc-2013-5000
  • Tran van Trung.  A tight bound for frameproof codes viewed in terms of separating hash families,
    Des. Codes Cryptogr. DOI 10.1007/s10623-013-9800-0 (2013)
  • T. Shongwe, T.G. Swart, H.C. Ferreira, Tran van Trung.  Good Synchronization Sequences for Permutation Codes,
    IEEE Transactions on Communications 60(5) (2012), pp. 1024--1028
  • M. Bazrafshan, Tran van Trung. Improved bounds for separating hash families,
    Des. Codes Cryptogr. DOI 10.1007/s10623-012-9673-7 (2012)
  • P. Marquardt, P. Svaba, Tran van Trung.  Pseudorandom number generators based on random covers for finite groups
    Designs, Codes and Cryptography 64 (2012), pp. 209--220
  • M. Bazrafshan, Tran van Trung. Bounds for separating hash families,
    J. Comb. Theory, Ser. A, 118 (2011), pp. 1129--1135
  • S.S. Magliveras, Tran van Trung. On Jacobsthal Binary Sequences
    NATO Science for Peace and Security Series-D: Information Security, Coding Theory and Related Combinatorics, 29 (2011), pp. 27--37
  • P. Svaba, Tran van Trung. Public key cryptosystem MST3: cryptanalysis and realization,
    J. Math. Cryptol., 4 (2010), pp. 271--315
  • W. Lempken, Tran van Trung, S.S. Magliveras, Wandi Wei.  A public key cryptosystem based on non-abelian finite groups,
    J. Cryptol., 22 (2009), pp. 62--74
  • S.S. Magliveras, Tran van Trung, Wandi Wei. Primitive sets in a lattice,
    Australasian Journal of Combinatorics, 40 (2008), pp. 173--186
  • S.S. Magliveras, P. Svaba, Tran van Trung, P. Zajac. On the security of a realization of cryptosystem MST3 ,
    Tatra Mt. Math. Pub. (2008) 41, 65--78
  • S. Martirosyan, Tran van Trung. Explicit constructions for perfect hash families,
    Des. Codes Cryptogr. , 46 (2008), pp. 97--112
  • P. Svaba, Tran van Trung. On generation of random covers for finite groups,
    Tatra Mt. Math. Publ., 37 (2007), pp. 105--112
  • C.J. Colbourn, S. Martirosyan, Tran van Trung, R.A. Walker II. Roux-type constructions for covering arrays of strengths three and four, 
    Designs, Codes and Cryptography, 41 (2006), pp. 35--57
  • Y.J. Ionin, Tran van Trung. Symmetric Designs,
    Handbook of Combinatorial Designs, 2nd Ed. C.J.Colbourn and J.H.Dinitz, CRC-Press (2006), pp. 110--123
  • V. Canda, Tran van Trung. A new mode of using all-or-nothing transforms,
    Tatra Mt. Math. Publ. 33 (2006), pp. 159--168
  • W. Lempken, Tran van Trung. On minimal logarithmic signatures of finite groups,
    Experimental Mathematics 14 (2005), pp. 257--269
  • S. Martirosyan, Tran van Trung. On t-covering arrays,
    Designs, Codes and Cryptography 32 (2004), pp. 323--339
  • O. Grosek, P. Horak, Tran van Trung.  On non-plolynomial latin squares,
    Designs, Codes and Cryptography 32 (2004), pp. 217--226
  • Wandi Wei, Tran van Trung, S.S. Magliveras, F. Hoffman.  Cryptographic primitives based on groups of hidden order,
    Tatra Mt. Math. J., 29 (2004), pp. 147--155
  • Tran van Trung, S. Martirosyan.  New constructions for IPP Codes,
    Designs, Codes and Cryptography 35 (2005), pp. 227--239
  • Tran van Trung, S. Martirosyan. On a Class of Traceability Codes,
    Designs, Codes and Cryptography, 31 (2004), pp. 125--132
  • V. Canda, Tran van Trung. Scalable Block Ciphers Based on Feistel-like Structure,
    Tatra Mt. Math.Publ. 25 (2002), pp. 39--66
  • V. Canda, Tran van Trung.  A new mode of using All-Or-Nothing Transforms,  Proceedings IEEE International Symposium on Information Theory, Lausanne, Switzerland, 2002, pp. 296-, doi:10.1109/ISIT.2002.1023568
  • S.S. Magliveras, D.R. Stinson, Tran van Trung. New approaches to designing public key cryptosystems using one-way functions and trap-doors in finite groups,
    Journal of Cryptology 15 (2002), pp. 285--297
  • V. Canda, Tran van Trung, S.S. Magliveras, T. Horvath.  Symmetric block ciphers based on group bases,
    Selected Areas in Cryptography, SAC'2000 Ed. D.~Stinson and S.~ Tavares, LNCS, (2001) pp.98--105
  • Tran van Trung. Construction of 3-designs using parallelism,
    J. Geom. 67 (2000), 223--235
  • D.R. Stinson, Tran van Trung, R. Wei.  Secure Frameproof Codes, Key Distribution Patterns, Group Testing Algorithms and Related Structures,
    Journal of Statistical Planning and Inference 86 (2000), 595--617
  • Tran van Trung. Recursive constructions for 3-designs and resolvable 3-designs,
    Journal of Statistical Planning and Inference 95 (2001), 341--358
  • R. Mathon, Tran van Trung. Directed t-Packings and Directed t-Steiner Systems,
    Designs, Codes and Cryptography 18 (1999) 187--198
  • Tran van Trung. Constructions for Near Resolvable Designs and BIBDs,
    J. Combin. Designs 7 (1999), 227--231
  • D.R. Stinson, Tran van Trung. New Results on Key Distribution Patterns and Broadcast Encryption,
    Designs, Codes and Cryptography 14 (1998), 261-279
  • R. Mathon, Tran van Trung. Unitals and Unitary Polarities in Symmetric Designs,
    Designs, Codes and Crytography 10 (1997), 237--250
  • Tran van Trung, Qiu-Rong Wu, D. Mesner. High order intersection numbers for t-designs,
    J. Stat. Planning Inf. 56 (1996), 257--268
  • Tran van Trung. A Generalization of a Theorem of Dehon for simple t-Designs, Designs, Codes and Cryptography 9 (1996), 105--114
  • Tran van Trung.  Symmetric designs,
    The CRC Handbook of Combinatorial Designs, ed. by C.J. Colbourn and J.H. Dinitz, (1996), pp 75--87
  • Tran van Trung.  On the construction of authentication and secrecy codes,
    Designs, Codes and Cryptography 5 (1995), 269--280
  • T. Horvath, S.S. Magliveras, Tran van Trung.  A Parallel Permutation Multiplier for a PGM Crypto-Chip,
    Advances in Cryptology-CRYPTO'94, edited by Yvo G.Desmedt), Lecture Notes in Computer Sciences 839, 108-113 (1994), Springer-Verlag
  • Tran van Trung.  Combinatorial characterization of certain universal classes of hash functions,
    J. Comb. Designs 2 (1994), 161--166
  • E. Spence, V.D. Tonchev, Tran van Trung.    A symmetric 2-(160,54,18) design,
    J. Comb. Designs 1 (1993), 65-68
  • Tran van Trung.  Some existence theorems for t-designs,
    Discrete Math. 128 (1994), 337--348
  • J. Bierbrauer, Tran van Trung.  Some highly symmetric authentication perpendicular arrays,
    Designs, Codes and Cryptography 1 (1992), 307-319
  • J. Bierbrauer, Tran van Trung.  Halving PGL(2,2^f), f odd: a series of cryptocodes,
    Designs, Codes and Cryptography 1 (1991), 141-148
  • E.S. Kramer, S.S. Magliveras, Tran van Trung, Qiu-Rong Wu.  Some perpendicular arrays for arbitrarily large t,
    Discrete Math. 96 (1991), 101--110
  • E.S. Kramer, S.S. Magliveras, Tran van Trung.  Possible automorphism groups of an S(3,5,26),
    JCMCC 12 (1992), 119--127
  • Tran van Trung.  Maximal arcs and related designs,
    J. Comb. Theory Ser.A 57 (1991), 294--301
  • Tran van Trung.  Nonembeddable quasi-residual designs,
    Contemporary Mathematics 111 (1990), 237--278
  • Tran van Trung.  Non-embeddable quasi-residual designs with k < v/2,
    J. Comb. Theory Ser.A 43 (1986), 133--137
  • Tran van Trung.  On the construction of t-designs and the existence of some new infinite families of simple 5-designs,
    Arch. Math. 47 (1986), 187--192
  • Tran van Trung.  A symmetric block design with parameters (61,16,4),
    J. Comb. Theory Ser.A 37 (1984), 374
  • Z. Janko, Tran van Trung.  A new biplane of order 9 with a small automorphism group,
    J. Comb. Theory Ser.A 42 (1986), 305--309
  • Z. Janko, Tran van Trung.  The existence of a symmetric block design for (70,24,8),
    Mitt. Math. Sem. Gießen 165 (1984), 17--18
  • Z. Janko, Tran van Trung.  Construction of two symmetric block designs for (71,21,6),
    Discr. Math. 55 (1985), 327--328
  • Z. Janko, Tran van Trung.  Construction of a new symmetric block design for (78,22,6) with the help of tactical decompositions,
    J. Comb. Theory Ser.A 40 (1985), 451--455
  • Tran van Trung.  On the existence of an infinite family of simple 5-designs,
    Math. Z. 187 (1984), 285--287
  • Z. Janko, Tran van Trung.  Answers to two questions about semi-symmetric designs,
    J. Comb. Theory Ser.A 41 (1986), 276--277
  • Tran van Trung.  The existence of symmetric block designs with parameters (41,16,6) and (66,26,10),
    J. Comb. Theory Ser.A 33 (1982), 201--204
  • Z. Janko, Tran van Trung.  The classification of projective planes of order 9 which possess an involution,
    J. Comb. Theory Ser.A 33 (1982), 65--75
  • Z. Janko, Tran van Trung.  Two new semibiplanes,
    J. Comb. Theory Ser.A 33 (1982), 102--105
  • Z. Janko, Tran van Trung.  Projective planes of order 10 do not have a collineation of order 3,
    J. Reine Angew. Math. 325 (1981), 189--209
  • Z. Janko, Tran van Trung.  Determination of projective planes of order 9 with a non-trivial perspectivity,
    Studia Sci. Math. Hungar. 16 (1981), 119
  • Z. Janko, Tran van Trung.  Projective planes of order 12 do not possess an elation of order 3,
    Studia Sci. Math. Hungar. 16 (1981), 115--118
  • Z. Janko, Tran van Trung.  Projective planes of order 12 do not have a four group as a collineation group,
    J. Comb. Theory Ser.A 32 (1982), 401--404
  • Z. Janko, Tran van Trung.  A generalization of a result of L. Baumert and M. Hall about projective planes of order 12,
    J. Comb. Theory Ser.A 32 (1982), 378--385
  • Z. Janko, Tran van Trung.  Projective planes of order 12 do not have a non-abelian group of order 6 as a collineation group,
    J. Reine Angew. Math. 326 (1981), 152--157
  • Z. Janko, Tran van Trung.  The full collineation group of any projective plane of order 12 is a {2,3}-group,
    Geom. Dedicata 12 (1982), 101--110
  • Z. Janko, Tran van Trung.  On projective planes of order 12 with an automorphism of order 13, Part II,
    Geom. Dedicata 12 (1982), 87--99
  • Z. Janko, Tran van Trung.  On projective planes of order 12 with an automorphism of order 13, Part I,
    Geom. Dedicata 11 (1981), 257--284
  • Tran van Trung.  Plans projectifs d'ordre 16 ayant un groupe de Frobenius d'ordre 34,
    Math. Z. 175 (1980), 97--102
  • Z. Janko, Tran van Trung.  On projective planes of order 12 which have a subplane of order 3,
    J. Comb. Theory Ser.A 29 (1980), 254--256
  • Z. Janko, Tran van Trung.  On projective planes of order twelve and twenty,
    Math. Z. 173 (1980), 199--201
  • Tran van Trung.  Eine Kennzeichnung der endlichen einfachen Gruppe J4 von Janko durch eine 2-lokale Untergruppe ,
    Rend. Sem. Mat. Univ. Padova 62 (1980), 35--45
  • Tran van Trung.  On the ''Monster'' simple group,
    J. Algebra 60 (1979), 559--562
  • Tran van Trung.  A general characterization of the simple group D4(2),
    J. Algebra 60 (1979), 538--545
  • Tran van Trung.  A characterization of the finite simple group 2D4(2) ,
    J. Algebra 60 (1979), 552--558
  • Tran van Trung.  A characterization of the groups D4(2n),
    J. Algebra 60 (1979), 520--537
  • Tran van Trung.  A note on groups with  ''large extraspecial'' subgroups of width 4 ,
    J. Algebra 60 (1979), 563--566
  • Tran van Trung.  The nonexistence of certain type of finite simple group,
    J. Algebra 60 (1979), 546--551
  • Tran van Trung.  Finite simple groups in which the centralizer M of some involution is solvable and the generalized Fitting group of M is extraspecial,
    Arch. Math. 31 (1978), 545--553

 Preprints

  • Point-missing s-resolvale t-designs: Infinite series of 4-designs with constant index  (PDF)
  • A method of construting 2-resolvable t-designs for t=3,4  (PDF)
  • An extending theorem for s-resolvable t-designs  (PDF)
  • On simple 3-designs having 2-resolutions  (PDF)
  • On t-designs and s-resolvable t-designs from hyperovals  (PDF)
  • Recursive constructions for s-resolvable t-designs  (PDF)
  • On existence theorems for simple t-designs  (PDF)
  • Construction of strongly aperiodic logarithmic signatures  (PDF)
  • A recursive construction for simple t-designs using resolutions  (PDF)
  • Simple t-designs: A recursive construction for arbitrary t  (PDF)
  • Construction of 3-designs using (1, σ)-resolution  (PDF)
  • On tight bounds for binary frameproof codes (with C. Guo, D.R.Stinson)  (PDF)
  • Shadow and Shade of Designs 4-(2f+1,6,10)  (with J. Bierbrauer)  (PDF)
  • A new look at an old construction: constructing (simple) 3-designs
     from resolvable 2-designs (with D. R. Stinson, C. M. Swanson)   (PDF)
  • MSTg: Cryptographically strong pseudorandom number
     generator and its realization  (with Pavol Svaba, Pascal Marquardt)  (PDF)
  •   Strongly aperiodic logarithmic signatures  (with Reiner Staszewski)   (PDF)
  • A tight bound for frameproof codes viewed in terms of separating hash families  (PDF)
  • Improved bounds for separating hash families  (with Marjan Bazrafshan)   (PDF)
  • A bound for separating hash families (with Marjan Bazrafshan)  (PDF)
  • Logarithmic signatures for abelian groups and their factorization (with Pavol Svaba, Paul Wolf)   (PDF)
  • On Jacobsthal binary sequences (with S. S. Magliveras, Wandi Wei )   (PDF)
  • Public key cryptosystem MST3: cryptanalysis and realization (with Pavol Svaba)   (PDF)
  • Explicit constructions for perfect hash families (with Sosina Martirosyan)   (PDF)
  • Primitive sets of a lattice and a generalization of Euclidean Algorithm (with S. S. Magliveras and Wandi Wei)   (PDF)
  • On generation of random covers for finite groups (with P. Svaba)   (PDF)
  • A public key cryptosystem based on non-abelian finite groups (with W. Lempken, S.S. Magliveras, Wandi Wei)   (PDF)
  • Roux-type Constructions for Covering Arrays of Strengths Three and Four (with C. Colbourn, S. Martirosyan, R. Walker II)   (PDF)
  • On Minimal Logarithmic Signatures of Finite Groups (with Wolfgang Lempken)   (PDF)
  • On non-polynomial Latin squares (with Otokar Grosek and Peter Horak)   (PDF)
  • Cryptographic primitives based on groups of hidden order (with Wandi Wei, Spyros Magliveras, Frederick Hoffman)  (PDF)
  • On t-Covering Arrays(with Sosina Martirosyan)   (PDF)
  • New Constructions for IPP Codes (with Sosina Martirosyan)  (PDF)
  • On a Class of Traceability Codes (with Sosina Martirosyan)   (PDF)
  • A New Mode of Using All-Or-Nothing Transforms (with V. Canda)  (PDF)
  • Scalable Block Ciphers Based on Feistel-like Structure (with V. Canda)  (PDF)
  • New approaches to designing public key cryptosystems using one-way functions and trap-doors in finite groups (with S. Magliveras and D. Stinson)   (PDF)
  • Symmetric Block Ciphers Based on Group Bases (with V. Canda, T.Horvath and S. Magliveras)  (PDF)
  • Secure Frameproof Codes, Key Distribution Patterns, Group Testing Algorithms and Related Structures (mit D. Stinson and R. Wei)  (PDF)
  • Recursive Constructions for 3-Designs and Resolvable 3-Designs  (PDF)

Students - Editorial Work

Students Supervised

PhD Students

  • Tamas Horvath, PhD (1998)
  • Valer Canda, PhD (2001)
  • Sosina Martirosyan, PhD (2003)
  • Lenka Fibikova, PhD (2003)
  • Marjan Bazrafshan, PhD (2011)
  • Pavol Svaba, PhD (2011)

 

 Diplom (Master) Students

  • Tobias Fleischer, Dip.-Math. (1998)
  • Dirk Schenke, Dipl.-Math. (1998)
  • Rainer Peters, Dipl.-Math. (2002)
  • Andreas Bardeck, Dip.-Math. (2003)
  • Kerstin Schrupke, Dipl.-Math.  (2004)
  • Daniela Jost , Dipl.-Math. (2004)
  • Stephan Schreven, Dipl.-Math. (2005)
  • Jörg Koitka, Dipl.-Math. (2005)
  • Anja Steinhoff, Dipl.-Math. (2005)
  • Philipp Alexander Lankes, Dipl.-Math. (2007)
  • Volker Stachowitz, Dipl.-Math. (2008)
  • Sema Seyhan, Dipl.-Math. (2009)
  • Dominik Linnemann, Dipl.-Math. (2009)
  • Matthias Frewer, Dipl.-Math. (2009)
  • Thomas Drews, Dipl.-Math. (2010)
  • Sebastian Sauer, Dipl.-Math. (2010)
  • Corinne Menne, Dipl.-Math. (2010)
  • Paul Wolf, Dipl.-Math. (2011)
  • Paul Skiba, Dipl.-Math. (2012)
  • Pascal Marquardt, Dipl.-Math. (2012)
  • Jan Tabeck, Dipl.-Math. (2012)
  • Daniel Janiszczak, Dipl.-Math. (2012)

Editorial Work

  • Associate editor of  Journal of Combinatorial Designs :  2000--2013
  • Co-founder of  Journal of Mathematical Cryptology         : 2006--2019
  • Co-founder of Mathematical Cryptology                             : 2020--2022
  • Co-Editor-in-Chief of Bulletin of the Institute of Combinatorics and its Applications  : 2016--

Address

Prof. Dr. Trung van Tran
Institut für Experimentelle Mathematik (IEM)
Fakultät für Mathematik
Universität Duisburg-Essen
Thea-Leymann-Straße 9
45127 Essen
Germany

Tel.: +49-201-183-2396
Email: trung@iem.uni-due.de