Tran van Trung's Home Page

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Education
Research Topics
Publications
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Students - Editorial Work
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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-(2^f+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

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

Tran van Trung's Home Page

Index

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

Education

Research Topics

Publications

Preprints

Students - Editorial Work

Students Supervised

PhD Students

Diplom (Master) Students

Editorial Work

Address