American Institute of Mathematical Sciences

Advanced
February  2011, 5(1): 59-68. doi: 10.3934/amc.2011.5.59

Infinite families of optimal splitting authentication codes secure against spoofing attacks of higher order

Yeow Meng Chee 1, , Xiande Zhang 1, and  Hui Zhang 2,

1. 

Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Singapore, Singapore
2. 

Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China

Received  May 2010 Revised  November 2010 Published  February 2011

We consider the problem of constructing optimal authentication codes with splitting. New infinite families of such codes are obtained. In particular, we establish the first known infinite family of optimal authentication codes with splitting that are secure against spoofing attacks of order two.
Keywords: splitting t-design., splitting authentication code, Authentication code.
Mathematics Subject Classification: Primary: 05B30, 94A60, 94C30; Secondary: 11T2.
Citation: Yeow Meng Chee, Xiande Zhang, Hui Zhang. Infinite families of optimal splitting authentication codes secure against spoofing attacks of higher order. Advances in Mathematics of Communications, 2011, 5 (1) : 59-68. doi: 10.3934/amc.2011.5.59
References:
[1]

A. E. Brouwer, A. Schrijver and H. Hanani, Group divisible designs with block-size four,, Discrete Math., 20 (1977), 1.  doi: 10.1016/0012-365X(77)90037-1.  Google Scholar

[2]

B. Du, Splitting balanced incomplete block designs with block size $3\times 2$,, J. Combin. Des. \textbf{12} (2004), 12 (2004), 404.  doi: 10.1002/jcd.20025.  Google Scholar

[3]

G. Ge, Y. Miao and L. Wang, Combinatorial constructions for optimal splitting authentication codes,, SIAM J. Discrete Math., 18 (2005), 663.  doi: 10.1137/S0895480103435469.  Google Scholar

[4]

H. Hanani, Balanced incomplete block designs and related designs,, Discrete Math., 11 (1975), 255.  doi: 10.1016/0012-365X(75)90040-0.  Google Scholar

[5]

A. Hartman, The fundamental construction for $3$-designs,, Discrete Math., 124 (1994), 107.  doi: 10.1016/0012-365X(92)00055-V.  Google Scholar

[6]

Q. X. Huang, On the decomposition of $K\sb n$ into complete $m$-partite graphs,, J. Graph Theory, 15 (1991), 1.  doi: 10.1002/jgt.3190150102.  Google Scholar

[7]

M. Huber, Combinatorial bounds and characterizations of splitting authentication codes,, Crypt. Commun., 2 (2010), 173.  doi: 10.1007/s12095-010-0020-4.  Google Scholar

[8]

L. Ji, An improvement on $H$ design,, J. Combin. Des., 17 (2009), 25.  doi: 10.1002/jcd.20184.  Google Scholar

[9]

K. Kurosawa and S. Obana, Combinatorial bounds on authentication codes with arbitration,, Des. Codes Crypt., 22 (2001), 265.  doi: 10.1023/A:1008398306907.  Google Scholar

[10]

J. L. Massey, Cryptography, a selective survey,, in, (1986), 3.   Google Scholar

[11]

W. H. Mills, On the existence of $H$ designs,, in, 79 (1990), 129.   Google Scholar

[12]

W. Ogata, K. Kurosawa, D. R. Stinson and H. Saido, New combinatorial designs and their applications to authentication codes and secret sharing schemes,, Discrete Math., 279 (2004), 383.  doi: 10.1016/S0012-365X(03)00283-8.  Google Scholar

[13]

G. J. Simmons, A game theory model of digital message authentication,, Congr. Numer., 34 (1982), 413.   Google Scholar

[14]

G. J. Simmons, Message authentication: a game on hypergraphs,, Congr. Numer., 45 (1984), 161.   Google Scholar

[15]

G. J. Simmons, Authentication theory/coding theory,, in, (1985), 411.  doi: 10.1007/3-540-39568-7_32.  Google Scholar

[16]

G. J. Simmons, Message authentication with arbitration of transmitter/receiver disputes,, in, (1987), 151.   Google Scholar

[17]

G. J. Simmons, A Cartesian product construction for unconditionally secure authentication codes that permit arbitration,, J. Cryptology, 2 (1990), 77.  doi: 10.1007/BF00204449.  Google Scholar

[18]

G. J. Simmons, A survey of information authentication,, in, (1992), 379.   Google Scholar

[19]

J. Wang, A new class of optimal 3-splitting authentication codes,, Des. Codes Crypt., 38 (2006), 373.  doi: 10.1007/s10623-005-1501-x.  Google Scholar

[20]

J. Wang and R. Su, Further results on the existence of splitting BIBDs and application to authentication codes,, Acta Appl. Math., 109 (2010), 791.  doi: 10.1007/s10440-008-9346-8.  Google Scholar

[21]

R. M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms,, J. Combin. Theory Ser. A, 13 (1972), 220.  doi: 10.1016/0097-3165(72)90028-3.  Google Scholar

[22]

R. M. Wilson, An existence theory for pairwise balanced designs. II. The structure of PBD-closed sets and the existence conjectures,, J. Combin. Theory Ser. A, 13 (1972), 246.  doi: 10.1016/0097-3165(72)90029-5.  Google Scholar

[23]

R. M. Wilson, Decompositions of complete graphs into subgraphs isomorphic to a given graph,, in, (1976), 647.   Google Scholar

show all references

References:
[1]

A. E. Brouwer, A. Schrijver and H. Hanani, Group divisible designs with block-size four,, Discrete Math., 20 (1977), 1.  doi: 10.1016/0012-365X(77)90037-1.  Google Scholar

[2]

B. Du, Splitting balanced incomplete block designs with block size $3\times 2$,, J. Combin. Des. \textbf{12} (2004), 12 (2004), 404.  doi: 10.1002/jcd.20025.  Google Scholar

[3]

G. Ge, Y. Miao and L. Wang, Combinatorial constructions for optimal splitting authentication codes,, SIAM J. Discrete Math., 18 (2005), 663.  doi: 10.1137/S0895480103435469.  Google Scholar

[4]

H. Hanani, Balanced incomplete block designs and related designs,, Discrete Math., 11 (1975), 255.  doi: 10.1016/0012-365X(75)90040-0.  Google Scholar

[5]

A. Hartman, The fundamental construction for $3$-designs,, Discrete Math., 124 (1994), 107.  doi: 10.1016/0012-365X(92)00055-V.  Google Scholar

[6]

Q. X. Huang, On the decomposition of $K\sb n$ into complete $m$-partite graphs,, J. Graph Theory, 15 (1991), 1.  doi: 10.1002/jgt.3190150102.  Google Scholar

[7]

M. Huber, Combinatorial bounds and characterizations of splitting authentication codes,, Crypt. Commun., 2 (2010), 173.  doi: 10.1007/s12095-010-0020-4.  Google Scholar

[8]

L. Ji, An improvement on $H$ design,, J. Combin. Des., 17 (2009), 25.  doi: 10.1002/jcd.20184.  Google Scholar

[9]

K. Kurosawa and S. Obana, Combinatorial bounds on authentication codes with arbitration,, Des. Codes Crypt., 22 (2001), 265.  doi: 10.1023/A:1008398306907.  Google Scholar

[10]

J. L. Massey, Cryptography, a selective survey,, in, (1986), 3.   Google Scholar

[11]

W. H. Mills, On the existence of $H$ designs,, in, 79 (1990), 129.   Google Scholar

[12]

W. Ogata, K. Kurosawa, D. R. Stinson and H. Saido, New combinatorial designs and their applications to authentication codes and secret sharing schemes,, Discrete Math., 279 (2004), 383.  doi: 10.1016/S0012-365X(03)00283-8.  Google Scholar

[13]

G. J. Simmons, A game theory model of digital message authentication,, Congr. Numer., 34 (1982), 413.   Google Scholar

[14]

G. J. Simmons, Message authentication: a game on hypergraphs,, Congr. Numer., 45 (1984), 161.   Google Scholar

[15]

G. J. Simmons, Authentication theory/coding theory,, in, (1985), 411.  doi: 10.1007/3-540-39568-7_32.  Google Scholar

[16]

G. J. Simmons, Message authentication with arbitration of transmitter/receiver disputes,, in, (1987), 151.   Google Scholar

[17]

G. J. Simmons, A Cartesian product construction for unconditionally secure authentication codes that permit arbitration,, J. Cryptology, 2 (1990), 77.  doi: 10.1007/BF00204449.  Google Scholar

[18]

G. J. Simmons, A survey of information authentication,, in, (1992), 379.   Google Scholar

[19]

J. Wang, A new class of optimal 3-splitting authentication codes,, Des. Codes Crypt., 38 (2006), 373.  doi: 10.1007/s10623-005-1501-x.  Google Scholar

[20]

J. Wang and R. Su, Further results on the existence of splitting BIBDs and application to authentication codes,, Acta Appl. Math., 109 (2010), 791.  doi: 10.1007/s10440-008-9346-8.  Google Scholar

[21]

R. M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms,, J. Combin. Theory Ser. A, 13 (1972), 220.  doi: 10.1016/0097-3165(72)90028-3.  Google Scholar

[22]

R. M. Wilson, An existence theory for pairwise balanced designs. II. The structure of PBD-closed sets and the existence conjectures,, J. Combin. Theory Ser. A, 13 (1972), 246.  doi: 10.1016/0097-3165(72)90029-5.  Google Scholar

[23]

R. M. Wilson, Decompositions of complete graphs into subgraphs isomorphic to a given graph,, in, (1976), 647.   Google Scholar

[1]

Masaaki Harada, Ethan Novak, Vladimir D. Tonchev. The weight distribution of the self-dual $[128,64]$ polarity design code. Advances in Mathematics of Communications, 2016, 10 (3) : 643-648. doi: 10.3934/amc.2016032
[2]

Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1
[3]

Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003
[4]

Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45
[5]

D. R. Stinson. Unconditionally secure chaffing and winnowing with short authentication tags. Advances in Mathematics of Communications, 2007, 1 (2) : 269-280. doi: 10.3934/amc.2007.1.269
[6]

Claude Carlet, Juan Carlos Ku-Cauich, Horacio Tapia-Recillas. Bent functions on a Galois ring and systematic authentication codes. Advances in Mathematics of Communications, 2012, 6 (2) : 249-258. doi: 10.3934/amc.2012.6.249
[7]

Iris Anshel, Derek Atkins, Dorian Goldfeld, Paul E. Gunnells. Ironwood meta key agreement and authentication protocol. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020073
[8]

V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511
[9]

Yunwen Liu, Longjiang Qu, Chao Li. New constructions of systematic authentication codes from three classes of cyclic codes. Advances in Mathematics of Communications, 2018, 12 (1) : 1-16. doi: 10.3934/amc.2018001
[10]

Jie Xu, Lanjun Dang. An efficient RFID anonymous batch authentication protocol based on group signature. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1489-1500. doi: 10.3934/dcdss.2019102
[11]

Olof Heden. The partial order of perfect codes associated to a perfect code. Advances in Mathematics of Communications, 2007, 1 (4) : 399-412. doi: 10.3934/amc.2007.1.399
[12]

Selim Esedoḡlu, Fadil Santosa. Error estimates for a bar code reconstruction method. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1889-1902. doi: 10.3934/dcdsb.2012.17.1889
[13]

Sascha Kurz. The $[46, 9, 20]_2$ code is unique. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020074
[14]

Yunmei Chen, Xianqi Li, Yuyuan Ouyang, Eduardo Pasiliao. Accelerated bregman operator splitting with backtracking. Inverse Problems & Imaging, 2017, 11 (6) : 1047-1070. doi: 10.3934/ipi.2017048
[15]

Eskil Hansen, Alexander Ostermann. Dimension splitting for time dependent operators. Conference Publications, 2009, 2009 (Special) : 322-332. doi: 10.3934/proc.2009.2009.322
[16]

M. Delgado Pineda, E. A. Galperin, P. Jiménez Guerra. MAPLE code of the cubic algorithm for multiobjective optimization with box constraints. Numerical Algebra, Control & Optimization, 2013, 3 (3) : 407-424. doi: 10.3934/naco.2013.3.407
[17]

Andrew Klapper, Andrew Mertz. The two covering radius of the two error correcting BCH code. Advances in Mathematics of Communications, 2009, 3 (1) : 83-95. doi: 10.3934/amc.2009.3.83
[18]

Masaaki Harada, Takuji Nishimura. An extremal singly even self-dual code of length 88. Advances in Mathematics of Communications, 2007, 1 (2) : 261-267. doi: 10.3934/amc.2007.1.261
[19]

José Gómez-Torrecillas, F. J. Lobillo, Gabriel Navarro. Information--bit error rate and false positives in an MDS code. Advances in Mathematics of Communications, 2015, 9 (2) : 149-168. doi: 10.3934/amc.2015.9.149
[20]

Jorge P. Arpasi. On the non-Abelian group code capacity of memoryless channels. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020058

2018 Impact Factor: 0.879

Tools

Metrics

  • PDF downloads (35)
  • HTML views (0)
  • Cited by (5)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences