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From skew-cyclic codes to asymmetric quantum codes
Infinite families of optimal splitting authentication codes secure against spoofing attacks of higher order
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 |
References:
[1] |
A. E. Brouwer, A. Schrijver and H. Hanani, Group divisible designs with block-size four, Discrete Math., 20 (1977), 1-10.
doi: 10.1016/0012-365X(77)90037-1. |
[2] |
B. Du, Splitting balanced incomplete block designs with block size $3\times 2$, J. Combin. Des. 12 (2004), 404-420.
doi: 10.1002/jcd.20025. |
[3] |
G. Ge, Y. Miao and L. Wang, Combinatorial constructions for optimal splitting authentication codes, SIAM J. Discrete Math., 18 (2005), 663-678.
doi: 10.1137/S0895480103435469. |
[4] |
H. Hanani, Balanced incomplete block designs and related designs, Discrete Math., 11 (1975), 255-369.
doi: 10.1016/0012-365X(75)90040-0. |
[5] |
A. Hartman, The fundamental construction for $3$-designs, Discrete Math., 124 (1994), 107-132.
doi: 10.1016/0012-365X(92)00055-V. |
[6] |
Q. X. Huang, On the decomposition of $K\sb n$ into complete $m$-partite graphs, J. Graph Theory, 15 (1991), 1-6.
doi: 10.1002/jgt.3190150102. |
[7] |
M. Huber, Combinatorial bounds and characterizations of splitting authentication codes, Crypt. Commun., 2 (2010), 173-185.
doi: 10.1007/s12095-010-0020-4. |
[8] |
L. Ji, An improvement on $H$ design, J. Combin. Des., 17 (2009), 25-35.
doi: 10.1002/jcd.20184. |
[9] |
K. Kurosawa and S. Obana, Combinatorial bounds on authentication codes with arbitration, Des. Codes Crypt., 22 (2001), 265-281.
doi: 10.1023/A:1008398306907. |
[10] |
J. L. Massey, Cryptography, a selective survey, in "Digital Communications '85: Proceedings of the Second Tirrenia International Workshop on Digital Communications'' (eds. E. Biglieri and G. Prati), Elsevier, (1986), 3-25. |
[11] |
W. H. Mills, On the existence of $H$ designs, in "Proceedings of the Twenty-first Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1990),'' 79 (1990), 129-141. |
[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), 383-405.
doi: 10.1016/S0012-365X(03)00283-8. |
[13] |
G. J. Simmons, A game theory model of digital message authentication, Congr. Numer., 34 (1982), 413-424. |
[14] |
G. J. Simmons, Message authentication: a game on hypergraphs, Congr. Numer., 45 (1984), 161-192. |
[15] |
G. J. Simmons, Authentication theory/coding theory, in "Advances in Cryptology - CRYPTO '84'' (eds. G.R. Blakely and D. Chaum), Springer-Verlag, (1985), 411-432.
doi: 10.1007/3-540-39568-7_32. |
[16] |
G. J. Simmons, Message authentication with arbitration of transmitter/receiver disputes, in "Advances in Cryptology - {EUROCRYPT} '87,'' Springer-Verlag, (1987), 151-165. |
[17] |
G. J. Simmons, A Cartesian product construction for unconditionally secure authentication codes that permit arbitration, J. Cryptology, 2 (1990), 77-104.
doi: 10.1007/BF00204449. |
[18] |
G. J. Simmons, A survey of information authentication, in "Contemporary Cryptology - The Science of Information Integrity ''(ed. G.J. Simmons), IEEE Press, (1992), 379-419. |
[19] |
J. Wang, A new class of optimal 3-splitting authentication codes, Des. Codes Crypt., 38 (2006), 373-381.
doi: 10.1007/s10623-005-1501-x. |
[20] |
J. Wang and R. Su, Further results on the existence of splitting BIBDs and application to authentication codes, Acta Appl. Math., 109 (2010), 791-803.
doi: 10.1007/s10440-008-9346-8. |
[21] |
R. M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms, J. Combin. Theory Ser. A, 13 (1972), 220-245.
doi: 10.1016/0097-3165(72)90028-3. |
[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), 246-273.
doi: 10.1016/0097-3165(72)90029-5. |
[23] |
R. M. Wilson, Decompositions of complete graphs into subgraphs isomorphic to a given graph, in "Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975),'' Winnipeg, Man., (1976), 647-659. |
show all references
References:
[1] |
A. E. Brouwer, A. Schrijver and H. Hanani, Group divisible designs with block-size four, Discrete Math., 20 (1977), 1-10.
doi: 10.1016/0012-365X(77)90037-1. |
[2] |
B. Du, Splitting balanced incomplete block designs with block size $3\times 2$, J. Combin. Des. 12 (2004), 404-420.
doi: 10.1002/jcd.20025. |
[3] |
G. Ge, Y. Miao and L. Wang, Combinatorial constructions for optimal splitting authentication codes, SIAM J. Discrete Math., 18 (2005), 663-678.
doi: 10.1137/S0895480103435469. |
[4] |
H. Hanani, Balanced incomplete block designs and related designs, Discrete Math., 11 (1975), 255-369.
doi: 10.1016/0012-365X(75)90040-0. |
[5] |
A. Hartman, The fundamental construction for $3$-designs, Discrete Math., 124 (1994), 107-132.
doi: 10.1016/0012-365X(92)00055-V. |
[6] |
Q. X. Huang, On the decomposition of $K\sb n$ into complete $m$-partite graphs, J. Graph Theory, 15 (1991), 1-6.
doi: 10.1002/jgt.3190150102. |
[7] |
M. Huber, Combinatorial bounds and characterizations of splitting authentication codes, Crypt. Commun., 2 (2010), 173-185.
doi: 10.1007/s12095-010-0020-4. |
[8] |
L. Ji, An improvement on $H$ design, J. Combin. Des., 17 (2009), 25-35.
doi: 10.1002/jcd.20184. |
[9] |
K. Kurosawa and S. Obana, Combinatorial bounds on authentication codes with arbitration, Des. Codes Crypt., 22 (2001), 265-281.
doi: 10.1023/A:1008398306907. |
[10] |
J. L. Massey, Cryptography, a selective survey, in "Digital Communications '85: Proceedings of the Second Tirrenia International Workshop on Digital Communications'' (eds. E. Biglieri and G. Prati), Elsevier, (1986), 3-25. |
[11] |
W. H. Mills, On the existence of $H$ designs, in "Proceedings of the Twenty-first Southeastern Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1990),'' 79 (1990), 129-141. |
[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), 383-405.
doi: 10.1016/S0012-365X(03)00283-8. |
[13] |
G. J. Simmons, A game theory model of digital message authentication, Congr. Numer., 34 (1982), 413-424. |
[14] |
G. J. Simmons, Message authentication: a game on hypergraphs, Congr. Numer., 45 (1984), 161-192. |
[15] |
G. J. Simmons, Authentication theory/coding theory, in "Advances in Cryptology - CRYPTO '84'' (eds. G.R. Blakely and D. Chaum), Springer-Verlag, (1985), 411-432.
doi: 10.1007/3-540-39568-7_32. |
[16] |
G. J. Simmons, Message authentication with arbitration of transmitter/receiver disputes, in "Advances in Cryptology - {EUROCRYPT} '87,'' Springer-Verlag, (1987), 151-165. |
[17] |
G. J. Simmons, A Cartesian product construction for unconditionally secure authentication codes that permit arbitration, J. Cryptology, 2 (1990), 77-104.
doi: 10.1007/BF00204449. |
[18] |
G. J. Simmons, A survey of information authentication, in "Contemporary Cryptology - The Science of Information Integrity ''(ed. G.J. Simmons), IEEE Press, (1992), 379-419. |
[19] |
J. Wang, A new class of optimal 3-splitting authentication codes, Des. Codes Crypt., 38 (2006), 373-381.
doi: 10.1007/s10623-005-1501-x. |
[20] |
J. Wang and R. Su, Further results on the existence of splitting BIBDs and application to authentication codes, Acta Appl. Math., 109 (2010), 791-803.
doi: 10.1007/s10440-008-9346-8. |
[21] |
R. M. Wilson, An existence theory for pairwise balanced designs. I. Composition theorems and morphisms, J. Combin. Theory Ser. A, 13 (1972), 220-245.
doi: 10.1016/0097-3165(72)90028-3. |
[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), 246-273.
doi: 10.1016/0097-3165(72)90029-5. |
[23] |
R. M. Wilson, Decompositions of complete graphs into subgraphs isomorphic to a given graph, in "Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975),'' Winnipeg, Man., (1976), 647-659. |
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