Abstract
Restricted strong partially balanced t-designs were first formulated by Pei, Li, Wang and Safavi-Naini in investigation of authentication codes with arbitration. In this article, we will prove that splitting authentication codes that are multi-fold perfect against spoofing can be characterized in terms of restricted strong partially balanced t-designs. We will also investigate the existence of restricted strong partially balanced 3-designs RSPBD 3-(v, b, 3 × 2; λ1, λ2, 1, 0)s, and show that there exists an RSPBD 3-(v, b, 3 × 2; λ1, λ2, 1, 0) for any \({v\equiv 9\ (\mbox{{\rm mod}}\ 16)}\) . As its application, we obtain a new infinite class of 3-fold perfect splitting authentication codes.
Similar content being viewed by others
References
Chee Y.M., Zhang X., Zhang H.: Infinite families of optimal splitting authentication codes secure against spoofing attacks of higher order. Adv. Math. Commun. 5, 59–68 (2011)
Du B.: Splitting balanced incomplete block designs with block size 3 × 2. J. Comb. Des. 12, 404–420 (2004)
Du B.: Splitting balanced incomplete block designs. Australas. J. Comb. 31, 287–298 (2005)
Ge G., Miao Y., Wang L.: Combinatorial constructions for optimal splitting authentication codes. SIAM J. Discret. Math. 18, 663–678 (2005)
Hanani H.: On quadruple systems. Can. J. Math. 12, 145–157 (1960)
Hartman A.: The fundamental construction for 3-designs. Discret. Math. 124, 107–132 (1994)
Hartman A., Phelps K.T.: Steiner quadruple systems. In: Dinitz, J.H., Stinson, D.R. (eds) Contemporary Design Theory, pp. 205–240. Wiley, New York (1992)
Hartman A., Phelps K.T.: Combinatorial bounds and characterizations of splitting authentication codes Cryptogr. Commun. 2 173–185 (2010).
Ji L.: An improvement on H design. J. Comb. Des. 17, 25–35 (2009)
Liang M., Du B.: Splitting balanced incomplete block designs with block size 2 × 4. J. Comb. Math. Comb. Comput. 63, 159–172 (2007)
Liang M., Du B.: A new class of splitting 3-designs. Des. Codes Cryptogr. doi:10.1007/s10623-010-9433-5.
Liang M., Du B.: Existence of optimal restricted strong partially balanced designs. Utilitas Math. (to appear).
Mills W.H.: On the covering of triples by quadruple. In: Proceedings of the 5th Southeastern Conference on Combinatorics, Graph Theory and Computing, Florida Atlantic University, Boca Raton, pp. 563–581 (1974).
Mills W.H.: On the existence of H designs. Congr. Numer. 79, 129–141 (1990)
Mohácsy H., Ray-Chaudhuri D.K.: Candelabra systems and designs. J. Stat. Plann. Infer. 106, 419–448 (2002)
Ogata W., Kurosawa K., Stinson D.R., Saido H.: New combinatorial designs and their applications to authentication codes and secret sharing schemes. Discret. Math. 279, 383–405 (2004)
Pei D.: Information-theoretic bounds for authentication codes and block designs. J. Cryptol. 8, 177–188 (1995)
Pei D.: Authentication Codes and Combinatorial Designs. Chapman Hall/CRC, Boca Raton, FL (2006)
Pei D., Li Y., Wang Y., Safavi-Naini R.: Characterization of authentication codes with arbitration. In: Lecture Notes in Computer Science, vol. 1587, pp. 303–313. Springer, Berlin-Heidelberg-New York (1999).
Wang J.: A new class of optimal 3-splitting authentication codes. Des. Codes Cryptogr. 38, 373–381 (2006)
Wang J., Su R.: Further results on the existence of splitting BIBDs and application to authentication codes. Acta Appl. Math. 109, 791–803 (2010)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by W. H. Haemers.
Rights and permissions
About this article
Cite this article
Liang, M., Du, B. A new class of 3-fold perfect splitting authentication codes. Des. Codes Cryptogr. 62, 109–119 (2012). https://doi.org/10.1007/s10623-011-9496-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-011-9496-y
Keywords
- Restricted strong partially balanced t-designs
- t-fold perfect splitting authentication codes
- Candelabra restricted strong partially balanced t-systems