New bound for affine resolvable designs and its application to authentication codes

  • Kaoru Kurosawa
  • Sanpei Kageyama
Session 5B: Combinatorial Designs
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


In this paper, we first prove that b≤ v+t− 1 for an “affine” (α1,⋯,αt)-resolvable design, where b denotes the number of blocks, v denotes the number of symbols and t denotes the number of classes. Our inequality is an opposite to the well known inequality b≥v+t−1 for a “balanced” (α1,⋯,αt)-resolvable design. Next, we present a more tight lower bound on the size of keys than before for authentication codes with arbitration by applying our inequality. Although this model of authentication codes is very important in practice, it has been too complicated to be analyzed. We show that the receiver's key has a structure of an affine α-resolvable design (α1=⋯=αt=α) and v corresponds to the number of keys under a proper assumption. (Note that our inequality is a lower bound on v.)


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Kaoru Kurosawa
    • 1
  • Sanpei Kageyama
    • 2
  1. 1.Department of Electrical and Electronic EngineeringTokyo Institute of TechnologyTokyoJapan
  2. 2.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan

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