Abstract
In this paper, we first prove that b≤ v+t− 1 for an “affine” (α 1,⋯,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” (α 1,⋯,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 (α 1=⋯=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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© 1995 Springer-Verlag Berlin Heidelberg
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Kurosawa, K., Kageyama, S. (1995). New bound for affine resolvable designs and its application to authentication codes. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030844
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DOI: https://doi.org/10.1007/BFb0030844
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