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

KUROSAWA Kaoru, KAGEYAMA Sanpei

本論文では、まず、"affine"(α_1,…,α_t)-resolvable designにおいて、b≦v+t-1が成り立つことを示す。ただし、bはブロック数、vはシンボル数、tはクラスの数を表す。この不等式は、"balanced" (α_1,…,α_t)-resolvable designにおいてよく知られているb≧u+t-1という不等式と、対をなすものである。次に、この不等式を調停者有り認証系に応用し、従来より厳しい鍵サイズの下限を示す。より具体的には、ある適当な仮定のもとで、受信者の鍵がaffine α-resolvable design (α_1=…=α_t=α)の構造を有し、vが鍵の数に対応することを示している。
In this paper, we first prove that b≦v+t-1 for an "affine" (α_1,…,α_t)-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,…,α_t)-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=…=α_t=α) and v corresponds to the number of keys under a proper assumption. (Note that, our inequality is a lower bound on v.)

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

Search this article

Description

Journal

References(19)*help

Keywords

Details 詳細情報について

Export

Report a problem