Construction of Cartesian authentication code from symplectic geometry
Wang Chun-sen · Ha'erbin gongye daxue xuebao · 2001
Letv1,v2be a 2-dimensional totally isotropic subspace, P0 be a fixed subspace of type(m0,s0) with v1 , v2 C P0 c v1 , v2 in 2 v -dimensional symplectic space. The set of source states S is the set of subspaces of type (2s + 1 , s -1) containing v1 ,v2 and contained in P0. The set of encoding rules E is the set of the subspaces of type(3 ,l) which contain v1 ,v2 and are not orthogonal toy2. The set of massages X is the set of the subspaces of type (2s +2,s) which contain v1 ,v2 intersect P0 at a subspace of type (2s + 1 ,s -1) and are not orthogonal to v2. We construct a class of Cartesian authentication code by defining s + e as the message for any s S and e E. Its size parameters are computed. Moreover, assume that the encoding rules are chosen according to a uniform probability distribution, the probability of a successful impersonation attack PI and that of a successful substitution attack Ps are computed.