利用有限域上辛几何构作一类Cartesian认证码

设〈v

Construction of Cartesian authentication code from symplectic geometry

Let〈v1,v2 〉be a 2-dimensional totally isotropic subspace, Po be a fixed subspace of type (m0,s0)with v1,v2〉 Po 〈v1,v2〉⊥in 2v-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 Po. The set of encoding rules E is the setof the subspaces of type (3,1) which contain 〈v1,v2〉and are not orthogonal to v2. The set of massages X is the set of the subspaces of type (2s+2,s) which contain 〈v1,v2〉intersect Po 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.