Construction Of Authentication Codes With Arbitration From The Geometry Of Singular Classical Groups

This paper construct two new authentication codes with arbitration from singular symplectic geomrtry and singular pseudo- symplectic geometry .The contents are arranged as below:Construction 1: Assume that n = 2ν+l,ν≥4, 1≤sq^{( 2ν+l)}, and U∩E=2ν+1>, then U^⊥is a subspace of type ( 2ν-r +k,t-r,l).Let the set of source states S={ s | s is a subspace of type ( 2t -r+k, t - r,k) and 1≤k ⊥};the set of transmitter's encoding rules E_T={ e_T | e_T is a subspace of type ( 2r + 1,r,1)and U (?) e_T };the set of receiver's decoding rules E_R={ e_R| e_R is a s -dimensional subspace in the singular pseudo-symplectic space F_q^(2ν+l)and U + e_R is a subspace of type ( r + s+1 ,s,1)} ;the set of messages M ={m |m is a subspace of type( 2t +k, t , k )and U (?) m };Define the encoding map f : S×E_T→M,( s ,e_T )m=s+e_T;The decoding map:Construction 2: Assume that n = 2ν+1+l,1≤rq^(2ν+1+l), then P^⊥is a subspace of type ( 2ν- r +1+l, 2(ν- r)+1,ν-r, 1 , l ). Let Q =< e_2ν+2>, the set of source states S={ s|sis a subspace of type ( r -1 +k, 0 , 0 , 0 , k ) and 1≤k T={ e_T | e_T is a subspace of type( 2t +2, 2t +1, t , 1, 1) and e_T∩P=Q, e_T (?) P^⊥};the set of receiver's decoding rules E R={ e R| e R is a subspace of type ( 2t -1, 2( t -1)+1, t -1, 1, 0),e R(?) P^⊥};the set of messages M ={ m | m is a subspace of type( r + 2t +k, 2t +1 , t , 1, k ) and m∩P is a subspace of type ( r -1 +k, 0, 0, 0 ,k ) , Q (?)m (?) P^⊥};Define the encoding map f : S×ET→M,( s ,eT )m=s+eT; The decoding map g : M×E_R→S∪{reject} It prove the above two six tuples( S , E_T ,E_R,M,f,g)are authentication codes with arbitration, and compute the parameters of the codes and the probabilities of success for different type of deceptions, respectively.