用有限局部环Z／2^kZ上m阶斜对称矩阵构作的卡氏验证码

Using skew symmetry matrices over Z/2kZ order m to construct Cartesian authentication code

设R=Z/2kZ(k>1),Wm(R)(m=2v+2≥4)是R上所有m阶斜对称矩阵构成的合同的斜对称矩阵构)={A∈Wm(R)|PAP′=Hr1}是Wm(R)中一切与Hr1集合,Wmr2r2A(R,Hr1r2 Δr2),其中Hr1=Dr1,Dr1=02—r1I(v),Wm成的集合,令F=∪A(R,Hr1r2r20≤r1<r2≤k-1-2—r1I(v)0,v≥1,0≤r1<r2≤k-1.利用F中矩阵构作一个Cartesian验证码,计算其全=2—k-12—r2Δr2-2—r20—部参数.

<Abstrcat>Let R=Z/2kZ,where k>1.Let W(m)(R)be the set of skew symmetrical matrices over R with order m,when m=2v+2≥4.LetWmA(R,H(r1)(r2))=｛A∈Wm(R)|PAP′=H(r1)(r2)｝,and Let F=∪0≤r1<r2≤k-1WmA(R,H(r1)(r2)),wheer H(r1)(r2)=D(1)Δ(r1)=02—(r1)I((v))-2—(r1)I((v))0,Δ(r2)=2—(k-1)2—(r2)-2—(r2)0—,v≥1,0≤r1<r2≤k-1.Using the skew symmetrical matrices in F,the author constructes a cartesian authentication code and compute the parameters of Cartesian authentication code.