由PG(n,q)构造的一类Cartesian认证码

A Class of Cartesian Athentication Codes from PG(n,q)

设P为域GF(q)上的n(n≥3)维射影空间PG(n,q)中的一个点,L是PG(n,q)中过P的一条线。取包含L的超平面组成的集合为信源集S,与L的交为{P}的超平面组成的集合为编码规则集E。与L的交为{P}的n-2-子空间组成的集合为信息集M。对任意π1∈S,π2∈E,定义f(π1,π2)=π1∩π2,得到一类Cartesian认证码,并计算了这个码的参数。假设编码规则按照一种均匀概率分布被选取,则成功模仿攻击的概率PI和成功替换攻击的概率PS也被计算。

Let P be a point in projective space PG（n,q） over GF（q）,L be a line through P in PG（n,q）.Let S be the source set composed of hyperplanes through L,E be the encode rules set composed of hyperplanes which intersect with L at P,M be the message set composed of n-2-subspaces which intersect with L at P.For any π1∈S,π2∈E,define f（π1,π2）=π1∩π2.A class of Cartesian authentication codes is presented.The parameters of these codes is computed.Assume that the encoding rules are chosen according to a uniform probability distribution,the largest probabilities of a successful impersonation attack PI and the largest probabilities of a successful substitution attack PS of these codes are also computed.