This paper proposes a new group signature scheme derived from a proxy signature scheme which can solve the above problems,and the order of cycle group adopted by this scheme is a public parameter,and the length of group public key is fixed.

The idea making use of producing matrix on the cycle group,this paper has discussed the property about R-grade cycle matrix and the question about R-grade cycle matrix diagonalization,brought to light the relations between one type diagonalization similar matrix and R-grade cycle matrix.

It is prove that groups of order p2 can be divided into two kinds in the isomorphism sense:(1) cycle group;(2)commutative group which can be written as a product of two cycle proper-subgroup of order p.