With the fast development of Internet, the size of routing table in the backbone router continues to grow rapidly. Forwarding Information Base (FIB), which is derived from routing table, is stored in line-card to conduct routing lookup. Since the line-card's memory is limited, it would be worthwhile to compress the FIB for consuming less storage. Therefore, various FIB compression algorithms are proposed [2-7]. However, there is no well-presented mathematical support for the feasibility of the FIB compression solution, nor any mathematical derivation to prove the correctness of these algorithms. To address these problems, we propose a universal mathematical method based on the Group2 theory. By defining a Group representing the Longest Prefix Matching Rule (LPM), the bound of the worst case of FIB compression solution can be figured out. Furthermore, in order to guarantee the ultimate correctness of FIB compression algorithms, Routing Table Equation Test (RTET) is proposed and implemented to verify the equivalence of the two routing tables before and after compression by traversing the 32-bit IP address space.