  A symmetric device-independent quantum key distribution (DIQKD) protocol is
proposed in this paper, with Holevo limit and subadditivity of von Neumann
entropy, one can bound Eve's ability with collective attack. Together with
symmetry of this protocol, the state Eve prepared for Alice and Bob, and at the
same time, her eavesdropping on Alice's and Bob's measurements can be
definitely inferred at the assumption that Eve aims at maximizing her
information gain. The optimal state under this circumstance can be solely
bounded with Alice and Bob's statistical results on the quantity of
Clauser-Horne-Shimony-Holt (CHSH) polynomial $S$, that is, our symmetric DIQKD
has the same secure basis as that of Ekert91 protocol.
