Security analysis of the decoy method with the Bennett-Brassard 1984 protocol for finite key lengths

First, this paper provides the sacrifice bit length with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the method, we can guarantee the security parameter for realizable quantum key distribution system. The generated key rates with finite key lengths are numerically evaluated. Second, the proposed method can perfectly estimate the additional channel parameters for decoy method in the asymptotic limit whereas existing methods only estimated it partially.