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

This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths, when we employ the decoy method. Using the formula, we can guarantee the security parameter for a realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.