Analysis for device independent quantum key distribution based on the law of large number

Measuring device-independent quantum key distribution scheme can remove all detectors´ side-channel flaw, combined with decoy state program to achieve absolute security of quantum key distribution. In this paper, the statistical law of large numbers fluctuate limited key length measuring device-independent quantum key distribution scheme in single-photon counting rate and BER (Bit Error Rate) were analyzed, and the key length of the single-photon N = 10⁶ ~ 10¹² counting rate and the key generation rate simulation were performed. Simulation results show that: in the optical fiber transmission, with decreasing key length 300km, the secure transmission distance, decreased respectively to 260km (N = 10¹⁰) and 75km (N = 10⁶). When N = 10¹², secure transmission distance is reached at 295km, close to the theoretical limit.