Time-bin encoding is more favorable in fiber-based implementation of quantum key distribution (QKD) than polarization encoding as it avoids issues inherent for polarization encoding, such as birefringence, caused by optical fibers. QKD only with passive devices is desirable to prevent side-channel attacks possible in the case of use of active devices such as modulators. The Bennett-Brassard 1984 (BB84) protocol is a strong candidate for an implementation with satisfying these; it can be implemented using time bins with a passive delayed interferometer that inevitably generates "satellite time bins", two pulses outside the phase-interference timing. Although time-bin encoding BB84 has been frequently demonstrated, there is no consensus whether satellite time bins can be used to extract a key. Besides, there is no security proof for either case. Here, we prove the security of time-bin encoding BB84 protocol with a passive delayed interferometer and threshold detectors. If satellite time bins are used for key generation, we show that an additional operation is necessary for security. The result is not limited only to BB84 but can be applied to Bennett-Brassard-Mermin 1992 and quantum conference key agreement based on time bins.
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