We show that key-specified interferometer path-length difference modulation (often referred to as coherence modulation), operating in the photon-counting regime with a broadband source, can provide a quantifiably high level of physics-guaranteed security for binary signal transmission. Each signal bit is associated with many photocounts, perhaps numbering in the thousands. Of great importance, the presence of an eavesdropper can be quickly detected. We first review the operation of key-specified coherence modulation at high light levels, illustrating by means of an example its lack of security against attack. We then show, using the same example, that, through the reduction of light intensities to photon-counting levels, a high level of security can be attained. A particular attack on the system is analyzed to demonstrate the quantifiability of the scheme's security, and various remaining research issues are discussed. A potential weakness of the scheme lies in a possible vulnerability to light amplification by an attacker.