Secure Relativistic Bit Commitment with Fixed Channel Capacity

Special relativity can be useful for secure bit commitment when mutually mistrustful parties Alice and Bob control two separated laboratories. Kent has proposed two relativistic bit commitment protocols, RBC1 and RBC2. However, RBC1 has a severe practical problem, as its implementation requires channel capacity exponentially increasing in time. RBC2 solves the problem by combining the technique developed by Rudich with RBC1, but it is somewhat complicated. Therefore, we improve RBC1 by adding a way of random choice such that the improved protocol just needs fixed capacity channel and is simpler than RBC2. Analysis shows that the improved protocol, named RBC3, is valid and secure.