Suppose that a huge file (e.g. 50 GB) is replicated and shared between Alice and Bob who are now far apart and are connected only by a communication channel with very low data bandwidth (e.g. 50 Kb/s). Alice and Bob need to check whether their copies are identical. This problem would have been easy if Alice and Bob were able to exchange and compare their copies. However, since Alice and Bob can only communicate over the given low bandwidth channel, they cannot afford sending lots of data over the channel. Devise an efficient protocol that requires Alice and Bob to communicate only avery small amount of data(e.g. 512 bits)in total, and yet allows them to determine whether their copies are identical with high confidence.