NR. 14.7 Encryption 14.7.1 Applications of encryption It is sometimes the case that a sender wishes to send a recipient a message which he wants to keep secret from an eavesdropper. This message, which in its usable form is called plaintext, must be transmitted over a channel to which the eavesdropper is presumed to have access. The process by which the sender and recipient can achieve secrecy is called encryption or encipherment. In encryption, the plaintext is transformed into a message called Figure 14.5 The trellis diagram for the coder of Figure the ciphertext in such a way that the recipient can recover the plaintext from the ciphertext, while the eavesdropper cannot. The transformation of plaintext to ciphertext and back is controlled by one or more strings of symbols or digits called keys. It appears at first sight that the number of candidate paths grows A further use of encryption is for authentication, when it is exponentially with each time-step. However, at time step i the necessary to check that you are communicating with the correct decoder only needs to keep track of the single best path SO far to each person and not an impostor. node; any worse path to that node cannot be part of the overall best path through the node. The number of paths to be remembered 14.7.2 Principles of encryption therefore remains constant and equal to the number of nodes. For each node the decoder must store the best path to that node and the Encryption algorithms have two possible components: substitution, total metric corresponding to that path. By comparing the actual n in which plaintext symbols are mapped to different symbols, and received digits at time-step i + 1 with those corresponding to each transposition, in which the locations of symbols in the ciphertext are possible path on the trellis from step i to step + 1, the decoder altered from the locations of the corresponding symbols in the calculates the additional metric for each path. From these, it selects plaintext. The need for substitution is obvious; many 