Authentication Theory/Coding Theory

We consider a communications scenario in which a transmitter attempts to inform a remote receiver of the state of a source by sending messages through an imperfect communications channel. There are two fundamentally different ways in which the receiver can end up being misinformed. The channel may be noisy so that symbols in the transmitted message can be received in error, or the channel may be under the control of an opponent who can either deliberately modify legitimate messages or else introduce fraudulent ones to deceive the receiver, i.e., what Wyner has called an "active wiretapper" [1]. The device by which the receiver improves his chances of detecting error (deception) is the same in either case: the deliberate introduction of redundant information into the transmitted message. The way in which this redundant information is introduced and used, though, is diametrically opposite in the two cases.For a statistically described noisy channel, coding theory is concerned with schemes (codes) that introduce redundancy in such a way that the most likely alterations to the encoded messages are in some sense close to the code they derive from. The receiver can then use a maximum likelihood detector to decide which (acceptable) message he should infer as having been transmitted from the (possibly altered) code that was received. In other words, the object in coding theory is to cluster the most likely alterations of an acceptable code as closely as possible (in an appropriate metric) to the code itself, and disjoint from the corresponding clusters about other acceptable codes.