  A wiretap protocol is a pair of randomized encoding and decoding functions
such that knowledge of a bounded fraction of the encoding of a message reveals
essentially no information about the message, while knowledge of the entire
encoding reveals the message using the decoder. In this paper we study the
notion of efficiently invertible extractors and show that a wiretap protocol
can be constructed from such an extractor. We will then construct invertible
extractors for symbol-fixing, affine, and general sources and apply them to
create wiretap protocols with asymptotically optimal trade-offs between their
rate (ratio of the length of the message versus its encoding) and resilience
(ratio of the observed positions of the encoding and the length of the
encoding). We will then apply our results to create wiretap protocols for
challenging communication problems, such as active intruders who change
portions of the encoding, network coding, and intruders observing arbitrary
boolean functions of the encoding.
  As a by-product of our constructions we obtain new explicit extractors for a
restricted family of affine sources over large fields (that in particular
generalizes the notion of symbol-fixing sources) which is of independent
interest. These extractors are able to extract the entire source entropy with
zero error.
  Keywords: Wiretap Channel, Extractors, Network Coding, Active Intrusion,
Exposure Resilient Cryptography.
