In the wiretap channel setting, one aims to get information-theoretic privacy
of communicated data based only on the assumption that the channel from sender
to receiver is noisier than the one from sender to adversary. The secrecy
capacity is the optimal (highest possible) rate of a secure scheme, and the
existence of schemes achieving it has been shown. For thirty years the ultimate
and unreached goal has been to achieve this optimal rate with a scheme that is
polynomial-time. (This means both encryption and decryption are proven
polynomial time algorithms.) This paper finally delivers such a scheme. In fact
it does more. Our scheme not only meets the classical notion of security from
the wiretap literature, called MIS-R (mutual information security for random
messages) but achieves the strictly stronger notion of semantic security, thus
delivering more in terms of security without loss of rate
