Is it possible to device lightweight (i.e. without asymmetric crypto and PKI; and without third party Trent) provably secure (in the exact security sense) scheme? Were there any attempts? Is it possible to make entity authentication using only one pre-shared secret key without MitM attacks?
Some remarks. By exact security I mean concrete security approach (by Bellare and Rogaway).
By entity authentication I mean to prove that it is me who interacts with device. MAC is not an option because everyone who can intercept my message can pretend that he is me actually.