We present a cryptosystem which is complete for the class of probabilistic public-key cryptosystems with bounded error. Besides traditional encryption schemes such as RSA and El Gamal, this class contains probabilistic encryption of Goldwasser-Micali as well as Ajtai-Dwork and NTRU cryptosystems. The latter two are known to make errors with ... more >>>

Three fundamental results of Levin involve algorithms or reductions
whose running time is exponential in the length of certain programs. We study the
question of whether such dependency can be made polynomial.

(1) Levin's ``optimal search algorithm'' performs at most a constant factor more slowly
than any other fixed ... more >>>