Abstract
We present a cryptosystem which is complete for the class of probabilistic public-key cryp- tosystems 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 some small positive probability. To our best knowledge, no complete public-key cryptosystem has been known before, whether encryp- tion/decryption errors are allowed or not. At the same time, other complete primitives such as Levin's universal one-way function (1) have been known for a long time.
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