We present attacks against the McEliece Public-Key Cryptosystem, the Atjai-Dwork Public-Key Cryptosystem, and variants of those systems. Most of these systems base their security on the apparent intractability of one or more problems. The attacks we present do not violate the intractability of the underlying problems, but instead obtain information about the private key or plaintext by watching the reaction of someone decrypting a given ciphertext with the private key. In the case of the McEliece system, we must repeat the attack for each ciphertext we wish to decrypt, whereas for the Ajtai-Dwork system, we are able to recover the private key.

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