Potential weaknesses in public key cryptosystem design and use are identified with emphasis on a particular vulnerability resulting from the encryption of ordinary natural language plaintext. This weakness occurs when an insufficiently long block length is used to encrypt low entropy natural language and ordinary numeric plaintext rendered in 8-bit character sets such as ASCII or EBCDIC. A computer-assisted, semi-exhaustive chosen plaintext attack is defined and shown to defeat such systems. Several methods are suggested for thwarting such attacks by maximizing input plaintext entropy prior to encryption.