In cryptography, cipher text is encrypted or encoded text that is unreadable by a human or computer without the proper algorithm to decrypt it into plain text. The impact of erroneous cipher texts on the performance of an encryption system was investigated in IEEE Transactions on Information Forensics and Security (April 2013). For one data encryption system, the probability of receiving an erroneous cipher text is assumed to be b, where 0 < β < 1.

The researchers showed that if an erroneous cipher text occurs, the probability of an error in restoring plain text using the decryption system is .5. When no error occurs in the received cipher text, the probability of an error in restoring plain text using the decryption system is ab, where 0 < a < 1. Use this information to give an expression for the probability of an error in restoring plain text using the decryption system.