Chapter 3.6, Problem 3.80ACA

Encryption systems with erroneous ciphertexts. In cryptography, ciphertext 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 ciphertexts 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 ciphertext is assumed to be {3, where 0 < β < 1. The researchers showed that if an erroneous ciphertext occurs, the probability of an error in restoring plain text using the decryption system is .5. When no error occurs in the received ciphertext, the probability of an error in restoring plain text using the decryption system is a./3, where 0 < α. < 1. Use this information to give an expression for the probability of an error in restoring plain text using the decryption system.