91Ó°ÊÓ

Alice and Bob communicate securely every day. Eve knows the parameters \(p\) and \(g\) of the Diffie-Hellman algorithm they use to choose their daily Rijndael keys. The prime modulus \(p\) is so large that Eve cannot solve discrete logarithm problems modulo \(p\). She has recorded all messages passing between them, including every \(y_{A}, y_{B}\) and the Rijndaelenciphered traffic. She notices that Alice's random number generator must be defective, since Alice sends the same \(y_{A}\) every day. However, Bob uses a new \(y_{B}\) every day. Eve tells Bob that she is madly in love with him, is jealous of his daily secret conversations with Alice, and has recorded today's ciphertext. Bob recalls that today's conversation with Alice was pretty boring and, in a moment of weakness, tells Eve today's symmetric key \(K_{B}\) (the whole \(K_{B}\), not just the part used for the Rijndael key) to let her read today's conversation and put her jealousy to rest. Given this information, how many days of recorded ciphertext can Eve decipher?