Can any one provide the detailed process or explanation of the problem4.5?

thanks!

. Say we have t plaintext-ciphertext pairs P, C E(K, P), where we assume that the key K selects one of the N! possible mappings. Imagine that we wish to find K by exhaustive search. We could generate key K' and test whether Ci E(K', P) for Isist.If K" encrypts each P, to its proper Ci, then we have evidence that K K However, it may be the case that the mappings E(K, .) and E(K',.) exactly agree on the t plaintext-cipher text pairs P, Ci and agree on no other pairs. a. What is the probability that E(K, . and E(K',.) are in fact distinct mappings? b. What is the probability that E(K, and E(K',.) agree on another t' plaintext- ciphertext pairs wher 0 sI's N -1? 4.5 For any block cipher, the fact that it is a nonlinear function is crucial to its security. To see this, suppose that we have a linear block cipher EL that encrypts 256-bit blocks of plaintext into 256-bit blocks of ciphertext. Let EL(k, m) denote the encryption of a 256-bit message m under a key k (the actual bit length of k is irrelevant). Thus, ELik, [mi m2]) = EL(k, m) EL(k, n ) for all 128-bit patterns mi, m2. Describd how, with 256 chosen ciphertexts, an adversary can decrypt any ciphertext without knowledge of the secret key k. (A "chosen ciphertext" means that an adver- sary has the ability to choose a ciphertext and then obtain its decryption. Here, you have 256 plaintext/ciphertext pairs to work with and you have the ability to choose the value of the ciphertexts.) 46 Suppose the DES F function mapped every 32-bit input R, regardless of the value of the input K to a. 32-bit string of zero b. R Then