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P1 P2 Pe||10* IV AESK AESK AESK C1 C2 Ce Figure 2: The scheme up for analyzing. 4. (35 points) Analyze This (1999). In this exercise, we are going to analyze the scheme in Figure 2. Moreover, we will perform a multi-target attack on this scheme. Assume that the instantiation of AES uses 10 rounds. 2 pt 3 pt 2 pt (a) What type of encryption is this? (b) What is the ideal counterpart of the used internal? (c) What is the length of the key used in this scheme? (d) Suppose you have obtained tuples (IV1, P1,C),..., (IVn, Pn,C), each consisting of an initialization 6 pt vector IVi, a 128-bit plaintext Pi, and ciphertext C = Enck;(IV; OP;), such that K1, ..., Kn are the associated keys. Show how you can use these tuples to perform a multi-target attack. (e) Describe the online queries that you can make to the encryption scheme to obtain the tuples in (d). 6 pt [Note that an encryption scheme consists of an encryption and a decryption algorithm.] (f) Suppose that n= 129, and that there are three tuples for which it holds that IV: OPi = IV; OP; = IVk OPk. Give the probability that one guess K is correct in the multi-target attack in (d) and (e). (g) Based on (f), give the security strength against the multi-target attack in (d) and (e). (Hint: Consider 6 pt the online and offline complexity. For the offline complexity, consider the expected complexity for probability p= 1.) (h) Argue whether the attack in (d) and (e) is more likely to be a multi-target attack on the PRP- security, on the SPRP-security or on the indistinguishability from a random oracle. 6 pt 4 pt