Problem 1. (100 points.) Define the family of functions F: {0, 1}256 x {0, 13256 {0, 1}256 by Algorithm FK1||K2 (21||22): Return AES-1(K1, X1 x2)||AES(K2, 22) for all K1, K2, 21, 22 E {0,1}128 Here | denotes string concatenation, '@' denotes bit-wise exclusive-or, and denotes the bit-wise complement of a string x. Let TAES denote the time for one computation of AES or AES-. Below, running-times are worst case and should be func- tions of Taes. For full credit avoid use of asymptotics. (Part A - 15 points.) Prove that F is a blockcipher according to the definition given in class. (Part B - 15 points.) What is the running-time of a 2-query exhaustive key search adversary against F? Problem 1. (100 points.) Define the family of functions F: {0, 1}256 x {0, 13256 {0, 1}256 by Algorithm FK1||K2 (21||22): Return AES-1(K1, X1 x2)||AES(K2, 22) for all K1, K2, 21, 22 E {0,1}128 Here | denotes string concatenation, '@' denotes bit-wise exclusive-or, and denotes the bit-wise complement of a string x. Let TAES denote the time for one computation of AES or AES-. Below, running-times are worst case and should be func- tions of Taes. For full credit avoid use of asymptotics. (Part A - 15 points.) Prove that F is a blockcipher according to the definition given in class. (Part B - 15 points.) What is the running-time of a 2-query exhaustive key search adversary against F