Question: Problem 2.1 (30 points) Let F:{0,1}k{0,1}m{0,1}n be a secure PRF. Consider the following function families: 1. F1:{0,1}k{0,1}m{0,1}2n specified for all x{0,1}m and all K{0,1}k by

Problem 2.1 (30 points) Let F:{0,1}k{0,1}m{0,1}n be a secure PRF. Consider

Problem 2.1 (30 points) Let F:{0,1}k{0,1}m{0,1}n be a secure PRF. Consider the following function families: 1. F1:{0,1}k{0,1}m{0,1}2n specified for all x{0,1}m and all K{0,1}k by F1(K,x)=F(K,x)F(K,x) 2. F2:{0,1}k{0,1}2m{0,1}2n specified for all x1,x2{0,1}m and all K{0,1}k by F2(K,x1x2)=F(K,x1)F(K,x1x2) Above, xy means concatenation of x and y,x means the bitwise complement of x, and is bitwise XOR. Prove that F1 and F2 are not secure PRFs

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