Suppose that f : {0, 1} m ? {0, 1} m is a preimage resistant bijection. Define h : {0, 1} 2m ? {0,..

Suppose that f : {0, 1} m ? {0, 1} m is a preimage resistant bijection. Define h : {0, 1} 2m ? {0, 1} m as follows. Given x ? {0, 1} 2m, write: x = x 0 ||x 00 where x 0 , x00 ? {0, 1} 2m. Then define h(x) = f(x 0 ? x 00). Prove that h is not second preimage resistant. (b) A message authentication code can be produced by a block cipher in CFB mode. Given a sequence of plaintext blocks, x1, . . . , xn, the IV is x1. Then the sequence, x2, . . . , xn is encrypted using key K in CFB mode, obtaining the ciphertext sequence y1, . . . , yn-1. Thus, yi = eK(yi-1) ? xi+1, where 1 = i < n and y0 = IV . Now define MAC=eK(yn-1). Compare the MAC with a MAC generated using CBC encryptions as follows: Take the IV to be 0, then encrypt the sequence x1, . . . , xn to produce the ciphertext sequence y 0 1 , . . . , y0 n , using y 0 i = eK(y 0 i-1 ? xi), where 1 = i < n and y 0 0 = IV . Here the MAC is defined as MAC0 = y 0 n . i. Prove by mathematical induction that, y 0 n = eK(yn-1). ii. Reason that MAC = MAC0 .