4. Suppose hi : { 0,1 }2m {0,1}"is a collision resistant hash function. (1) Define hz: {0,1 }4m {0,1 }m as follows: a. Write xe{0,134m as x-x |r2, where xi, x2 E50,12 b. Define h2(x)-hi(hi(xi)I/hi(x2)) Prove that h2 is collision resistant. (2) For an integer i22, define a hash function h: 0,12m0,1m recursively from h-1, as follows: a. Write x e[0,1)21 as x-xilr2, where xi, x2E[0,1jm b. Define h(x)-hi(h-i(r)| h-i(2). Prove that hi is collision resistant