EXPLAIN IN DETILS PLEASE  . As stated in Sect. 3.5.2, one important property which makes DES secure is that the S-boxes are nonlinear. In this problem we verify this property by computing the output of S1 for several pairs of inputs. Show that S1(x1)⊕S1(x2) = S1(x1 ⊕x2), where “⊕” denotes bitwise XOR, for: 1. x1 = 000000, x2 = 000001 2. x1 = 111111, x2 = 100000 3. x1 = 101010, x2 = 010101

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Disjoint set forest

The concept of the disjoint set forest was introduced by Bernard A. Galler and Michael J. Fischer in 1964. The disjoint set forest is a method of implementing disjoint sets quickly. In the disjoint-set forest, each tree member points only to its parent. The root of every tree includes its representative and its parent. The disjoint set forest is a special kind of forest that performs Union and Find operations in near-constant amortized time.