# an 1 u define the hash function ha by ha x n 1

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Unformatted text preview: . , an-1 U , define the hash function ha by ha (x) = n-1 j=0 min-heap, worst-case hash table, worst-case hash table, average-case (a) Show that if the family H of hash functions is 2-universal, then it is universal. aj xj mod p . Let H = {ha }. This is the family of hash functions shown in lecture to be universal. Show that H is not 2-universal. (Hint: Find a key for which all hash functions in H produce the same value.) Handout 14: Problem Set 4 (c) Suppose that we modify H slightly from part (b): For any a U and for any b p , define ha,b (x) = n-1 j=0 3 aj xj + b mod p . and H = ha,b . Argue that H is 2-universal. (Hint: Consider fixed x U and y U , with xi = yi for some i. What happens to ha,b (x) and ha,b (y) as ai and b range over p ?) (d) Suppose that Alice and Bob secretly agree on a hash function h from a 2-universal family H of hash functions. Each h H maps from a univer...
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