To identify whether family H of hash function is universal if it’s 2-Universal.

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Answer 1

Question

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

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Prove the theorem Suppose that a hash function h is chosen randomly from a universal collection of hash functions and has been used to hash n keys into a table T of size m, using chaining to resolve collisions. If key k is not in the table, then the expected length E Œnh.k/ of the list that key k hashes to is at most the load factor ˛ D n=m. If key k is in the table, then the expected length E Œnh.k/ of the list containing key k is at most 1 C ˛.

Given a known set of keys, a perfect hash function is one that translates every key to adifferent bucket index. For example, given the set of keys {'alpha', 'beta', 'gamma', 'delta’},the following is a perfect hash function:m = 4; hash(k) = (initial letter of k - 'a') modulo 4a. Under what circumstances does it make sense to seek a perfect hash function? Explain.b. How can a perfect hash function be exploited in implementing a hash table? Explain.c. Given the following set of keys:{CA, MX, US}find a perfect hash function with m = 3,d. Given the following set of keys:{AT, BE, DE, DK, ES, FI, FR, GR, IE, IT, LU, NL, PT, SE, UK}find a perfect hash function with m < 20.

Computer Science (a) Let h be a collision resistant hash function. Now consider the following function H that is defined for binary strings of even length. Let x = x1||x2 with x1 ∈ F2n and x2 ∈ Fn2 . Then H(x) = h(x1 ⊕ x2). Prove that this function is not collision resistant.

Answer 2

Question

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

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Answer 3

Question

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 4

Question

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

Answer 6

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

Answer 7

Chapter 11, Problem 4P

(a)

Program Plan Intro

To identify whether family H of hash function is universal if it’s 2-Universal.

Answer 8

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

Answer 9

(b)

Program Plan Intro

To show that family H of hash function is universal but not 2-Universal.

Answer 10

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

Answer 11

(c)

Program Plan Intro

To determine that modified family H’ of hash function from family H is 2-Universal class.

Answer 12

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

Answer 13

(d)

Program Plan Intro

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

Answer 14

Expert Solution & Answer

Answer 15

Expert Solution & Answer

Answer 16

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Answer 17

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E

To identify whether family H of hash function is universal if it’s 2-Universal.

Solution Summary: The author explains that family H of hash function is universal if it's 2-Universal.

Concept explainers

To identify whether family H of hash function is universal if it’s 2-Universal.

To show that family H of hash function is universal but not 2-Universal.

To determine that modified family H’ of hash function from family H is 2-Universal class.

Find the probability of advisory succeeds in bob’s fooling in to accepting is at most 1/m where m is the message sent by Alice.

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Chapter 11 Solutions