Ask Question, Ask an Expert

+1-415-315-9853

info@mywordsolution.com

Ask Computer Engineering Expert

problem1. Which of the following statements is true for a trapdoor function f?

a. The function f can be computed efficiently, no algorithm can invert it unless with negligible probability or unless the algorithm is given a trapdoor

 b. The function f cannot be computed efficiently but there exists an algorithm that computes it efficiently using a trapdoor

 c. The function f cannot be computed efficiently but there exists a polynomial-time algorithm that can invert f's output on a random input unless with negligible probability;  moreover, there exists an algorithm that, given a trapdoor, can compute f

 d. The function f can be computed efficiently but no polynomial-time algorithm can invert f's output on a random input unless with negligible probability; moreover, there exists an algorithm that, given a trapdoor, can compute f's inverse function

 

problem2. Which of the following statements summarizes the properties of a hard-core predicate P for a one-way function f?

 a. P is hard to compute given the input of f but easy to compute using the output of f

 b. P is easy to compute given the input of f but hard to compute using the output of f

 c. P is hard to compute given the input of f and hard to compute using the output of f

 d. none of the above

 

problem3. For a still merely intuitive notion of "secure" (e.g., it is hard to guess info about the plaintext from the ciphertext), which cryptographic primitives are sufficient to construct a "secure" public-key cryptosystem?

 a. a one-way function f and a hard-core predicate P for f

 b. a one-way trapdoor function f and a hard-core predicate P for f

 c. a one-way trapdoor permutation f

 d. a hard-core predicate P for f

 

problem4.  Consider algorithms B.10, B.11, B.12, and B.13 in the [KL] textbook. Which one(s) among these does not run in polynomial time in its input length?

 a. B.10 and B.11

 b. B.10 and B.12

 c. B.11 and B.13

 d. B.12

 

problem5. Factoring is the problem of computing, on input a positive integer n, a factorization of n in terms of prime powers. This problem can be "easy (i.e., there exists a polynomial-time algorithm that solves it) or "(conjectured to be) hard" (i.e., there seems to be no polynomial-time algorithm that solves it) depending on the (sub)set of integers from which n is chosen. In which of these cases factoring n is easy?

 a. n is a power of 2

 b. n is a prime

 c. n is a prime power (see exercise 7.11 in [KL])

 d. All of the above

 

problem6. Factoring is the problem of computing, on input a positive integer n, a factorization of n in terms of integer powers of prime numbers. This problem can be "easy” (i.e., there exists a polynomial-time algorithm that solves it) or "(conjectured to be) hard” (i.e., there seems to be no polynomial-time algorithm that solves it) depending on the (sub)set of integers from which n is chosen. De?ne the trial division algorithm D to solve the factoring problem and study its running time t_D(n). Given this algorithm and its running time, we want to infer considerations on factoring n being easy or conjectured to be hard when n is chosen among products of two primes (i.e., n = pq for some primes p, q). Let m_easy(n) be a value for min(p, q) such that factoring n is easy and m_hard(n) be a value for min(p, q) such that factoring n may be conjectured to be hard. Which functions would you select as most meaningful for t_D(n), m_easy(n), m_hard(n)?

 a. t_D(n)=O(n2); m_easy(n)=O(log n); m_hard(n)=O(square root of n);

 b. t_D(n)=O(square root of n); m_easy(n)=O(square root of n); m_hard(n)=O(n);

 c. t_D(n)=O(square root of n); m_easy(n)=O(polylog n); m_hard(n)=O(n);

 d. t_D(n)=O(square root of n); m_easy(n)=O(polylog n); m_hard(n)=O(square root of n);

 

problem7. Computing discrete logarithms is the problem that takes as input the description of a cyclic group (G;*), the group's order m, the group's generator g, an element y in G, and asks to compute an integer x in Zm such that g *...*g = y, where there are x-1 occurrences of *. This problem can be "easy" (i.e., there exists a polynomial-time algorithm that solves it) or "(conjectured to be) hard" (i.e., there seems to be no polynomial-time algorithm that solves it) depending on the group G considered. In which of these cases computing discrete logarithms is easy?

 a. G is Zm, * is addition mod m

 b. G is Zm, * is multiplication mod m

 c. G is Zm, * is division mod m

 d. All of the above

  

problem8. Consider the problem of computing discrete logarithms in a cyclic group (G,?), with group’s order m; that is, given the group’sgenerator g, an element y ∈ G, compute an integer x ∈ Zm such that g ? • • • ? g = y, where there are x − 1 occurrences of ?. Then consider the exhaustive search algorithm to search for the discrete logarithm of y in base g for a cyclic group G of order m. Given this algorithm and its running time t(m,n), we want to infer considerations on computing discrete logarithm in G being easy or conjectured to be hard depending on the choices of m as a function of the length n of the group elements. Let m_easy(n) be a value for m such that computing discrete logarithms in G is easy and m_hard(n) be a value for m such that computing discrete logarithms in G may be conjectured to be hard. Which functions would you select as most meaningful for m_easy(n), m_hard(n)?

 a. m_easy(n)=O(n); m_hard(n)=omega(n)

 b. m_easy(n)=O(poly(n)); m_hard(n)=O(poly(n))

 c. m_easy(n)=O(poly(n)); m_hard(n)=omega(poly(n))

 d. m_easy(n)=O(n); m_hard(n)=O(n)

 

problem9.  Consider the following functions.

1) g1:{0,1}n-->{0,1}n, defined as g1(x)=x xor p, for each x in {0,1}n and for some known value p in {0,1}n

2) g2:{0,1}n-->{0,1}n, defined as a monotone function over the set {0,1}n

3) g3:{0,1}2n-->{0,1}n, defined as g3(x1,x2)=x1 xor x2 for each (x1,x2) in {0,1}2n

Which of the following is true?

 

a. g1 is one-way, g2 and g3 are not one-way

 b. g2 is one-way, g1 and g3 are not one-way

 c. g3 is one-way, g1 and g2 are not one-way

 d. none of them is one-way

 

problem10. Let f be a one-way function. Consider the following functions.

1) g1(x1,x2)=(f(x1),x2) for each (x1,x2) in its domain

2) g2(x)=(f(x),f(f(x))) for each x in its domain

3) g3(x1,x2)=(f(x1),x1 xor x2) for each (x1,x2) in its domain

Which of the following is true?

 a. If f is one-way then g1 is one-way, g2 and g3 are not one-way

 b. If f is one-way then g2 is one-way, g1 and g3 are not one-way

 c. If f is one-way then g1 and g2 are one-way, g3 is not one-way

d. If f is one-way then g1, g2 and g3 are one-way

 

problem 11 You have to choose the length of the modulus n for the RSA trapdoor permutation in use within your public-key cryptosystem. The attacker has one of the following resources: (a) a single computer, (b) a collection of computers distributed across the Internet, or (c) a quantum computer.

Which of the following lengths for n would you choose?

 a. (a): 1024; (b): 2048; (c): 4096

 b. (a): 1024; (b): 2048; (c): I would not use RSA

 c. (a): 2048; (b): 1024; (c): I would not use RSA

 d. (a): 512; (b): 1024; (c): 2048

 

problem12. Which of these assumptions is sufficient to construct a one-way function?

 a. The hardness of factoring integers that are product of two primes of the same length

 b. The hardness of computing discrete logarithms modulo primes

 c. The hardness of inverting the RSA function

 d. Any of the above

 

problem13. Which of these assumptions is known to be sufficient to construct a one-way permutation?

 a. The hardness of factoring integers that are product of two primes of the same length

 b. The hardness of computing discrete logarithms modulo primes

 c. The hardness of inverting the RSA function

 d. The hardness of computing discrete logarithms modulo primes or inverting the RSA function

 

problem14. Which of these assumptions is known to be sufficient to construct a trapdoor permutation?

 a. The hardness of factoring integers that are product of two primes of the same length

 b. The hardness of computing discrete logarithms modulo primes

 c. The hardness of inverting the RSA function

 d. All of the above

 

problem15. Which of these assumptions is sufficient to construct a hard-core predicate?

 a. The hardness of factoring integers that are product of two primes of the same length

 b. The hardness of computing discrete logarithms modulo primes

 c. The hardness of inverting the RSA function

 d. Any of the above

 

Computer Engineering, Engineering

  • Category:- Computer Engineering
  • Reference No.:- M9632

Have any Question? 


Related Questions in Computer Engineering

This is an investment opportunity and investment will occur

This is an investment opportunity and investment will occur at time 0 and sales commence at time 1. Initial cost: $28M Unit sales: 400,000 This year's selling price per unit: $60 This year's variable cost per unit: $42 L ...

What are the advantages of a virtualized data center over a

What are the advantages of a virtualized data center over a classic data center?

For each of the schedules of transactions t1 t2 and t3

For each of the schedules of transactions T1, T2, and T3 below: do each of the following: i. Insert shared and exclusive locks, and insert unlock actions. Place a shared lock immediately in front of each read action that ...

What are labor costs in ms project how do we assign labor

What are labor COSTS in MS project? How do we assign labor COSTS to a task in MS Project? Describe AND provide a screen shot of the steps. There are different kinds of non-labor costs, including expendables like supplies ...

Consider the specific application environment in your

Consider the specific application environment in your organization, how would different QA alternatives compare? In addition, is cost a critical factor in your market segment? How would it affect the choice of different ...

Paper should be approximately 10 pages single spaceshould

Paper should be approximately 10 pages (single space) Should be referenced if you extract some info from other website because there is a special program to check all over the net for plagiarism. Paper topics. 1. Thoroug ...

Within a database their are a variety of locks available

Within a database their are a variety of locks available, many developers do not use locks explicitly. They use stored procedures which lock the data that they need. Stored procedures also promote code reuse in multiple ...

Write a script that creates six sub-plots in two columns

Write a script that creates six sub-plots in two columns each with three rows. Each plot should have an appropriate title and labels on the x and y axes. The plot in the top left sub-plot should be y = cos(θ) for values ...

A syracuse university freshman likes chipotle burritos and

A Syracuse University freshman likes Chipotle burritos and Starbucks lattes. The price of one burrito is $1 and the price of one latte is $0.50. However, Starbucks is running the following promotion: If a freshman brings ...

Read the following case study for a brief description of a

Read the following case study for a brief description of a taxi company called Fast Cabs. Each office has a manager, several taxi owners, drivers and administrative staff. The manager is responsible for the day-to-day ru ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate