To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0 < d < ϕ ( n ) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Question

Want to see the full answer?

Answer 1

Question

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

Let N = {0, 1, 2, . . .} be the set of Natural Numbers. Given an n ∈ N, which of the followingconditions are necessary, and which of these conditions are sufficient, for the Natural Number,n, to be a factor of 10.(a) 1 is a factor of n.(b) 1 is a factor of 2n.(c) −n is a factor of 10.(d) 10 is a multiple of n.(e) n is divisible by 2.(f) n^2 is divisible of 5.(g) n = 10.

- In RSA, let e=5, n=55. Can you find d ≡ 1/e (mod cp(n))? Why? - Let e=13, n=55. Find d ≡ 1/e (mod cp(n)) provided that d exists. If d does not exist, explain the reason for the nonexistence of d.

2. Honest Goblins are Easy to Find At Hogwarts a new shipment of n goblins has arrived. To be of any use, a goblin must be completely truthful (never lies). Unfortunately, not all of the n goblins in the shipment are truth tellers. Only some are truth-tellers, and some are deceivers. It is your task to design an algorithm to separate the truth-teller goblins from the deceiver goblins. To do this, you have one tool available: You may combine any two goblins and have them state whether the other goblin is a truth-teller or a deceiver. A truth-teller will always say correctly what the other goblin is, but a deceiver may lie (but also may sometimes tell the truth to REALLY confuse you). For any two goblins that you test, the following can be concluded from the goblin responses: Goblin A says Goblin B says Conclusion B is a truth-teller A is a truth-teller both are truth-tellers or both are deceivers B is a truth-teller A is a deceiver at least one is a deceiver B is a deceiver A is a…

Answer 2

Question

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Answer 6

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Answer 7

Chapter 31.7, Problem 2E

Program Plan Intro

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 11

Ch. 31.1 - Prob. 1E Ch. 31.1 - Prob. 2E Ch. 31.1 - Prob. 3E Ch. 31.1 - Prob. 4E Ch. 31.1 - Prob. 5E Ch. 31.1 - Prob. 6E Ch. 31.1 - Prob. 7E Ch. 31.1 - Prob. 8E Ch. 31.1 - Prob. 9E Ch. 31.1 - Prob. 10E

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0 < d < ϕ ( n ) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Solution Summary: The author explains that if Alice's public exponent e is 3 and the secret expponent ( d) is obtained by an adversary, then the opponent can factor Alice’s modulus

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Want to see the full answer?

Chapter 31 Solutions

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0 &lt; d &lt; ϕ ( n ) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Solution Summary: The author explains that if Alice's public exponent e is 3 and the secret expponent ( d) is obtained by an adversary, then the opponent can factor Alice’s modulus

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0<d<ϕ(n) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .

Want to see the full answer?

Chapter 31 Solutions

To verify that if Alice’s public exponent e is 3 and the secret exponent d , where 0 < d < ϕ ( n ) obtained by an adversary, then opponent can factor Alice’s modulus n in time-polynomial in the no. of bits in n .