Cryptography Week 5 Quiz Answer

Cryptography Week 5 Quiz Answer

By University Of Maryland

Cryptography Quiz 5

Number Theory

Q1) Consider the following algorithm for factoring an integer N provided as input in binary): For i = 2 to (i, N/i). Which of the following statements is true?

• This algorithm is not correct, because it will sometimes fail to find a factorization of N even if N is composite.

• This algorithm is not correct, because it will sometimes output a non-trivial factorization of N even when N is prime.

• This algorithm runs in sub-linear time, and always factors N if N is composite.

• This algorithm is correct, but it runs in exponential time.

Q2) Which of the following is NOT a group?

• The integers under addition. 

• The set {0, 1, 2,..., 27} under addition modulo 28.

• The set {1,3,7,9} under multiplication modulo 10.

• The integers under multiplication.

Q3) Which of the following is the multiplicative inverse of 10 modulo 15?

• There is none, since gcd(10, 15) =1.

• 5

• 10 

• 1

Q4) What is [5⁸⁰ mod 79]? (Note that 79 is prime. Don't use a calculator/computer!)

• 25

Q5) How many elements are in the group Z₄₀₃? (Note that 403 = 13. 31.)

• 403

• 402 

• 290

• 360

Q6) Which of the following gives the 3rd root of 92 modulo 187 ? (Note that 187 = 11. 17.)

• [92¹⁰⁷ mod 187] 

• [92¹⁶⁰ mod 187]

• [92³mod 187]

• [92¹⁰⁷ mod 160]

Q7) Which of the following problems is hard if the RSA assumption holds? In all the below, N is a product of distinct, large primes p and q, and e is relatively prime o (N).

• Given N, e, and a uniform value y € Z_N, find x such that x^c = y mod N.

• Given N, e, and a uniform value x € Z_N, find x such that x^c = y mod 

• Given N and e, find a, y such that x = y mod N. 

• Given N and e, find a such that = 8 mod N.

Q8) Which of the following is a generator of Z_i3?

• 4

• 2

• Z_i3 does not have a generator since it is not a cyclic group.

• 3

Q9) Z₂₃ is a cyclic group with generator 5. In this group, what is DHS(2.20)? 1/1 point

• 17

• 5

• 9

• 22

Q10) Let G be a cyclic group of order q and with generator g. Based only on the assumption that the discrete-logarithm problem is hard for this group, which of the following problems is hard?

• Find x, y such that gʻ = y.

• Given uniform 3 € Z, and uniformy e G, compute y* .g.

• Given a uniform y € G, find x such that g^x = y.

• Given a uniform 2 € Zg, find y such that gʻ = y.

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