GATEBOOK_CN4_19

Question

Consider RSA with p = 31 and q = 47.
I. n = 1457
II. z= 1200
III. 7 is acceptable choice for e

Which of the following is true ?
A. Only I
B. Only I and II
C. Only I and III
D. All of I,II and II

 

I am Getting answer (C), but answer is given (D).

As per kurose Ross, Z is defined to be $(p-1)(q-1)$

Comments

Assuming Z is the same as $\phi(n)$ or the Euler totient function, you are correct. It should be 1380.

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I too agree $C$ should be the answer

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How r they calculating $e$ , when $d$ is not given?

I think option $A)$ should be ans

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You don't need $d$ to calculate $e$. In fact, it's using $e$, that we calculate $d$.

The only condition for $e$ is that $gcd(e, \phi(n)) = 1$ @srestha

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yes

but we should know one of $d$ or $e$

rt?

7 is acceptable choice for e

this is not correct

because it might happen 5,3 also acceptable for e 

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You are right, we can use 5 and 3 also. However, the question asks whether $e$ is acceptable or not and since $gcd(7, 1457) = 1$, it is an acceptable choice. We don't care about the other values of $e$.