In a RSA cryptosystem a particular A uses two prime numbers p 13 and q 17 to generate her public and private keys If the public key of Ais 35 Then the private key of A is gate computer science 2017

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## In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________. -gate computer science 2017

A) 11
B) 13
C) 16
D) 17

By:satyashiromani

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A) 11

Explanation:
In an RSA cryptosystem, for public key:
GCD( ϕ(n) , e) = 1

And, for private key:
(e * d) mod ϕ(n) = 1

Where,
ϕ(n) = (p -1)*(q - 1) = (13 - 1)(17 - 1) =12*16 = 192
Such that 1 < e, d < ϕ(n)

Therefore, the private key is:
(35 * d) mod ϕ(n) = 1
d = 11

This explanation is contributed by Deepak Raj

deepuckraj

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