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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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## Answers

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

Oshal-Borkar

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