Question

In a public key system, the cipher text received is C = 10 if RSA encryption used with a public key(e = 11, n = 77) to deduce the plain text. Determine the value of ϕ(n)?

(a) 49

(b) 60

(c) 123

(d) 70

I got this question at a job interview.

My question is based upon Cryptography in portion Number Theory and Cryptography of Discrete Mathematics

Answer 1

The correct answer is (b) 60

For explanation: Given n = 77, that means p and q must be 7 and 11 that is they must be co-prime to each other. Now we know that ϕ(n) = (p – 1) (q – 1)

ϕ(n) = (7 – 1) (11 – 1)

ϕ(n) = 6*10

ϕ(n) = 60.