GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 60

In an RSA Cryptosystem, Suppose n = 101*113, e1 = 8765, and e2 = 7653. Note: 101 and 113 are primes.

Which of the following option is not correct ?
(A) Value of e1 as public key is not valid.
(B) Value of e2 as public key is not valid.
(C) Value of private key d is 9517.
(D) Decrypted message of cipher-text c = 3233 is 10101.

Answer: (B)
Explanation:

gcd(e1, ϕ(n)) = 5, so e1 is invalid (because of not co-prime).
gcd(e2, ϕ(n)) = 1, so e2 is valid.

xgcd(e2, ϕ(n)) = (1, −1683, 1150), so d = (−1683 (mod ϕ(n))) = 9517.

(3233)d(mod n) = 10101.

So, value of e2 as public key is valid, option (B) is false.
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