1
2
3
4
5
6
7
8
right first attempt
right
wrong

NTC PS03EMTH55 (01-11-2023)
Question 1. Which of the following is a primitive root modulo 11?
i)
3
ii)
5
iii)
7
iv)
9

Question 2. Let a,m . Consider the following statements.
(i)
b such that ab 1(modm).
(ii)
gcd (a,m) = 1.
Which of the following is true?
i)
(i) (ii) but (ii) (i)
ii)
(i) (ii) and (ii) (i)
iii)
(ii) (i) but (i) (ii)
iv)
(i) (ii) and (ii) (i)

Question 3. Let p be a prime satisfying p 3(mod4) and a be an integer. Then     a solution of the congruence x2 a(modp).
i)
a(p+1)4(modp) is
ii)
a(p+1)2(modp) is
iii)
a(p+3)4(modp) is
iv)
there need not be

Question 4. An attack in which an eavesdropper has access to an oracle that decrypts arbitrary ciphertexts is known as a     attack.
i)
chosen ciphertext
ii)
man-in-the-middle
iii)
known plaintext
iv)
chosen plaintext

Question 5. A number whose prime factors are all less than or equal to k is called a     number.
i)
composite
ii)
Miller-Rabin
iii)
k-smooth
iv)
Carmichael

Question 6. ϕ(100) =     .
i)
4
ii)
10
iii)
40
iv)
99

Question 7. The discriminant of an elliptic curve E : Y 2 = X3 + AX + B is given by     .
i)
27A2 + 4B3
ii)
27A3 + 4B2
iii)
4A2 + 27B3
iv)
4A3 + 27B2

Question 8. Let E : Y 2 = X3 + X + 2 be an elliptic curve over 𝔽5. Then #E(𝔽5) =     .
i)
3
ii)
4
iii)
25
iv)
none of these