Question 1. $\frac{5}{7}\equiv$    $(mod11)$.

	i)	$9$
	ii)	$8$
	iii)	$7$
	iv)	doesn’t exist

Question 2. If $p=$     , then ${ord}_p(8640)=0$.

	i)	$2$
	ii)	$3$
	iii)	$5$
	iv)	$7$

Question 3. A     time algorithm is considered to be the fastest algorithm.

	i)	polynomial
	ii)	exponential
	iii)	sub-exponential
	iv)	none of these

Question 4. Let $G$ be a group and let $g\in G$ be an element of order $N\ge 2$. The Shanks’s algorithm solves the discrete logarithm problem $g^x=h$ in     steps.

	i)	$O(\sqrt{N}\cdot \log <!--FUNCTION\; APPLICATION-->N)$
	ii)	$O(\sqrt{N})$
	iii)	$O(\log <!--FUNCTION\; APPLICATION-->N)$
	iv)	$O(N\cdot \log <!--FUNCTION\; APPLICATION-->N)$

Question 5. A Carmichael number cannot be     .

	i)	composite
	ii)	divisible by $5$
	iii)	even
	iv)	a product of distinct primes

Question 6. An attack executed by an eavesdropper Even when she has full control over Alice and Bob’s communication network is called a     attack.

	i)	chosen ciphertext
	ii)	chosen plaintext
	iii)	man-in-the-middle
	iv)	known plaintext

Question 7. For an elliptic curve $E:Y^2=X^3+AX+B$ and points $P=(x_1,y_1)$, $Q=(x_2,y_2)$ on $E$, the slope of the tangent at the point $P$ is given by     .

	i)	$\frac{3x_1^2+A}{B}$
	ii)	$4A^3+27B^2$
	iii)	$\frac{y_2-y_1}{x_2-x_1}$
	iv)	$\frac{3x_1^2+A}{2y_1}$

Question 8. Let $E:Y^2=X^3+X+2$ be an elliptic curve over ${𝔽}_5$. Then $(1,2)+$     $=O$.

	i)	$(1,3)$
	ii)	$(1,2)$
	iii)	$(4,0)$
	iv)	$O$