Question 1. The number of primitive roots modulo $13$ is     .

	i)	$1$
	ii)	$3$
	iii)	$4$
	iv)	$12$

Question 2. ${ord}_2(a)={ord}_3(a)$ if $a=$     .

	i)	$72$
	ii)	$108$
	iii)	$180$
	iv)	$432$

Question 3. The     algorithm reduced the discrete logarithm problem for elements of arbitrary order to the discrete logarithm problem for elements of prime power order.

	i)	Pohlig-Hellman
	ii)	Euclidean
	iii)	Shanks’s
	iv)	extended Euclidean

Question 4. A square root of $2$ modulo $31$     .

	i)	is $4$
	ii)	is $21$
	iii)	is $23$
	iv)	doesn’t exist

Question 5. The solution of $x^{17}\equiv 2(mod43)$ is     .

	i)	$23$
	ii)	$32$
	iii)	$41$
	iv)	none of these

Question 6. In RSA, if $p=3$, $q=11$ are the primes and $e=7$ is the encryption exponent, then the decryption exponent $d=$     .

	i)	$3$
	ii)	$19$
	iii)	$23$
	iv)	none of these

Question 7. The discriminant of the elliptic curve $E:Y^2=X^3-3X+3$ is     .

	i)	$-27$
	ii)	$135$
	iii)	$216$
	iv)	none of these

Question 8. The fastest known algorithm to solve the elliptic curve discrete logarithm problem in $E({𝔽}_p)$ takes approximately     steps.

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