Question 1.     $\in {\left(\mathbb{Z}∕12\mathbb{Z}\right)}^{\ast }$.

	i)	$2$
	ii)	$3$
	iii)	$4$
	iv)	$5$

Question 2. The number of primitive roots modulo $31$ is     .

	i)	$8$
	ii)	$9$
	iii)	$30$
	iv)	none of these

Question 3. In an Elgamal PKC with parameters $g=2$ and $p=7$, Alice’s public key is $4$, whereas Bob’s message is $3$ and his ephemeral key is $4$. Then the ciphertext of Bob sent to Alice is     .

	i)	$(2,6)$
	ii)	$(2,5)$
	iii)	$(3,6)$
	iv)	$(3,5)$

Question 4. A square root of $3$ modulo $19$     .

	i)	$4$
	ii)	$15$
	iii)	does not exists
	iv)	none of these

Question 5. Let $C=\{m\in \mathbb{N}\mid m\text{ is composite}\}$. Which of the following is true?

	i)	For all $m\in C$, every Miller-Rabin witness of $m$ is a Fermat-witness.
	ii)	For all $m\in C$, every Fermat-witness of $m$ is a Miller-Rabin witness.
	iii)	There is $m\in C$ with a Fermat-witness which is not a Miller-Rabin witness.
	iv)	None of these.

Question 6. $\varphi (n)\ne \pi (n)$ for $n=$     .

	i)	$8$
	ii)	$10$
	iii)	$12$
	iv)	none of these

Question 7.     has a $4$-to-$1$ message expansion.

	i)	RSA PKC
	ii)	Elgamal PKC
	iii)	Elliptic Elgamal PKC
	iv)	ECDH key-exchange

Question 8. For an elliptic curve $E:Y^2=X^3-15X+18$ and $P=(3,0)\in E$, $2P=$     .

	i)	$P$
	ii)	$(-3,0)$
	iii)	$(6,0)$
	iv)	$O$