Question 1. The division step in Euclidean algorithm is executed at most     times.

	i)	${\log <!--FUNCTION\; APPLICATION-->}_2(b)+1$
	ii)	$2{\log <!--FUNCTION\; APPLICATION-->}_2(b)$
	iii)	${\log <!--FUNCTION\; APPLICATION-->}_2(b)+2$
	iv)	$2{\log <!--FUNCTION\; APPLICATION-->}_2(b)+1$

Question 2. Let $p$ be a prime such that $a^{p-1}\equiv 1(modp)$. Then     must be necessarily true.

	i)	$\gcd <!--FUNCTION\; APPLICATION-->(a,p)\ne 1$
	ii)	$a$ is primitive root
	iii)	order of $a$ is $p-1$
	iv)	none of these

Question 3. The discrete logarithm problem for the group ${𝔽}_p$ is solvable in     time.

	i)	linear
	ii)	exponential
	iii)	quadratic
	iv)	sub-exponential

Question 4. The function     $\ne O$(    ).

	i)	$x{\cos <!--FUNCTION\; APPLICATION-->}^2(x)$, ${\cos <!--FUNCTION\; APPLICATION-->}^2(x)$
	ii)	$(x+2){\cos <!--FUNCTION\; APPLICATION-->}^2(x)$, $2x$
	iii)	$(x+2){\cos <!--FUNCTION\; APPLICATION-->}^2(x)$, $x^2$
	iv)	$x{\cos <!--FUNCTION\; APPLICATION-->}^2(x)$, $x+2$

Question 5. In RSA, the smallest possible value of the encryption exponent, for which ciphertext is different plaintext, is     .

	i)	$1$
	ii)	$2$
	iii)	$3$
	iv)	none of these

Question 6.     is a witness for the compositeness of $6$.

	i)	$4$
	ii)	$3$
	iii)	$2$
	iv)	$1$

Question 7. The curve $Y^2=$     is not an elliptic curve.

	i)	$X^3-X$
	ii)	$X^3-3X+3$
	iii)	$X^3+3X+8$
	iv)	$X^3+X^2$

Question 8. Let $t_p$ denote the trace of Frobenius for an elliptic curve over ${𝔽}_p$. Then $|t_p|$     .

	i)	$\le 2\sqrt{p}$
	ii)	$\le \sqrt{p}$
	iii)	$\ge 2\sqrt{p}$
	iv)	$\le \sqrt{2p}$