DO IN ASSEMMBLY A common operation in cryptography is to compute $c=x^e,$ where $e$ is a constant. A typical choice for $e$ is

the value $65537=2^{16}+1$ because there exists a fast assembly routine for this value using a technique called

repeated squaring.

Repeated squaring can be used to quickly calculate exponents that are a power of two. For example, $x^4$ can

be computed as $(x^2{)}^2$ using two imul $q$ instructions. Similarly, $x^{2^{16}}$ can be computed using sixteen imul $q$

instructions.

The routine works like this:

Save $x$ in a temporary variable $($such as a register$).$

Compute $y=x^{2^{16}}$ using repeated squaring and store $y$ in another temporary variable $($such as another

register$).$

Return $z=x*y,$ which is $x^{65537}$ because $x*x^{2^{16}}=x^{2^{16}+1}$ by the laws of exponents.

Implement this fast exponentiation routine in x$86-64$ assembly. You must use a loop for the repeated squar$-$

ing, properly align memory, follow x$86-64$ register conventions, and provide a comment for each assembly

instruction.

You should use assume that $e=65537$ is a constant and imulq instructions will not overflow. ${?}^1$ The only

parameter will be $x.$ You do not have to implement any test cases.

An example function prototype in $C$ for your implementation is as follows:

$//$ Compute $x^{-}65537$

int$64\_$t fast$\_$exponentiate $($int$64\_$t x$)$;

Some example calls:

fast$\_$exponentiate $(0)$

fast$\_$exponentiate$(2)$

fast$\_$exponentiate$(17)$