At least one of the answers above is NOT correct.

$(1$ point$)$ The speed of RSA hinges on the ability to do large modular exponentiations quickly.

While $e$ can be made small, $d$ generally cannot.

A popular method for fast modular exponentiation is the Square and Multiply algorithm.

Suppose that $N=1343$ and $d=749.$ We want to use the Square and Multiply algorithm to quickly decrypt

$y=1005.$

a$)$ Express $d$ as a binary string $($e$.$g$.10110110).$

b$)$ Supposing that initially $r=y=1005,$ enter the order of square operations $($SQ$)$ and multiply operations

$($MUL$)$ that must be performed on $r$ to compute $y^d$modN. Enter as a comma separated list, for example

$SQ\frac{,}{M}UL,SQ,SQ,SQ\frac{,}{M}UL,SQ,SQ\frac{,}{M}UL,SQ,SQ$

c$)$ What is $x=y^d$modN $?$