$(1$ 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$=1357$

and d$=851.$ We want to use the Square and Multiply algorithm to quickly decrypt y$=165$

$.$

a$)$ Express d

as a binary string $($e$.$g$.$

$10110110).$

b$)$ Supposing that initially r$=$y$=165$

$,$ enter the order of square operations $($SQ$)$ and multiply operations $($MUL$)$ that must be performed on r to compute ydmodN. Enter as a comma separated list, for example SQ$,$MUL,SQ$,$SQ$,$SQ$,$MUL,SQ$,$SQ$,$MUL,SQ$,$SQ

$.$

c$)$ What is x$=$ydmodN

$?$