- #1

- 318

- 141

From the paper https://people.csail.mit.edu/rivest/Rsapaper.pdf

Can someone explain the green highlight to me please? Sorry that I can't type much because this is the final week. Thanks.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter Leo Liu
- Start date

- #1

- 318

- 141

From the paper https://people.csail.mit.edu/rivest/Rsapaper.pdf

Can someone explain the green highlight to me please? Sorry that I can't type much because this is the final week. Thanks.

- #2

Gaussian97

Homework Helper

- 679

- 405

It should be evident from equation 5

- #3

- 15,952

- 14,421

From ##(5)## we have

\begin{align*}

ed\equiv 1 \mod \phi(n) &\Longleftrightarrow \phi(n)\,|\,(ed-1) \\

&\Longleftrightarrow \phi(n)\cdot k = ed-1 \text{ for some } k \in \mathbb{Z}\\

&\Longleftrightarrow \phi(n)\cdot k +1 = ed \text{ for some } k \in \mathbb{Z}\\

&\Longrightarrow M^{\phi(n)\cdot k +1} =M^{ed}

\end{align*}

\begin{align*}

ed\equiv 1 \mod \phi(n) &\Longleftrightarrow \phi(n)\,|\,(ed-1) \\

&\Longleftrightarrow \phi(n)\cdot k = ed-1 \text{ for some } k \in \mathbb{Z}\\

&\Longleftrightarrow \phi(n)\cdot k +1 = ed \text{ for some } k \in \mathbb{Z}\\

&\Longrightarrow M^{\phi(n)\cdot k +1} =M^{ed}

\end{align*}

Last edited:

Share:

- Replies
- 3

- Views
- 301