- #1

Leo Liu

- 345

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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.

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- I
- Thread starter Leo Liu
- Start date

- #1

Leo Liu

- 345

- 146

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

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It should be evident from equation 5

- #3

- 17,645

- 18,322

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*}

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