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In 1985, Montgomery introduced a new clever way to represent the numbers $\mathbb{Z}/n \mathbb{Z}$ such that arithmetic, especially the multiplications become easier.

In 1985, Montgomery introduced a new clever way to represent the numbers $\mathbb{Z}/n \mathbb{Z}$ such that arithmetic, especially the modular multiplications become easier.

Now, the advantage is clear. Since $r= 2^{k}$ the division and $bmod$ operations are cheap by shifting or masking.

Now, the advantage is clear. Since $r= 2^{k}$ the division and $\bmod$ operations are cheap by shifting or masking.

The Montgomery in 1985 introduced a new clever way to represent the numbers $\mathbb{Z}/n \mathbb{Z}$ such that arithmetic, especially the multiplications become easier.

In 1985, Montgomery introduced a new clever way to represent the numbers $\mathbb{Z}/n \mathbb{Z}$ such that arithmetic, especially the multiplications become easier.