Modular Arithmetic

Reduce Modulo

Find the remainder after division by a modulus. This is toy arithmetic only, not deployable security.

Example

Find the remainder after division by a modulus.

highlighted = computed this step

Step 1 — Set up

Set up the exact toy cryptography values.

a, m(17, 5)\begin{array}{c|c}\text{a, m}&\text{(17, 5)}\end{array}

Step 2 — Quotient

Compute the highlighted cryptography value.

a // m3\begin{array}{c|c}\text{a // m}&\hlmath{\text{3}}\end{array}

Step 3 — Remainder

Compute the highlighted cryptography value.

a mod m2\begin{array}{c|c}\text{a mod m}&\hlmath{\text{2}}\end{array}

Step 4 — Result

Compute the highlighted cryptography value.

residue2\begin{array}{c|c}\text{residue}&\hlmath{\text{2}}\end{array}
cryptography The values in this lesson are deliberately tiny so every modular arithmetic step can be checked exactly.