Modular Arithmetic

Modular Add and Multiply

Reduce sums and products modulo a small modulus. This is toy arithmetic only, not deployable security.

Example

Reduce sums and products modulo a small modulus.

highlighted = computed this step

Step 1 — Set up

Set up the exact toy cryptography values.

m, a, b(7, 5, 4)\begin{array}{c|c}\text{m, a, b}&\text{(7, 5, 4)}\end{array}

Step 2 — Raw sum

Compute the highlighted cryptography value.

a+b9\begin{array}{c|c}\text{a+b}&\hlmath{\text{9}}\end{array}

Step 3 — Sum residue

Compute the highlighted cryptography value.

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

Step 4 — Raw product

Compute the highlighted cryptography value.

a*b20\begin{array}{c|c}\text{a*b}&\hlmath{\text{20}}\end{array}

Step 5 — Product residue

Compute the highlighted cryptography value.

(a*b) mod m6\begin{array}{c|c}\text{(a*b) mod m}&\hlmath{\text{6}}\end{array}
cryptography The values in this lesson are deliberately tiny so every modular arithmetic step can be checked exactly.