Modular Arithmetic

Congruence Classes

List small congruence classes modulo m. This is toy arithmetic only, not deployable security.

cryptography The values in this lesson are deliberately tiny so every modular arithmetic step can be checked exactly.

Example

List small congruence classes modulo m.

highlighted = computed this step

Step 1 — Modulus

Set up the exact toy cryptography values.

m4\begin{array}{c|c}\text{m}&\text{4}\end{array}

Step 2 — Class 0

Compute the highlighted cryptography value.

[0] mod m[0, 4, 8]\begin{array}{c|c}\text{[0] mod m}&\hlmath{\text{[0, 4, 8]}}\end{array}

Step 3 — Class 1

Compute the highlighted cryptography value.

[1] mod m[1, 5, 9]\begin{array}{c|c}\text{[1] mod m}&\hlmath{\text{[1, 5, 9]}}\end{array}

Step 4 — Class 2

Compute the highlighted cryptography value.

[2] mod m[2, 6, 10]\begin{array}{c|c}\text{[2] mod m}&\hlmath{\text{[2, 6, 10]}}\end{array}

Step 5 — Class 3

Compute the highlighted cryptography value.

[3] mod m[3, 7, 11]\begin{array}{c|c}\text{[3] mod m}&\hlmath{\text{[3, 7, 11]}}\end{array}