Modular Arithmetic

Congruence Classes

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

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