Symmetric and Hashing

Polynomial Hash Table

Hash a tiny message with a visible rolling recurrence. This is toy arithmetic only, not deployable security.

cryptography This lesson makes each hash update an explicit row instead of hiding it inside a black box.

Example

Hash a tiny message with a visible rolling recurrence.

highlighted = computed this step

Step 1 — Set up

Set up the exact toy cryptography values.

message, base, modulus((7, 5, 4), 5, 17)\begin{array}{c|c}\text{message, base, modulus}&\text{((7, 5, 4), 5, 17)}\end{array}

Step 2 — Hash byte 1

Compute the highlighted cryptography value.

index, byte, before, raw, hash(1, 7, 0, 7, 7)\begin{array}{c|c}\text{index, byte, before, raw, hash}&\hlmath{\text{(1, 7, 0, 7, 7)}}\end{array}

Step 3 — Hash byte 2

Compute the highlighted cryptography value.

index, byte, before, raw, hash(2, 5, 7, 40, 6)\begin{array}{c|c}\text{index, byte, before, raw, hash}&\hlmath{\text{(2, 5, 7, 40, 6)}}\end{array}

Step 4 — Hash byte 3

Compute the highlighted cryptography value.

index, byte, before, raw, hash(3, 4, 6, 34, 0)\begin{array}{c|c}\text{index, byte, before, raw, hash}&\hlmath{\text{(3, 4, 6, 34, 0)}}\end{array}

Final Step — Hash

Compute the highlighted cryptography value.

toy hash0\begin{array}{c|c}\text{toy hash}&\hlmath{\text{0}}\end{array}