RSA Small

Compute Private Exponent

Find d so ed is congruent to one modulo phi. This is toy arithmetic only, not deployable security.

Example

Find d so ed is congruent to one modulo phi.

highlighted = computed this step

Step 1 — Set up

Set up the exact toy cryptography values.

e, phi(3, 40)\begin{array}{c|c}\text{e, phi}&\text{(3, 40)}\end{array}

Step 2 — Candidate

Compute the highlighted cryptography value.

d27\begin{array}{c|c}\text{d}&\hlmath{\text{27}}\end{array}

Step 3 — Check

Compute the highlighted cryptography value.

ed mod phi1\begin{array}{c|c}\text{ed mod phi}&\hlmath{\text{1}}\end{array}
cryptography The values in this lesson are deliberately tiny so every modular arithmetic step can be checked exactly.