Decrypt Small Message - Cryptography Step by Step

Decrypt the tiny RSA ciphertext. This is toy arithmetic only, not deployable security.

Example

Decrypt the tiny RSA ciphertext. Decryption raises the ciphertext to the private exponent and reduces modulo n, exactly undoing the public-exponent step used to encrypt. It works because the two exponents are chosen to be inverses with respect to the group of units mod n, so applying one after the other returns the original message.

highlighted = computed this step

Step 1 — Set up

Set up the exact toy cryptography values.

\begin{array}{c|c}\text{c, d, n}&\text{(13, 27, 55)}\end{array}

Step 2 — Plaintext

Compute the highlighted cryptography value.

\begin{array}{c|c}\text{m}&\hlmath{\text{7}}\end{array}

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