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How does decryption recover a message from ciphertext?

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A Vigenere cipher table displays the alphabet in both the top row and left column, with rows shifted to create a grid for encryption and decryption. Highlighted letters illustrate how to use the table. An explanation and example using the words cipher, key, and plaintext appears to the right. — cryptology In encrypting plaintext, the cipher letter is found at the intersection of the column headed by the plaintext letter and the row indexed by the key letter. To decrypt ciphertext, the plaintext letter is found at the head of the column determined by the intersection of the diagonal containing the cipher letter and the row containing the key letter.

In cryptology, decryption is the process of converting ciphertext—information disguised to be unintelligible—back into its original, readable format.1

The recovery of a message relies on the specific algorithm used to encrypt the data and a corresponding key. The mechanism depends on the type of system employed:

Symmetric Encryption: This system uses the same key for both encryption and decryption. The receiver must possess this secret key to invert the transformation applied by the sender.1
Asymmetric Encryption: Also known as public-key cryptography, this method uses a pair of keys. While one key is used to encrypt the data, a mathematically related but distinct key is required to decrypt it.1

In practice, decryption involves applying the correct key to the ciphertext to reverse the encryption procedures. If an unauthorized party attempts to recover the message without the key, they must engage in cryptanalysis, which may involve brute-force attacks on the key space or mathematical analysis to exploit weaknesses in the algorithm.2