Symmetric-key cryptography

An encryption scheme $\{E_e|e\in \mathcal{K}\}$ and $\{D_d|d\in \mathcal{K}\}$ is symmetric-key if for each associated pair $(e,d)$ it is computationally easy to determine $d$ knowing only $e$ and to determine $e$ from $d$. In practice, $e=d$. Sender and recipient share a common key.

There are two requirements for secure use of symmetric encryption:

1. Strong encryption algorithm: at minimum, an attacker who has access to algorithm and one or more ciphertexts should be unable to decipher ciphertext. An even stronger algorithm would prevent an attacker from decrypting ciphertext or discovering the key even if they have access to the ciphertexts with the original plaintext.
2. Sender and receiver must obtain copies of secret key in secure fashion (and keep key secure): nobody must be able to discover the key.

As such, we only need to keep the key secret.