Cryptographic System
- Tags
- cryptography
Is a [see page 4, system] in cryptography which takes a plaintext input, encrypts it using a key to
produce some ciphertext and can decrypt the ciphertext using maybe a different key
to retrieve the original plaintext.
\begin{align*}
\text{Ciphertext} &= \text{Encryption}(\text{Plaintext}, \text{Key1}) \
\text{Plaintext} &= \text{Decryption}(\text{Ciphertext}, \text{key2})
\end{align*}
With \( Key1 \) being the public key and \( Key2 \) being the private key.
The security of a cryptographic-system depends on the secrecy of the key/s, not the specific encryption/decryption algorithm. Being able to derive the keys is sufficient to having cracked the system.
Many cryptographic systems make extensive use of the XOR operator because \( A \xor B \xor B = A \)
Components of a cryptographic system
We [see page 6, define]:
| Term | Name | Description |
|---|---|---|
| \( A \) | Alphabet | The alphabet |
| \( \textit{M} \subseteq {A}^{*} \) | Messages | The set of all possible combinations of the alphabet |
| \( M \in \textit{M} \) | plaintext | A message in the powerset of the alphabet |
| \( C \) | Ciphertext alphabet | The alphabet for the ciphertext that may or may not equal \( A \) |
| \( K \) | Keys | The set of valid keys which can be used in an encryption/decryption |
| \( E_e \forall e \in K \) | Encrypter | A bijective function mapping from a plaintext message \( M \) to a ciphertext message \( C \) |
| \( D_d \forall d \in K \) | Decrypter | A bijective function mapping from a ciphertext message \( C \) to a plaintext message \( M \) |