Cryptosystem

In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, most commonly for achieving confidentiality (encryption).

Typically, a cryptosystem consists of three algorithms: one for key generation, one for encryption, and one for decryption. The term cipher (sometimes cypher) is often used to refer to a pair of algorithms, one for encryption and one for decryption. Therefore, the term cryptosystem is most often used when the key generation algorithm is important. For this reason, the term cryptosystem is commonly used to refer to public key techniques; however both "cipher" and "cryptosystem" are used for symmetric key techniques.

Mathematically, a cryptosystem or encryption scheme can be defined as a tuple ${\displaystyle ({\mathcal {P}},{\mathcal {C}},{\mathcal {K}},{\mathcal {E}},{\mathcal {D}})}$ with the following properties.

For each ${\displaystyle e\in {\mathcal {K}}}$, there is ${\displaystyle d\in {\mathcal {K}}}$ such that ${\displaystyle D_{d}(E_{e}(p))=p}$ for all ${\displaystyle p\in {\mathcal {P}}}$.

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