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.
Formal definition.
Mathematically, a cryptosystem or encryption scheme can be defined as a tuple formula_1 with the following properties.
For each formula_9, there is formula_10 such that formula_11 for all formula_12.
Note; typically this definition is modified in order to distinguish an encryption scheme as being either a symmetric-key or public-key type of cryptosystem.
Examples.
A classical example of a cryptosystem is the Caesar cipher. A more contemporary example is the RSA cryptosystem.