There are two different meanings of the word cryptosystem. One is used by the cryptographic community, while the other is the meaning understood by the public.

General meaning

In this meaning, the term cryptosystem is used as shorthand for "cryptographic system". A cryptographic system is any computer system that involves cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

. Such systems include for instance, a system for secure electronic mail

E-mail

Electronic mail, commonly known as email or e-mail, is a method of exchanging digital messages from an author to one or more recipients. Modern email operates across the Internet or other computer networks. Some early email systems required that the author and the recipient both be online at the...

 which might include methods for digital signature

Digital signature

A digital signature or digital signature scheme is a mathematical scheme for demonstrating the authenticity of a digital message or document. A valid digital signature gives a recipient reason to believe that the message was created by a known sender, and that it was not altered in transit...

s, cryptographic hash function

Cryptographic hash function

A cryptographic hash function is a deterministic procedure that takes an arbitrary block of data and returns a fixed-size bit string, the hash value, such that an accidental or intentional change to the data will change the hash value...

s, key management

Key management

Key management is the provisions made in a cryptography system design that are related to generation, exchange, storage, safeguarding, use, vetting, and replacement of keys. It includes cryptographic protocol design, key servers, user procedures, and other relevant protocols.Key management concerns...

 techniques, and so on. Cryptographic systems are made up of cryptographic primitive

Cryptographic primitive

Cryptographic primitives are well-established, low-level cryptographic algorithms that are frequently used to build computer security systems. These routines include, but are not limited to, one-way hash functions and encryption functions.- Rationale :...

s, and are usually rather complex. Because of this, breaking a cryptosystem is not restricted to breaking the underlying cryptographic algorithms - usually it is far easier to break the system as a whole, eg, through the not uncommon misconceptions of users in respect to the cryptosystem.

Meaning in the context of cryptography

In this meaning, a cryptosystem refers to a suite of algorithm

Algorithm

In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...

s needed to implement a particular form of encryption

Encryption

In cryptography, encryption is the process of transforming information using an algorithm to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key. The result of the process is encrypted information...

 and decryption.

Typically, a cryptosystem consists of three algorithms: one for key

Key (cryptography)

In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm or cipher. Without a key, the algorithm would produce no useful result. In encryption, a key specifies the particular transformation of plaintext into ciphertext, or vice versa...

 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

Symmetric-key algorithm

Symmetric-key algorithms are a class of algorithms for cryptography that use trivially related, often identical, cryptographic keys for both encryption of plaintext and decryption of ciphertext. The encryption key is trivially related to the decryption key, in that they may be identical or there is...

 techniques.

"Cryptographic system" vs. "cryptosystem"

The Internet Security Glossary RFC 2828 dissuades from using the term "cryptosystem", giving the following definitions.
cryptosystem ISD

Internet standard

In computer network engineering, an Internet Standard is a normative specification of a technology or methodology applicable to the Internet. Internet Standards are created and published by the Internet Engineering Task Force .-Overview:...

s SHOULD NOT use this term as an abbreviation for cryptographic system. (For rationale, see: crypto.)
crypto

Except as part of certain long-established terms listed in this Glossary, ISD

Internet standard

In computer network engineering, an Internet Standard is a normative specification of a technology or methodology applicable to the Internet. Internet Standards are created and published by the Internet Engineering Task Force .-Overview:...

s SHOULD NOT use this abbreviated term because it may be misunderstood. Instead, use "cryptography" or "cryptographic".