# Cryptosystem > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Cryptosystem > Markdown URL: https://mediated.wiki/source/Cryptosystem.md > Source: https://en.wikipedia.org/wiki/Cryptosystem > Source revision: 1269888215 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Cryptosystem" – news · newspapers · books · scholar · JSTOR (August 2024) (Learn how and when to remove this message) This article needs additional or more specific categories. Please help out by adding categories to it so that it can be listed with similar articles. (January 2025) Suite of cryptographic algorithms needed to implement a particular security service In [cryptography](/source/Cryptography), a **cryptosystem** is a suite of [cryptographic algorithms](/source/Cryptographic_algorithm) needed to implement a particular security service, such as confidentiality ([encryption](/source/Encryption)).[1] Typically, a cryptosystem consists of three algorithms: one for [key generation](/source/Key_generation), one for encryption, and one for decryption. The term *[cipher](/source/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](/source/Public_key_cryptography) techniques; however both "cipher" and "cryptosystem" are used for [symmetric key](/source/Symmetric-key_algorithm) techniques. ## Formal definition Mathematically, a cryptosystem or encryption scheme can be defined as a [tuple](/source/Tuple) ( P , C , K , E , D ) {\displaystyle ({\mathcal {P}},{\mathcal {C}},{\mathcal {K}},{\mathcal {E}},{\mathcal {D}})} with the following properties. 1. P {\displaystyle {\mathcal {P}}} is a set called the "plaintext space". Its elements are called plaintexts. 1. C {\displaystyle {\mathcal {C}}} is a set called the "ciphertext space". Its elements are called ciphertexts. 1. K {\displaystyle {\mathcal {K}}} is a set called the "key space". Its elements are called keys. 1. E = { E k : k ∈ K } {\displaystyle {\mathcal {E}}=\{E_{k}:k\in {\mathcal {K}}\}} is a set of functions E k : P → C {\displaystyle E_{k}:{\mathcal {P}}\rightarrow {\mathcal {C}}} . Its elements are called "encryption functions". 1. D = { D k : k ∈ K } {\displaystyle {\mathcal {D}}=\{D_{k}:k\in {\mathcal {K}}\}} is a set of functions D k : C → P {\displaystyle D_{k}:{\mathcal {C}}\rightarrow {\mathcal {P}}} . Its elements are called "decryption functions". For each e ∈ K {\displaystyle e\in {\mathcal {K}}} , there is d ∈ K {\displaystyle d\in {\mathcal {K}}} such that D d ( E e ( p ) ) = p {\displaystyle D_{d}(E_{e}(p))=p} for all p ∈ P {\displaystyle p\in {\mathcal {P}}} .[2] Note; typically this definition is modified in order to distinguish an encryption scheme as being either a [symmetric-key](/source/Symmetric-key_algorithm) or [public-key](/source/Public-key_cryptography) type of cryptosystem. ## Examples A classical example of a cryptosystem is the [Caesar cipher](/source/Caesar_cipher). A more contemporary example is the [RSA](/source/RSA_(cryptosystem)) cryptosystem. Another example of a cryptosystem is the [Advanced Encryption Standard](/source/Advanced_Encryption_Standard) (AES). AES is a widely used symmetric encryption algorithm that has become the standard for securing data in various applications. [Paillier cryptosystem](/source/Paillier_cryptosystem) is another example used to preserve and maintain privacy and sensitive information. It is featured in electronic voting, electronic lotteries and electronic auctions.[3] ## See also - [List of cryptosystems](/source/List_of_cryptosystems) - [Semantic security](/source/Semantic_security) ## References 1. **[^](#cite_ref-1)** Menezes, A.; Oorschot, P. van; Vanstone, S. (1997). [*Handbook of Applied Cryptography*](https://archive.org/details/handbookofapplie0000mene) (5th ed.). CRC Press. [ISBN](/source/ISBN_(identifier)) [0-8493-8523-7](https://en.wikipedia.org/wiki/Special:BookSources/0-8493-8523-7). 1. **[^](#cite_ref-2)** Buchmann, Johannes A. (13 July 2004). *Introduction to Cryptography* (2nd ed.). Springer. [ISBN](/source/ISBN_(identifier)) [0-387-20756-2](https://en.wikipedia.org/wiki/Special:BookSources/0-387-20756-2). 1. **[^](#cite_ref-3)** Xia, Zhe; Yang, Xiaoyun; Xiao, Min; He, Debiao (2016). ["Provably Secure Threshold Paillier Encryption Based on Hyperplane Geometry"](https://link.springer.com/chapter/10.1007/978-3-319-40367-0_5). In Liu, Joseph K.; Steinfeld, Ron (eds.). *Information Security and Privacy*. Lecture Notes in Computer Science. Vol. 9723. Cham: Springer International Publishing. pp. 73–86. [doi](/source/Doi_(identifier)):[10.1007/978-3-319-40367-0_5](https://doi.org/10.1007%2F978-3-319-40367-0_5). [ISBN](/source/ISBN_(identifier)) [978-3-319-40367-0](https://en.wikipedia.org/wiki/Special:BookSources/978-3-319-40367-0). v t e Cryptography General History of cryptography Outline of cryptography Classical cipher Cryptographic protocol Authentication protocol Cryptographic primitive Cryptanalysis Cryptocurrency Cryptosystem Cryptographic nonce Cryptovirology Hash function Cryptographic hash function Key derivation function Secure Hash Algorithms Digital signature Kleptography Key (cryptography) Key exchange Key generator Key schedule Key stretching Keygen Machines Ransomware Random number generation Cryptographically secure pseudorandom number generator (CSPRNG) Pseudorandom noise (PRN) Secure channel Insecure channel Subliminal channel Encryption Decryption End-to-end encryption Harvest now, decrypt later Information-theoretic security Plaintext Codetext Ciphertext Shared secret Trapdoor function Trusted timestamping Key-based routing Onion routing Garlic routing Kademlia Mix network Mathematics Cryptographic hash function Block cipher Stream cipher Symmetric-key algorithm Authenticated encryption Public-key cryptography Quantum key distribution Quantum cryptography Post-quantum cryptography Message authentication code Random numbers Steganography Category Authority control databases GND --- Adapted from the Wikipedia article [Cryptosystem](https://en.wikipedia.org/wiki/Cryptosystem) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Cryptosystem?action=history)). 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