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Cryptosystem

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Suite of cryptographic algorithms needed to implement a particular security service

Incryptography, acryptosystem is a suite ofcryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption).^[1]

Typically, a cryptosystem consists of three algorithms: one forkey generation, one for encryption, and one for decryption. The termcipher (sometimescypher) is often used to refer to a pair of algorithms, one for encryption and one for decryption. Therefore, the termcryptosystem is most often used when the key generation algorithm is important. For this reason, the termcryptosystem is commonly used to refer topublic key techniques; however both "cipher" and "cryptosystem" are used forsymmetric key techniques.

Formal definition

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

${\mathcal {P}}$ is a set called the "plaintext space". Its elements are called plaintexts.
${\mathcal {C}}$ is a set called the "ciphertext space". Its elements are called ciphertexts.
${\mathcal {K}}$ is a set called the "key space". Its elements are called keys.
${\mathcal {E}}=\{E_{k}:k\in {\mathcal {K}}\}$ is a set of functions $E_{k}:{\mathcal {P}}\rightarrow {\mathcal {C}}$ . Its elements are called "encryption functions".
${\mathcal {D}}=\{D_{k}:k\in {\mathcal {K}}\}$ is a set of functions $D_{k}:{\mathcal {C}}\rightarrow {\mathcal {P}}$ . Its elements are called "decryption functions".

For each $e\in {\mathcal {K}}$ , there is $d\in {\mathcal {K}}$ such that $D_{d}(E_{e}(p))=p$ for all $p\in {\mathcal {P}}$ .^[2]

Note; typically this definition is modified in order to distinguish an encryption scheme as being either asymmetric-key orpublic-key type of cryptosystem.

Examples

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A classical example of a cryptosystem is theCaesar cipher. A more contemporary example is theRSA cryptosystem.

Another example of a cryptosystem is theAdvanced Encryption Standard (AES). AES is a widely used symmetric encryption algorithm that has become the standard for securing data in various applications.

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]

References

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^Menezes, A.; Oorschot, P. van; Vanstone, S. (1997).Handbook of Applied Cryptography (5th ed.). CRC Press.ISBN 0-8493-8523-7.
^Buchmann, Johannes A. (13 July 2004).Introduction to Cryptography (2nd ed.). Springer.ISBN 0-387-20756-2.
^Xia, Zhe; Yang, Xiaoyun; Xiao, Min; He, Debiao (2016)."Provably Secure Threshold Paillier Encryption Based on Hyperplane Geometry". 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:10.1007/978-3-319-40367-0_5.ISBN 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
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Authority control databases	GND

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