# Cryptosystem

A cryptosystem is generally a system that has to do with cryptography . The term is used as a fixed term in the name RSA cryptosystem . However, the term cryptosystem means different things in different contexts. Some authors limit the term cryptosystem to encryption methods . Others also use it for other cryptographic systems such as digital signatures .

Because of this ambiguity, the outdated RFC 2828 advised against the use of this term. In the current RFC 4949 , which replaced RFC 2828 , the term "cryptosystem" is defined as a contraction of "cryptographic system". The definition of a cryptographic system includes both possible meanings, but the more general one is preferred. Both RFCs are not an Internet standard, but are classified as informational.

## Formal definition

Mathematically, a cryptosystem is defined as the tuple , which has the following properties. ${\ displaystyle ({\ mathcal {P}}, {\ mathcal {C}}, {\ mathcal {K}}, {\ mathcal {E}}, {\ mathcal {D}})}$ 1. ${\ displaystyle {\ mathcal {P}}}$ is the plain text. The elements of are the plaintext.${\ displaystyle {\ mathcal {P}}}$ 2. ${\ displaystyle {\ mathcal {C}}}$ is the encrypted text (or ciphertext). The elements of are the ciphertext.${\ displaystyle {\ mathcal {C}}}$ 3. ${\ displaystyle {\ mathcal {K}}}$ is defined as the key. The elements of are key${\ displaystyle {\ mathcal {K}}}$ 4. ${\ displaystyle {\ mathcal {E}} = \ {E_ {k}: k \ in {\ mathcal {K}} \}}$ with the function . Is the encryption function for .${\ displaystyle E_ {k}: {\ mathcal {P}} \ rightarrow {\ mathcal {C}}}$ ${\ displaystyle {\ mathcal {P}}}$ 5. ${\ displaystyle {\ mathcal {D}} = \ {D_ {k}: k \ in {\ mathcal {K}} \}}$ with the function . Is the decryption function for .${\ displaystyle D_ {k}: {\ mathcal {C}} \ rightarrow {\ mathcal {P}}}$ ${\ displaystyle {\ mathcal {C}}}$ ${\ displaystyle \ forall e \ in {\ mathcal {K}}: d \ in {\ mathcal {K}}}$ that . ${\ displaystyle D_ {d} (E_ {e} (p)) = p \ quad \ forall p \ in {\ mathcal {P}}}$ ## Individual evidence

1. Johannes Buchmann : Introduction to Cryptography . 4th enlarged edition. Springer, Berlin a. a. 2008, ISBN 978-3-540-74451-1 , pp.  59 .
2. Bruce Schneier : Applied Cryptography . Protocols, Algorithms and Source Code in C . Addison-Wesley, Bonn a. a. 1996, ISBN 3-89319-854-7 , pp.  4 .
3. Friedrich L. Bauer : Deciphered secrets. Methods and maxims of cryptology . 3rd, revised and expanded edition. Springer, Berlin a. a. 2000, ISBN 3-540-67931-6 , pp.  7 .
4. Albrecht Beutelspacher : Kryptologie: An introduction to the science of encryption, concealment and concealment. Without any secrecy, but not without deceitful rogue, presented for the benefit and delight of the general public . 9th, updated edition. Vieweg + Teubner, Wiesbaden 2009, ISBN 978-3-8348-0253-8 , pp.  2 .
5. ^ R. Shirey: RFC 2828 - Internet Security Glossary (2000-05)
cryptosystem
(D) ISDs 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, ISDs SHOULD NOT use this abbreviated term because it may be misunderstood. Instead, use "cryptography" or "cryptographic".
6. ^ R. Shirey: RFC 4949 - Internet Security Glossary, Version 2 (2007-08)
cryptosystem
(I) Contraction of the "cryptographic system".
cryptographic system
1. (I) A set of cryptographic algorithms together with the key management processes that support use of the algorithms in some application context.
Usage: IDOCs SHOULD use definition 1 because it covers a wider range of algorithms than definition 2.
2. (O) "A collection of transformations from plain text into cipher text and vice versa [which would exclude digital signature, cryptographic hash, and key-agreement algorithms], the particular transformation (s) to be used being selected by keys. The transformations are normally defined by a mathematical algorithm. " [X509]
7. Johannes A. Buchmann: Introduction to Cryptography , 2nd. Edition, Springer ,, ISBN 0-387-20756-2 .