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Because of this ambiguity, the outdated RFC 2828 advised against the use of this term.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 . ${\displaystyle D_{d}(E_{e}(p))=p\quad \forall p\in {\mathcal {P}}}$

See also

• Threshold value cryptosystem

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 .