formulasearchengine - User contributions [en]

Affine cipher

2014-02-17T19:16:59Z

128.239.41.150: /* Description */

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Dark state

2014-02-07T22:11:22Z

128.239.178.185: /* Three-level systems */ Removed syntax errors

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Relational algebra

2014-02-04T03:10:05Z

128.239.168.146: /* {{visible anchor|Division}} (÷) */ Division result was incorrect

{{About|encrypted information|an overview of cryptographic technology in general|Cryptography}}
[[File:Zimmermann Telegram.jpeg|thumb|right|250px|The [[Zimmermann Telegram]] (as it was sent from Washington to Mexico) encrypted as ciphertext.]]

In [[cryptography]], '''ciphertext''' (or '''cyphertext''') is the result of [[encryption]] performed on [[plaintext]] using an algorithm, called a [[cipher]].<ref>{{cite book |author=Berti, Hansche, Hare |title=Official (ISC)² Guide to the [[CISSP]] Exam |publisher=Auerbach Publications |year=2003 |pages=379 |isbn=0-8493-1707-X}}</ref> Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext that is unreadable by a human or computer without the proper cipher to decrypt it. [[Decryption]], the inverse of encryption, is the process of turning ciphertext into readable plaintext. Ciphertext is not to be confused with [[codetext]] because the latter is a result of a [[Code (cryptography)|code]], not a cipher.

== Symmetric key example ==
Let <math>m\!</math> be the plaintext message that Alice wants to secretly transmit to Bob and let <math>E_k\!</math> be the encryption cipher, where <math>_k\!</math> is a [[secret key]]. Alice must first transform the plaintext into ciphertext, <math>c\!</math>, in order to securely send the message to Bob.

: <math>c = E_k(m)\!</math><ref name="Fundamentals">{{cite book|isbn=0-7923-8675-2 |title=Fundamentals of Cryptology |publisher=Kluwer Academic Publishers |year=2000 |first=Henk C.A. |last=van Tilborg |page=3}}</ref>

Both Alice and Bob must know the choice of key, <math>k\!</math>, or else the ciphertext is useless. Once the message is encrypted as ciphertext, Alice can safely transmit it to Bob (assuming no one else knows the key). In order to read Alice's message, Bob must decrypt the ciphertext using <math>{E_k}^{-1}\!</math> which is known as the decryption cipher, <math>D_k\!</math>.

: <math>D_k(c) = D_k(E_k(m)) = m\!</math><ref name="Fundamentals" />

== Types of ciphers ==
{{Main|Cipher}}
The [[history of cryptography]] begins thousands of years ago and contains a variety of different types of encryption. Earlier algorithms were performed by hand and are substantially different from modern [[algorithm]]<nowiki/>s, which are generally executed by a machine.

=== Historical ciphers ===
Historical pen and paper ciphers used in the past are sometimes known as [[classical cipher]]s. They include:

* '''[[Substitution cipher]]''': the units of plaintext are replaced with ciphertext ([[Caesar cipher]] and [[One-time pad]])
* '''[[Transposition cipher]]''': the ciphertext is a [[permutation]] of the plaintext ([[Rail fence|Rail fence cipher]])
* '''[[Polyalphabetic substitution|Polyalphabetic substitution cipher]]''': a substitution cipher using multiple substitution alphabets ([[Vigenère cipher]] and [[Enigma machine]])
* '''[[Permutation cipher]]''': a transposition cipher in which the key is a permutation

Historical ciphers are not generally used as a standalone encryption solution because they are quite easy to crack. Many of the classical ciphers can be cracked using [[Brute force attack|brute force]] or by analyzing only ciphertext with the exception of the one-time pad.

=== Modern ciphers ===
Modern ciphers are more secure than classical ciphers and are designed to withstand a wide range of attacks. An attacker should not be able to find the key used in a modern cipher, even if he knows any amount of plaintext and corresponding ciphertext. Modern encryption methods can be divided into the following categories:

* '''[[Private-key cryptography]]''' ([[symmetric key algorithm]]): the same key is used for encryption and decryption
* '''[[Public-key cryptography]]''' ([[asymmetric key algorithm]]): two different keys are used for encryption and decryption

In a symmetric key algorithm (e.g., [[Data Encryption Standard|DES]] and [[Advanced Encryption Standard|AES]]), the sender and receiver must have a shared key set up in advance and kept secret from all other parties; the sender uses this key for encryption, and the receiver uses the same key for decryption. In an asymmetric key algorithm (e.g., [[RSA (algorithm)|RSA]]), there are two separate keys: a ''public key'' is published and enables any sender to perform encryption, while a ''private key'' is kept secret by the receiver and enables only him to perform correct decryption.

Symmetric key ciphers can be divided into [[block cipher]]s and [[stream cipher]]s. Block ciphers operate on fixed-length groups of bits, called blocks, with an unvarying transformation. Stream ciphers encrypt plaintext digits one at a time on a continuous stream of data and the transformation of successive digits varies during the encryption process.

== Cryptanalysis ==
[[Image:Zimmermann-telegramm-offen.jpg|thumb|250px|right|The [[Zimmermann Telegram]] decrypted into plaintext (and translated into English).]]
{{Main|Cryptanalysis}}
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key. Cryptanalysis is also referred to as codebreaking or [[Password cracking|cracking the code]]. Ciphertext is generally the easiest part of a [[cryptosystem]] to obtain and therefore is an important part of cryptanalysis. Depending on what information is available and what type of cipher is being analyzed, crypanalysts can follow one or more [[attack model]]s to crack a cipher.

=== Attack models ===
*'''[[Ciphertext-only attack|Ciphertext-only]]''': the cryptanalyst has access only to a collection of ciphertexts or codetexts
*'''[[Known-plaintext attack|Known-plaintext]]''': the attacker has a set of ciphertexts to which he knows the corresponding plaintext
*'''[[Chosen-plaintext attack]]''': the attacker can obtain the ciphertexts corresponding to an arbitrary set of plaintexts of his own choosing
**'''Batch chosen-plaintext attack''': where the cryptanalyst chooses all plaintexts before any of them are encrypted. This is often the meaning of an unqualified use of "chosen-plaintext attack".
**'''Adaptive chosen-plaintext attack''': where the cryptanalyst makes a series of interactive queries, choosing subsequent plaintexts based on the information from the previous encryptions.
*'''[[Chosen-ciphertext attack]]''': the attacker can obtain the plaintexts corresponding to an arbitrary set of ciphertexts of his own choosing
**'''[[Adaptive chosen-ciphertext attack]]'''
**'''[[Indifferent chosen-ciphertext attack]]'''
*'''[[Related-key attack]]''': like a chosen-plaintext attack, except the attacker can obtain ciphertexts encrypted under two different keys. The keys are unknown, but the relationship between them is known; for example, two keys that differ in the one bit.

The ciphertext-only attack model is the weakest because it implies that the cryptanalyst has nothing but ciphertext. Modern ciphers rarely fail under this attack.<ref>{{cite book |last=Schneier |first=Bruce |title=Secrets & Lies |publisher=Wiley Computer Publishing Inc |pages=90–91 |isbn=0-471-25311-1}}</ref>

== Famous ciphertexts ==
{{Main|List of ciphertexts}}
[[Image:Shugborough inscription.jpg|thumb|650px|right|The Shugborough inscription, England]]
*The [[Babington Plot]] ciphers
*The [[Shugborough inscription]]
*The [[Zimmermann Telegram]]
*[[The Magic Words are Squeamish Ossifrage]]
*The [[cryptogram]] in "[[The Gold-Bug]]"
*[[Beale ciphers]]
*[[Kryptos]]
*[[Zodiac Killer]] ciphers

== See also ==
* [[:RED/BLACK concept]]
* [[:Frequency analysis]]
* [[:Books on cryptography]]
* [[:Cryptographic hash function]]
* [[:Category:Uncracked codes and ciphers]]

==References==
{{Reflist|2}}

== Further reading ==
{{Wiktionary}}
* Helen Fouché Gaines, “Cryptanalysis”, 1939, Dover. ISBN 0-486-20097-3
* [[David Kahn (writer)|David Kahn]], ''The Codebreakers - The Story of Secret Writing'' (ISBN 0-684-83130-9) (1967)
* [[Abraham Sinkov]], ''Elementary Cryptanalysis: A Mathematical Approach'', Mathematical Association of America, 1966. ISBN 0-88385-622-0

{{Cryptography navbox}}

[[Category:Cryptography]]

Equivalence partitioning

2012-07-04T17:16:48Z

128.239.26.119:

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Metzler matrix

2012-06-04T19:41:00Z

128.239.171.252: /* See also */ Fixed capitalization of Stochastic matrix

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