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Introduction to Cryptography
Cryptography
Cryptography or cryptology (from
Ancient Greek: “hidden, secret”; and “to write”, or “study”, respectively [1] ) is the practice and study of techniques for
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secure communicationin the presence of third parties called
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adversaries. [2] More generally, cryptography is about constructing and analyzing
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protocolsthat prevent third parties or the public from reading private messages; [3] various aspects in
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information securitysuch as data	This is mylink
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confidentiality,
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data integrity,
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authentication, and
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non-repudiation [4] are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of
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mathematics,
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computer science,
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electrical engineering,
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communication science, and
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physics. Applications of cryptography include
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electronic commerce,
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chip-based payment cards,
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digital currencies,
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computer passwords, and
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military communications.
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Cryptography prior to the modern age was effectively synonymous with
encryption , the conversion of information from a readable state to apparent
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nonsense. The originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature
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often uses the namesAlice (“A”) for the sender, Bob (“B”) for the intended recipient, and Eve (“eavesdropper“) for the adversary. [5] Since the development of
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rotor cipher machinesin
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World WarIand the advent of
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computersin	This is mylink
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World WarII, the methods used to carry out cryptology have become increasingly complex and its application more widespread.
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Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic
algorithmsare designed around
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computational hardness assumptions, making such algorithms hard to break in practice by any adversary. It is theoretically possible to break such a system, but it is infeasible to do so by any known practical means. These schemes are therefore termed computationally secure; theoretical advances, e.g., improvements in
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integer factorizationalgorithms, and faster computing technology require these solutions to be continually adapted. There exist
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information-theoretically secureschemes that provably cannot be broken even with unlimited computing power—an example is the
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one-time pad—but these schemes are more difficult to use in practice than the best theoretically breakable but computationally secure mechanisms.
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The growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography’s potential for use as a tool for

espionageand	This is mylink
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seditionhas led many governments to classify it as a weapon and to limit or even prohibit its use and export. [6] In some jurisdictions where the use of cryptography is legal, laws permit investigators to
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compel the disclosureof encryption keys for documents relevant to an investigation. [7] [8] Cryptography also plays a major role in
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digital rights managementand	This is mylink
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copyright infringementof digital media. [9]
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Terminology
The first use of the termcryptograph(as opposed tocryptogram) dates back to the 19th century—originating from The Gold-Bug , a novel byEdgar Allan Poe.
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Until modern times, cryptography referred almost exclusively to
encryption, which is the process of converting ordinary information (called
plaintext) into unintelligible form (called
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ciphertext).
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Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A

cipher (or	A wide range of translator expertise This is mylink
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cypher) is a pair of algorithms that create the encryption and the reversing decryption. The detailed operation of a cipher is controlled both by the algorithm and in each instance by a “key“. The key is a secret (ideally known only to the communicants), usually a short string of characters, which is needed to decrypt the ciphertext. Formally, a “cryptosystem” is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms which correspond to each key. Keys are important both formally and in actual practice, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes.

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Historically, ciphers were often used directly for encryption or decryption without additional procedures such as
authenticationor integrity checks. There are two kinds of cryptosystems:
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symmetricand	This is mylink
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asymmetric. In symmetric systems the same key (the secret key) is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems as they generally use shorter key lengths. Asymmetric systems use a public key to encrypt a message and a private key to decrypt it. Use of asymmetric systems enhances the security of communication.
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Examples of asymmetric systems include RSA (Rivest-Shamir-Adleman), and ECC (Elliptic Curve Cryptography). Symmetric models include the commonly used AES (Advanced Encryption Standard) which replaced the older DES (Data Encryption Standard).
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In
colloquialuse, the term “code” is often used to mean any method of encryption or concealment of meaning. However, in cryptography,
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codehas a more specific meaning. It means the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a

code word(for example, “wallaby” replaces “attack at dawn”).
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Cryptanalysisis the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.e., it is the study of how to crack encryption algorithms or their implementations.
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Some use the terms
cryptographyand	This is mylink
cryptologyinterchangeably in English, while others (including US military practice generally) use
cryptographyto refer specifically to the use and practice of cryptographic techniques and
cryptologyto refer to the combined study of cryptography and cryptanalysis.
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English is more flexible than several other languages in which
cryptology(done by cryptologists) is always used in the second sense above.
RFC2828advises thatsteganographyis sometimes included in cryptology.
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https://tools.ietf.org/html/rfc2828
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The study of characteristics of languages that have some application in cryptography or cryptology (e.g. frequency data, letter combinations, universal patterns, etc.) is called cryptolinguistics.
History of Cryptography	Cryptography Cryptography or cryptology (from
Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion of
messagesfrom a comprehensible form into an incomprehensible one and back again at the other end, rendering it unreadable by interceptors or eavesdroppers without secret knowledge (namely the key needed for decryption of that message). Encryption attempted to ensure
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secrecyin	This is mylink
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communications, such as those of
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spies, military leaders, and
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diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity
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authentication,
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digital signatures,
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interactive proofsand	This is mylink
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secure computation, among others.
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Computer era
Prior to the early 20th century, cryptography was mainly concerned with
linguisticand	This is mylink
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lexicographicpatterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of
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information theory,
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computational complexity,
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statistics,
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combinatorics,
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abstract algebra,
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number theory, and finite mathematics generally. Cryptography is also a branch of
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engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and
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security engineering); other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces. There is also active research examining the relationship between cryptographic problems and
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quantum physics(see	This is mylink
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quantum cryptographyand	This is mylink
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quantum computer).
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Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on



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binary
bitsequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly. However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity. Nonetheless, good modern ciphers have stayed ahead of cryptanalysis; it is typically the case that use of a quality cipher is very efficient (i.e., fast and requiring few resources, such as memory or CPU capability), while breaking it requires an effort many orders of magnitude larger, and vastly larger than that required for any classical cipher, making cryptanalysis so inefficient and impractical as to be effectively impossible.
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Advent of modern cryptography	Cryptography
Cryptanalysisof the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at
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Bletchley Parkduring WWII spurred the development of more efficient means for carrying out repetitious tasks. This culminated in the development of the
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Colossus, the world’s first fully electronic, digital,
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programmablecomputer, which assisted in the decryption of ciphers generated by the German Army’s
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Lorenz SZ40/42machine.	This is mylink
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Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970’s. In recent times, IBM personnel designed the algorithm that became the Federal (i.e., US)

Data Encryption Standard;
https://en.wikipedia.org/wiki/Data_Encryption_Standard	https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/Bryan_Singer
Whitfield Diffieand	This is mylink
https://en.wikipedia.org/wiki/Whitfield_Diffie	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Telepathic
Martin Hellmanpublished	This is mylink
https://en.wikipedia.org/wiki/Martin_Hellman	https://en.wikipedia.org/wiki/Marvel_Comics https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Telekinetic
their key agreement algorithm;
https://en.wikipedia.org/wiki/Diffie-Hellman	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
https://en.wikipedia.org/wiki/Cryptography#cite_note-dh2-30	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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and the
RSAalgorithm was published in	This is mylink
https://en.wikipedia.org/wiki/RSA_(algorithm)	https://en.wikipedia.org/wiki/RealD_3D https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather
Martin Gardner‘s
https://en.wikipedia.org/wiki/Martin_Gardner	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Telekinetic https://en.wikipedia.org/wiki/Jean_Grey
Scientific American column. Following their work in 1976, it became popular to consider cryptography systems based on mathematical problems that are easy to state but have been found difficult to solve.
https://en.wikipedia.org/wiki/Scientific_American	https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX

https://en.wikipedia.org/wiki/Cryptography#cite_note-31	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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Since then, cryptography has become a widely used tool in communications,
computer networks, and
https://en.wikipedia.org/wiki/Computer_network	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Peter_Maximoff
computer securitygenerally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are
https://en.wikipedia.org/wiki/Computer_security	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather

intractable, such as the
https://en.wikipedia.org/wiki/Computational_complexity_theory#Intractability	https://en.wikipedia.org/wiki/Auschwitz_concentration_camp
integer factorizationor the	This is mylink
https://en.wikipedia.org/wiki/Integer_factorization	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/4DX
discrete logarithmproblems, so there are deep connections with
https://en.wikipedia.org/wiki/Discrete_logarithm	https://en.wikipedia.org/wiki/Dan_Harris_(screenwriter) https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro
abstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. The
https://en.wikipedia.org/wiki/Abstract_mathematics	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Astral_plane https://en.wikipedia.org/wiki/Telepathic


one-time padis one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that
https://en.wikipedia.org/wiki/One-time_pad	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Rose_Byrne https://en.wikipedia.org/wiki/X-Men


RSAis secure, and some other systems, but even so proof of unbreakability is unavailable since the underlying mathematical problem remains open. In practice, these are widely used, and are believed unbreakable in practice by most competent observers. There are systems similar to RSA, such as one by
https://en.wikipedia.org/wiki/RSA_(cryptosystem)	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Rose_Byrne https://en.wikipedia.org/wiki/X-Men


Michael O. Rabinthat are provably secure provided factoring
https://en.wikipedia.org/wiki/Michael_O._Rabin	https://en.wikipedia.org/wiki/Michael_Dougherty https://en.wikipedia.org/wiki/Michael_Fassbender https://en.wikipedia.org/wiki/Marvel_Comics
n = pqis impossible; it is quite unusable in practice. The

discrete logarithm problemis the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem.
https://en.wikipedia.org/wiki/Discrete_logarithm_problem	https://en.wikipedia.org/wiki/Dan_Harris_(screenwriter) https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX
https://en.wikipedia.org/wiki/Cryptography#cite_note-32	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments while working on their designs. For instance, continuous improvements in computer processing power have increased the scope of

brute-force attacks, so when specifying
https://en.wikipedia.org/wiki/Brute-force_attack	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/X-Men
key lengths, the required key lengths are similarly advancing.
https://en.wikipedia.org/wiki/Key_length	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather
https://en.wikipedia.org/wiki/Cryptography#cite_note-fortify-33	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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The potential effects of
quantum computingare already being considered by some cryptographic system designers developing
https://en.wikipedia.org/wiki/Quantum_computing	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Sentinel_(comics) https://en.wikipedia.org/wiki/Bryan_Singer
post-quantum cryptography; the announced imminence of small implementations of these machines may be making the need for preemptive caution rather more than merely speculative. [4]
https://en.wikipedia.org/wiki/Post-quantum_cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Astral_plane
https://en.wikipedia.org/wiki/Cryptography#cite_note-hac-4	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
Symmetric-key cryptography
Main article:Symmetric-key algorithm
https://en.wikipedia.org/wiki/Symmetric-key_algorithm	https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather
https://en.wikipedia.org/wiki/File:Symmetric_key_encryption.svg	https://en.wikipedia.org/wiki/Telekinetic https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/Montreal
https://upload.wikimedia.org/wikipedia/commons/thumb/2/27/Symmetric_key_encryption.svg/250px-Symmetric_key_encryption.svg.png
diagram showing encrypt with a key and decrypt process
Symmetric-key cryptography, where a single key is used for encryption and decryption
Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key (or, less commonly, in which their keys are different, but related in an easily computable way). This was the only kind of encryption publicly known until June 1976.

https://en.wikipedia.org/wiki/Cryptography#cite_note-dh2-30	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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https://en.wikipedia.org/wiki/File:International_Data_Encryption_Algorithm_InfoBox_Diagram.svg
https://upload.wikimedia.org/wikipedia/commons/thumb/a/af/International_Data_Encryption_Algorithm_InfoBox_Diagram.svg/220px-International_Data_Encryption_Algorithm_InfoBox_Diagram.svg.png
logic diagram showing International Data Encryption Algorithm cypher process
One round (out of 8.5) of theIDEAcipher, used in most versions ofPGPand OpenPGP compatible software for time-efficient encryption of messages
https://en.wikipedia.org/wiki/International_Data_Encryption_Algorithm	https://en.wikipedia.org/wiki/Teleportation_in_fiction https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/Weather
https://en.wikipedia.org/wiki/Pretty_Good_Privacy	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Jean_Grey https://en.wikipedia.org/wiki/Cerebro
Symmetric key ciphers are implemented as either
block ciphersor	This is mylink My mother hasblueeyes.
https://en.wikipedia.org/wiki/Block_ciphers	https://en.wikipedia.org/wiki/Psylocke https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/4DX
stream ciphers. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.
https://en.wikipedia.org/wiki/Stream_ciphers	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/Cerebro

The
Data Encryption Standard(DES) and the
https://en.wikipedia.org/wiki/Data_Encryption_Standard	https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/Bryan_Singer
Advanced Encryption Standard(AES) are block cipher designs that have been designated
https://en.wikipedia.org/wiki/Advanced_Encryption_Standard	https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion
cryptography standardsby the US government (though DES’s designation was finally withdrawn after the AES was adopted).
https://en.wikipedia.org/wiki/Cryptography_standards	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London
https://en.wikipedia.org/wiki/Cryptography#cite_note-aes-34	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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Despite its deprecation as an official standard, DES (especially its still-approved and much more secure
triple-DESvariant) remains quite popular; it is used across a wide range of applications, from ATM encryption
https://en.wikipedia.org/wiki/Triple-DES	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Telepathic https://en.wikipedia.org/wiki/X-Men
https://en.wikipedia.org/wiki/Cryptography#cite_note-atm-35	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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to
https://en.wikipedia.org/wiki/E-mail_privacy	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
e-mail privacy
https://en.wikipedia.org/wiki/Cryptography#cite_note-opgp-36	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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and
secure remote access.
https://en.wikipedia.org/wiki/Secure_Shell	https://en.wikipedia.org/wiki/Tye_Sheridan https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro
https://en.wikipedia.org/wiki/Cryptography#cite_note-ssh-37	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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Many other block ciphers have been designed and released, with considerable variation in quality. Many, even some designed by capable practitioners, have been thoroughly broken, such as

FEAL. [4]	A wide range of translator expertise
https://en.wikipedia.org/wiki/FEAL	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
https://en.wikipedia.org/wiki/Cryptography#cite_note-hac-4	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
https://en.wikipedia.org/wiki/Cryptography#cite_note-schneierbook-38	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Sophie_Turner
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Stream ciphers, in contrast to the ‘block’ type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the
one-time pad. In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material.
https://en.wikipedia.org/wiki/One-time_pad	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Rose_Byrne https://en.wikipedia.org/wiki/X-Men


RC4is a widely used stream cipher; see	This is mylink
https://en.wikipedia.org/wiki/RC4	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/RealD_3D
Category:Stream ciphers. [4] Block ciphers can be used as stream ciphers; see
https://en.wikipedia.org/wiki/Category:Stream_ciphers	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/William_Stryker https://en.wikipedia.org/wiki/Cerebro
https://en.wikipedia.org/wiki/Cryptography#cite_note-hac-4	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
Block cipher modes of operation.
https://en.wikipedia.org/wiki/Block_cipher_modes_of_operation	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Psylocke https://en.wikipedia.org/wiki/Peter_Maximoff
Cryptographic hash functionsare a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed length
https://en.wikipedia.org/wiki/Cryptographic_hash_functions	https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/London

hash, which can be used in (for example) a digital signature. For good hash functions, an attacker cannot find two messages that produce the same hash.
https://en.wikipedia.org/wiki/Hash_function	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion

MD4is a long-used hash function that is now broken;
https://en.wikipedia.org/wiki/MD4	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Montreal
MD5, a strengthened variant of MD4, is also widely used but broken in practice. The US
https://en.wikipedia.org/wiki/MD5	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Montreal

National Security Agencydeveloped the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew;
https://en.wikipedia.org/wiki/National_Security_Agency	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/4DX
SHA-1is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the
https://en.wikipedia.org/wiki/SHA-1	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
SHA-2family improves on SHA-1, but is vulnerable to clashes as of 2011; and the US standards authority thought it “prudent” from a security perspective to develop a new standard to “significantly improve the robustness of
https://en.wikipedia.org/wiki/SHA-2	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
NIST‘s overall hash algorithm toolkit.”
https://en.wikipedia.org/wiki/National_Institute_of_Standards_and_Technology
https://en.wikipedia.org/wiki/Cryptography#cite_note-39	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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Thus, a
hash function design competitionwas meant to select a new U.S. national standard, to be called
https://en.wikipedia.org/wiki/NIST_hash_function_competition	https://en.wikipedia.org/wiki/Teleportation_in_fiction https://en.wikipedia.org/wiki/Auschwitz_concentration_camp https://en.wikipedia.org/wiki/London
SHA-3, by 2012. The competition ended on October 2, 2012 when the NIST announced that
https://en.wikipedia.org/wiki/SHA-3	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London

Keccakwould be the new SHA-3 hash algorithm.
https://en.wikipedia.org/wiki/Keccak	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
https://en.wikipedia.org/wiki/Cryptography#cite_note-40	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
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Unlike block and stream ciphers that are invertible, cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data. Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security.

Message authentication codes(MACs) are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt; [4] this additional complication blocks an attack scheme against baredigest algorithms, and so has been thought worth the effort.
https://en.wikipedia.org/wiki/Message_authentication_code	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Auschwitz_concentration_camp https://en.wikipedia.org/wiki/X-Men
https://en.wikipedia.org/wiki/Cryptography#cite_note-hac-4	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/4DX
https://en.wikipedia.org/wiki/Md5	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Montreal
Modern cryptography	Cryptography
The modern field of cryptography can be divided into several areas of study. The chief ones are discussed here; see

Topics in Cryptographyfor more.	This is mylink
https://en.wikipedia.org/wiki/Topics_in_Cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Telekinetic https://en.wikipedia.org/wiki/4DX
Public-key cryptography	Cryptography
https://en.wikipedia.org/wiki/File:Public_key_encryption.svg	https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/Telekinetic https://en.wikipedia.org/wiki/X-Men
https://upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Public_key_encryption.svg/250px-Public_key_encryption.svg.png
diagram of Public-key cryptography showing public key and private key
Public-key cryptography, where different keys are used for encryption and decryption.
Symmetric-key cryptosystems use the same key for encryption and decryption of a message, although a message or group of messages can have a different key than others. A significant disadvantage of symmetric ciphers is the

key managementnecessary to use them securely. Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well. The number of keys required increases as the
https://en.wikipedia.org/wiki/Key_management	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Jean_Grey


squareof the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret.
https://en.wikipedia.org/wiki/Square_(algebra)	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/4DX
https://en.wikipedia.org/wiki/File:Diffie_and_Hellman.jpg	https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Telepathic
https://upload.wikimedia.org/wikipedia/commons/thumb/8/88/Diffie_and_Hellman.jpg/220px-Diffie_and_Hellman.jpg
headshots of Whitfield Diffie and Martin Hellman