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Introduction to Cryptography
Cryptography
Cryptography or cryptology (from
https://en.wikipedia.org/wiki/Ancient_Greek_language	https://en.wikipedia.org/wiki/Ancient_Egypt https://en.wikipedia.org/wiki/Na%27vi_language https://en.wikipedia.org/wiki/Jean_Grey
Ancient Greek: “hidden, secret”; and “to write”, or “study”, respectively [1] ) is the practice and study of techniques for
https://en.wikipedia.org/wiki/Cryptography#cite_note-1	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-10
https://en.wikipedia.org/wiki/Secure_communication	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Sentinel_(comics) https://en.wikipedia.org/wiki/Communist_Poland
secure communicationin the presence of third parties called
https://en.wikipedia.org/wiki/Adversary_(cryptography)	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
adversaries. [2] More generally, cryptography is about constructing and analyzing
https://en.wikipedia.org/wiki/Cryptography#cite_note-rivest90-2	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-29
https://en.wikipedia.org/wiki/Communications_protocol	https://en.wikipedia.org/wiki/Communist_Poland https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/X-Mansion
protocolsthat prevent third parties or the public from reading private messages; [3] various aspects in
https://en.wikipedia.org/wiki/Cryptography#cite_note-modern-crypto-3	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-6
https://en.wikipedia.org/wiki/Information_security	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London
information securitysuch as data
https://en.wikipedia.org/wiki/Confidentiality	https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX
confidentiality,
https://en.wikipedia.org/wiki/Data_integrity	https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4 https://en.wikipedia.org/wiki/Avatar_3
data integrity,
https://en.wikipedia.org/wiki/Authentication	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Telepathic https://en.wikipedia.org/wiki/X-Men
authentication, and
https://en.wikipedia.org/wiki/Non-repudiation	https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/4DX
non-repudiation [4] are central to modern cryptography. Modern cryptography exists at the intersection of the disciplines of	non-repudiation [4] are central to modern cryptography. adversaries. [2] More generally, cryptography is about constructing and analyzing
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/Avatar_(2009_film)#cite_note-6

https://en.wikipedia.org/wiki/Mathematics	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Telepathic https://en.wikipedia.org/wiki/4DX
mathematics,
https://en.wikipedia.org/wiki/Computer_science	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Ancient_Egypt
computer science,
https://en.wikipedia.org/wiki/Electrical_engineering	https://en.wikipedia.org/wiki/Genetic_engineering https://en.wikipedia.org/wiki/Telekinetic https://en.wikipedia.org/wiki/Astral_plane
electrical engineering,
https://en.wikipedia.org/wiki/Communication_science	https://en.wikipedia.org/wiki/Science_fiction_film https://en.wikipedia.org/wiki/Communist_Poland https://en.wikipedia.org/wiki/Motion_capture
communication science, and
https://en.wikipedia.org/wiki/Physics	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Psylocke
physics. Applications of cryptography include	Applications of cryptography include physics.
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https://en.wikipedia.org/wiki/Electronic_commerce	https://en.wikipedia.org/wiki/Epic_film https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/James_Cameron
electronic commerce,
https://en.wikipedia.org/wiki/Credit_card_chip	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men
chip-based payment cards,
https://en.wikipedia.org/wiki/Digital_currencies	https://en.wikipedia.org/wiki/Weta_Digital https://en.wikipedia.org/wiki/Telepresence https://en.wikipedia.org/wiki/Ancient_Egypt
digital currencies,
https://en.wikipedia.org/wiki/Password	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Psylocke
computer passwords, and
https://en.wikipedia.org/wiki/Military_communications	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
military communications.
Cryptography prior to the modern age was effectively synonymous with
https://en.wikipedia.org/wiki/Encryption	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion
encryption , the conversion of information from a readable state to apparent
https://en.wikipedia.org/wiki/Nonsense	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London
nonsense. The originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature	The originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries.
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https://en.wikipedia.org/wiki/Alice_and_Bob	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/Jon_Landau
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
https://en.wikipedia.org/wiki/Eavesdropper	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/East_Berlin
https://en.wikipedia.org/wiki/Cryptography#cite_note-codesintro-5	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-6
https://en.wikipedia.org/wiki/Rotor_machine	https://en.wikipedia.org/wiki/Rose_Byrne https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Dolby_Cinema
rotor cipher machinesin
https://en.wikipedia.org/wiki/World_War_I	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
World WarIand the advent of
https://en.wikipedia.org/wiki/Computer	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather
computersin
https://en.wikipedia.org/wiki/World_War_II	https://en.wikipedia.org/wiki/Warren_Worthington_III https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
World WarII, the methods used to carry out cryptology have become increasingly complex and its application more widespread.
Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic
https://en.wikipedia.org/wiki/Algorithm	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/X-Men
algorithmsare designed around
https://en.wikipedia.org/wiki/Computational_hardness_assumption	https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4 https://en.wikipedia.org/wiki/Avatar_3
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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	A
https://en.wikipedia.org/wiki/Integer_factorization	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
integer factorizationalgorithms, and faster computing technology require these solutions to be continually adapted. There exist	integer factorizationalgorithms, and faster computing technology require these solutions to be continually adapted.
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https://en.wikipedia.org/wiki/Information_theoretic_security	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Teleportation_in_fiction
information-theoretically secureschemes that provably cannot be broken even with unlimited computing power—an example is the
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
one-time pad—but these schemes are more difficult to use in practice than the best theoretically breakable but computationally secure mechanisms.
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	The growth of cryptographic technology has raised a number of legal issues in the information age.
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https://en.wikipedia.org/wiki/Espionage	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/Epic_film
espionageand
https://en.wikipedia.org/wiki/Sedition	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion
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
https://en.wikipedia.org/wiki/Cryptography#cite_note-cryptolaw-6	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-6
https://en.wikipedia.org/wiki/Key_disclosure_law	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Jean_Grey https://en.wikipedia.org/wiki/Cerebro
compel the disclosureof encryption keys for documents relevant to an investigation. [7] [8] Cryptography also plays a major role in
https://en.wikipedia.org/wiki/Cryptography#cite_note-UK_law-7	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-6
https://en.wikipedia.org/wiki/Cryptography#cite_note-RangerSteve1-8	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-autogenerated2-14
https://en.wikipedia.org/wiki/Digital_rights_management	https://en.wikipedia.org/wiki/Weta_Digital https://en.wikipedia.org/wiki/Gas_giant https://en.wikipedia.org/wiki/X-Men
digital rights managementand
https://en.wikipedia.org/wiki/Copyright_infringement	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Bryan_Singer
copyright infringementof digital media. [9]
https://en.wikipedia.org/wiki/Cryptography#cite_note-AACS-9	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-6
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.
https://en.wikipedia.org/wiki/The_Gold-Bug	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Tye_Sheridan https://en.wikipedia.org/wiki/Weather
https://en.wikipedia.org/wiki/Edgar_Allan_Poe	https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4 https://en.wikipedia.org/wiki/Avatar_3
https://en.wikipedia.org/wiki/Cryptography#cite_note-10	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-10 https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5
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Until modern times, cryptography referred almost exclusively to
encryption, which is the process of converting ordinary information (called
https://en.wikipedia.org/wiki/Plaintext	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Psylocke
plaintext) into unintelligible form (called
https://en.wikipedia.org/wiki/Ciphertext	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/4DX
ciphertext).
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Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A	Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext.
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https://en.wikipedia.org/wiki/Cipher	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/4DX
cipher (or
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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https://en.wikipedia.org/wiki/Key_(cryptography)	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men
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	A
https://en.wikipedia.org/wiki/Cryptosystem	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/X-Men
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Historically, ciphers were often used directly for encryption or decryption without additional procedures such as
https://en.wikipedia.org/wiki/Authentication	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Telepathic https://en.wikipedia.org/wiki/X-Men
authenticationor integrity checks. There are two kinds of cryptosystems:	authenticationor integrity checks. integer factorizationor the
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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/Weta_Digital
symmetricand
https://en.wikipedia.org/wiki/Public-key_cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Psylocke https://en.wikipedia.org/wiki/4DX
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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https://en.wikipedia.org/wiki/Cryptography#cite_note-12	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-10
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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).	Symmetric models include the commonly used AES (Advanced Encryption Standard) which replaced the older DES (Data Encryption Standard). Examples of asymmetric systems include RSA (Rivest-Shamir-Adleman), and ECC (Elliptic Curve Cryptography).
https://en.wikipedia.org/wiki/Rivest-Shamir-Adleman	https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men
https://en.wikipedia.org/wiki/Elliptic_Curve_Cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Epic_film https://en.wikipedia.org/wiki/Wellington

https://en.wikipedia.org/wiki/Advanced_Encryption_Standard	https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
https://en.wikipedia.org/wiki/Data_Encryption_Standard	https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
https://en.wikipedia.org/wiki/Cryptography#cite_note-13	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-10
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In
https://en.wikipedia.org/wiki/Colloquial	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/X-Men
colloquialuse, the term “code” is often used to mean any method of encryption or concealment of meaning. However, in cryptography,	colloquialuse, the term “code” is often used to mean any method of encryption or concealment of meaning.
https://en.wikipedia.org/wiki/Code_(cryptography)	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro

codehas a more specific meaning. It means the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a	It means the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a codehas a more specific meaning.
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https://en.wikipedia.org/wiki/Code_word	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/X-Men
code word(for example, “wallaby” replaces “attack at dawn”).
https://en.wikipedia.org/wiki/Cryptanalysis	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/Cerebro
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.
Some use the terms
cryptographyand
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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https://en.wikipedia.org/wiki/Cryptography#cite_note-websters-15	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-Reuters-25
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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.
https://en.wikipedia.org/wiki/Request_for_Comments_(identifier)	https://en.wikipedia.org/wiki/James_Cameron https://en.wikipedia.org/wiki/Mystique_(film_character) https://en.wikipedia.org/wiki/X-Men_(film_series)
RFC2828advises thatsteganographyis sometimes included in cryptology.
https://tools.ietf.org/html/rfc2828
https://en.wikipedia.org/wiki/Steganography	https://en.wikipedia.org/wiki/Stephen_Lang https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX
https://en.wikipedia.org/wiki/Cryptography#cite_note-16	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/X-Men:_Apocalypse#cite_note-5 https://en.wikipedia.org/wiki/Avatar_(2009_film)#cite_note-10
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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
Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion of
https://en.wikipedia.org/wiki/Information	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Mansion
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	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).
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https://en.wikipedia.org/wiki/Secrecy	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/X-Men
secrecyin
https://en.wikipedia.org/wiki/Communications	https://en.wikipedia.org/wiki/Communist_Poland https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/4DX
communications, such as those of
https://en.wikipedia.org/wiki/Spy	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
spies, military leaders, and
https://en.wikipedia.org/wiki/Diplomat	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/X-Men
diplomats. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity	In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity
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https://en.wikipedia.org/wiki/Authentication	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Telepathic https://en.wikipedia.org/wiki/X-Men
authentication,
https://en.wikipedia.org/wiki/Digital_signature	https://en.wikipedia.org/wiki/Weta_Digital https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
digital signatures,
https://en.wikipedia.org/wiki/Interactive_proof_system	https://en.wikipedia.org/wiki/Mystique_(film_character) https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX
interactive proofsand
https://en.wikipedia.org/wiki/Secure_multiparty_computation	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
secure computation, among others.
Computer era
Prior to the early 20th century, cryptography was mainly concerned with
https://en.wikipedia.org/wiki/Language	https://en.wikipedia.org/wiki/Na%27vi_language https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London
linguisticand
https://en.wikipedia.org/wiki/Lexicographic_code	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/Epic_film
lexicographicpatterns. Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of	Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of
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https://en.wikipedia.org/wiki/Information_theory	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Motion_capture
information theory,
https://en.wikipedia.org/wiki/Computational_complexity_theory	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/3D_television https://en.wikipedia.org/wiki/Telepathic
computational complexity,
https://en.wikipedia.org/wiki/Statistics	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
statistics,
https://en.wikipedia.org/wiki/Combinatorics	https://en.wikipedia.org/wiki/Marvel_Comics https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro
combinatorics,
https://en.wikipedia.org/wiki/Abstract_algebra	https://en.wikipedia.org/wiki/Astral_plane https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/Montreal
abstract algebra,
https://en.wikipedia.org/wiki/Number_theory	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Cerebro
number theory, and finite mathematics generally. Cryptography is also a branch of	number theory, and finite mathematics generally.
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https://en.wikipedia.org/wiki/Engineering	https://en.wikipedia.org/wiki/Genetic_engineering https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/East_Berlin
engineering, but an unusual one since it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and
https://en.wikipedia.org/wiki/Security_engineering	https://en.wikipedia.org/wiki/Genetic_engineering https://en.wikipedia.org/wiki/Sophie_Turner https://en.wikipedia.org/wiki/Sigourney_Weaver
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	security engineering); other kinds of engineering (e.g., civil or chemical engineering) need deal only with neutral natural forces.
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https://en.wikipedia.org/wiki/Quantum_physics	https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Gas_giant
quantum physics(see
https://en.wikipedia.org/wiki/Quantum_cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/Motion_capture
quantum cryptographyand
https://en.wikipedia.org/wiki/Quantum_computer	https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Gas_giant
quantum computer).
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	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.
	A
	A
	A
https://en.wikipedia.org/wiki/Binary_numeral_system	https://en.wikipedia.org/wiki/Astral_plane https://en.wikipedia.org/wiki/Bryan_Singer https://en.wikipedia.org/wiki/East_Berlin
binary
https://en.wikipedia.org/wiki/Bit	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
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.	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
https://en.wikipedia.org/wiki/Cryptanalysis	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Mansion https://en.wikipedia.org/wiki/Cerebro
Cryptanalysisof the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at	Cryptanalysisof the new mechanical devices proved to be both difficult and laborious.
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https://en.wikipedia.org/wiki/Bletchley_Park	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Avatar_5
Bletchley Parkduring WWII spurred the development of more efficient means for carrying out repetitious tasks. This culminated in the development of the	Bletchley Parkduring WWII spurred the development of more efficient means for carrying out repetitious tasks.
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https://en.wikipedia.org/wiki/Colossus_computer	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Weather
Colossus, the world’s first fully electronic, digital,
https://en.wikipedia.org/wiki/Computer_programming	https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Bryan_Singer
programmablecomputer, which assisted in the decryption of ciphers generated by the German Army’s
https://en.wikipedia.org/wiki/Lorenz_SZ40/42	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/London https://en.wikipedia.org/wiki/X-Men
Lorenz SZ40/42machine.
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)	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)
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https://en.wikipedia.org/wiki/Data_Encryption_Standard	https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
Data Encryption Standard;
https://en.wikipedia.org/wiki/Whitfield_Diffie	https://en.wikipedia.org/wiki/Weta_Digital https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/4D_film
Whitfield Diffieand
https://en.wikipedia.org/wiki/Martin_Hellman	https://en.wikipedia.org/wiki/Wellington https://en.wikipedia.org/wiki/Marvel_Comics https://en.wikipedia.org/wiki/Humanoid
Martin Hellmanpublished
https://en.wikipedia.org/wiki/Diffie-Hellman	https://en.wikipedia.org/wiki/4D_film https://en.wikipedia.org/wiki/3D_film https://en.wikipedia.org/wiki/Humanoid
their key agreement algorithm;
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/Avatar_(2009_film)#cite_note-6
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and the
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
RSAalgorithm was published in
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
Martin Gardner‘s
https://en.wikipedia.org/wiki/Scientific_American	https://en.wikipedia.org/wiki/Science_fiction_film https://en.wikipedia.org/wiki/Epic_film https://en.wikipedia.org/wiki/Ancient_Egypt
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.	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.
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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/Avatar_(2009_film)#cite_note-6
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Since then, cryptography has become a widely used tool in communications,
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 networks, and
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
computer securitygenerally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are	Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are programmablecomputer, which assisted in the decryption of ciphers generated by the German Army’s cryptographyto refer specifically to the use and practice of cryptographic techniques and
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https://en.wikipedia.org/wiki/Computational_complexity_theory#Intractability	https://en.wikipedia.org/wiki/Auschwitz_concentration_camp
intractable, such as the
https://en.wikipedia.org/wiki/Integer_factorization	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
integer factorizationor the
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/Weta_Digital
discrete logarithmproblems, so there are deep connections with
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
abstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. The	There are very few cryptosystems that are proven to be unconditionally secure.
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	A
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
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
	A
	A
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
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	RSAis secure, and some other systems, but even so proof of unbreakability is unavailable since the underlying mathematical problem remains open. 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.
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	A
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/Michelle_Rodriguez
Michael O. Rabinthat are provably secure provided factoring
n = pqis impossible; it is quite unusable in practice. The	n = pqis impossible; it is quite unusable in practice. interactive proofsand
	A
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/Habitable_moon
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/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/Avatar_(2009_film)#cite_note-6
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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	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.
	A
https://en.wikipedia.org/wiki/Brute-force_attack	https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4 https://en.wikipedia.org/wiki/Avatar_3
brute-force attacks, so when specifying
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
key lengths, the required key lengths are similarly advancing.
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/Avatar_(2009_film)#cite_note-6
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The potential effects of
https://en.wikipedia.org/wiki/Quantum_computing	https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Sentinel_(comics)
quantum computingare already being considered by some cryptographic system designers developing
https://en.wikipedia.org/wiki/Post-quantum_cryptography	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/Motion_capture
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/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/Avatar_(2009_film)#cite_note-6
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/Weta_Digital
https://en.wikipedia.org/wiki/File:Symmetric_key_encryption.svg	https://en.wikipedia.org/wiki/Genetic_engineering https://en.wikipedia.org/wiki/Science_fiction_film https://en.wikipedia.org/wiki/Telekinetic
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.	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).
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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/Avatar_(2009_film)#cite_note-6
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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/Fictional_universe_of_Avatar https://en.wikipedia.org/wiki/Weta_Digital
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
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
block ciphersor
https://en.wikipedia.org/wiki/Stream_ciphers	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Montreal https://en.wikipedia.org/wiki/Stephen_Lang
stream ciphers. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.	A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.
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The
https://en.wikipedia.org/wiki/Data_Encryption_Standard	https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
Data Encryption Standard(DES) and the
https://en.wikipedia.org/wiki/Advanced_Encryption_Standard	https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5 https://en.wikipedia.org/wiki/Avatar_4
Advanced Encryption Standard(AES) are block cipher designs that have been designated
https://en.wikipedia.org/wiki/Cryptography_standards	https://en.wikipedia.org/wiki/Principal_photography https://en.wikipedia.org/wiki/Jon_Landau https://en.wikipedia.org/wiki/Avatar_5
cryptography standardsby the US government (though DES’s designation was finally withdrawn after the AES was adopted).
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/Avatar_(2009_film)#cite_note-6
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Despite its deprecation as an official standard, DES (especially its still-approved and much more secure
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
triple-DESvariant) remains quite popular; it is used across a wide range of applications, from ATM encryption
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/Avatar_(2009_film)#cite_note-6
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to
https://en.wikipedia.org/wiki/E-mail_privacy	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/Epic_film https://en.wikipedia.org/wiki/4D_film
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/Avatar_(2009_film)#cite_note-6
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and
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
secure remote access.
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/Avatar_(2009_film)#cite_note-6
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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	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
	A
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
FEAL. [4]
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/Avatar_(2009_film)#cite_note-6
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
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
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.	In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates.
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	A
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
RC4is a widely used stream cipher; see
https://en.wikipedia.org/wiki/Category:Stream_ciphers	https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Cerebro https://en.wikipedia.org/wiki/Montreal
Category:Stream ciphers. [4] Block ciphers can be used as stream ciphers; see
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/Avatar_(2009_film)#cite_note-6
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/James_Cameron
Block cipher modes of operation.
https://en.wikipedia.org/wiki/Cryptographic_hash_functions	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Science_fiction_film https://en.wikipedia.org/wiki/Epic_film
Cryptographic hash functionsare a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed length	Cryptographic hash functionsare a third type of cryptographic algorithm.
	A
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
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.	For good hash functions, an attacker cannot find two messages that produce the same hash. hash, which can be used in (for example) a digital signature.
	A
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
MD4is a long-used hash function that is now broken;
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
MD5, a strengthened variant of MD4, is also widely used but broken in practice. The US	MD5, a strengthened variant of MD4, is also widely used but broken in practice.
	A
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/Motion_capture
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/SHA-1	https://en.wikipedia.org/wiki/4DX https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/London
SHA-1is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the
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
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/National_Institute_of_Standards_and_Technology	https://en.wikipedia.org/wiki/Fictional_universe_of_Avatar#Astronomy_and_geology https://en.wikipedia.org/wiki/Fictional_universe_of_Avatar
NIST‘s overall hash algorithm toolkit.”
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/Avatar_(2009_film)#cite_note-6
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Thus, a
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/Motion_capture
hash function design competitionwas meant to select a new U.S. national standard, to be called
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
SHA-3, by 2012. The competition ended on October 2, 2012 when the NIST announced that	The competition ended on October 2, 2012 when the NIST announced that
	A
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
Keccakwould be the new SHA-3 hash algorithm.
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/Avatar_(2009_film)#cite_note-6
40
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.	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.
	A
https://en.wikipedia.org/wiki/Message_authentication_code	https://en.wikipedia.org/wiki/Motion_capture https://en.wikipedia.org/wiki/Weather https://en.wikipedia.org/wiki/Auschwitz_concentration_camp
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/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/Avatar_(2009_film)#cite_note-6
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
The modern field of cryptography can be divided into several areas of study. The chief ones are discussed here; see	The modern field of cryptography can be divided into several areas of study.
	A
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
Topics in Cryptographyfor more.
Public-key cryptography
https://en.wikipedia.org/wiki/File:Public_key_encryption.svg	https://en.wikipedia.org/wiki/Science_fiction_film https://en.wikipedia.org/wiki/Epic_film https://en.wikipedia.org/wiki/Ancient_Egypt
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	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
https://en.wikipedia.org/wiki/Key_management	https://en.wikipedia.org/wiki/X-Men https://en.wikipedia.org/wiki/Humanoid https://en.wikipedia.org/wiki/4DX
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	Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well.
	A
	A
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
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/File:Diffie_and_Hellman.jpg	https://en.wikipedia.org/wiki/4D_film https://en.wikipedia.org/wiki/3D_film https://en.wikipedia.org/wiki/Epic_film
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