![Lorenz-SZ42-2](https://upload.wikimedia.org/wikipedia/commons/4/4d/Lorenz-SZ42-2.jpg)
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''
-logia'', "study", respectively
), is the practice and study of techniques for
secure communication
Secure communication is when two entities are communicating and do not want a third party to listen in. For this to be the case, the entities need to communicate in a way that is unsusceptible to eavesdropping or interception. Secure communication ...
in the presence of
adversarial behavior.
More generally, cryptography is about constructing and analyzing
protocols
Protocol may refer to:
Sociology and politics
* Protocol (politics), a formal agreement between nation states
* Protocol (diplomacy), the etiquette of diplomacy and affairs of state
* Etiquette, a code of personal behavior
Science and technology
...
that prevent third parties or the public from reading private messages.
Modern cryptography exists at the intersection of the disciplines of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
,
information security
Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorize ...
,
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
,
digital signal processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...
,
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
, and others.
Core concepts related to
information security
Information security, sometimes shortened to InfoSec, is the practice of protecting information by mitigating information risks. It is part of information risk management. It typically involves preventing or reducing the probability of unauthorize ...
(
data confidentiality,
data integrity
Data integrity is the maintenance of, and the assurance of, data accuracy and consistency over its entire Information Lifecycle Management, life-cycle and is a critical aspect to the design, implementation, and usage of any system that stores, proc ...
,
authentication
Authentication (from ''authentikos'', "real, genuine", from αὐθέντης ''authentes'', "author") is the act of proving an assertion, such as the identity of a computer system user. In contrast with identification, the act of indicati ...
, and
non-repudiation Non-repudiation refers to a situation where a statement's author cannot successfully dispute its authorship or the validity of an associated contract. The term is often seen in a legal setting when the authenticity of a signature is being challenged ...
) are also central to cryptography.
Practical applications of cryptography include
electronic commerce
E-commerce (electronic commerce) is the activity of electronically buying or selling of products on online services or over the Internet. E-commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain manageme ...
,
chip-based payment cards,
digital currencies
Digital currency (digital money, electronic money or electronic currency) is any currency, money, or money-like asset that is primarily managed, stored or exchanged on digital computer systems, especially over the internet. Types of digital cu ...
,
computer passwords, and
military communications
Military communications or military signals involve all aspects of communications, or conveyance of information, by armed forces. Military communications span from pre-history to the present. The earliest military communications were delivered b ...
.
Cryptography prior to the modern age was effectively synonymous with
encryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
, converting readable information (
plaintext
In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted.
Overview
With the advent of comp ...
) to unintelligible
nonsense
Nonsense is a communication, via speech, writing, or any other symbolic system, that lacks any coherent meaning. Sometimes in ordinary usage, nonsense is synonymous with absurdity or the ridiculous
To be ridiculous is to be something which is ...
text (
ciphertext
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...
), which can only be read by reversing the process (
decryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
). The sender of an encrypted (coded) message shares the decryption (decoding) technique only with intended recipients to preclude access from adversaries. The cryptography literature
often uses the names "Alice" (or "A") for the sender, "Bob" (or "B") for the intended recipient, and "Eve" (or "E") for the
eavesdropping
Eavesdropping is the act of secretly or stealthily listening to the private conversation or communications of others without their consent in order to gather information.
Etymology
The verb ''eavesdrop'' is a back-formation from the noun ''eaves ...
adversary.
Since the development of
rotor cipher machines in
World War I
World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...
and the advent of
computer
A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...
s in
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, cryptography methods have become increasingly complex and their applications more varied.
Modern cryptography is heavily based on
mathematical theory
A mathematical theory is a mathematical model of a branch of mathematics that is based on a set of axioms. It can also simultaneously be a body of knowledge (e.g., based on known axioms and definitions), and so in this sense can refer to an area o ...
and computer science practice; cryptographic
algorithm
In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
s are designed around
computational hardness assumption
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where ''efficiently'' typically means "in polynomial time"). It is not known how to prove (uncondition ...
s, making such algorithms hard to break in actual practice by any adversary. While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure"; theoretical advances (e.g., improvements in
integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are suf ...
algorithms) and faster computing technology require these designs to be continually reevaluated, and if necessary, adapted.
Information-theoretically secure schemes that cannot be broken even with unlimited computing power, such as the
one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...
, are much more difficult to use in practice than the best theoretically breakable, but computationally secure, schemes.
The growth of cryptographic technology has raised
a number of legal issues in the
Information Age
The Information Age (also known as the Computer Age, Digital Age, Silicon Age, or New Media Age) is a historical period that began in the mid-20th century. It is characterized by a rapid shift from traditional industries, as established during ...
. Cryptography's potential for use as a tool for
espionage
Espionage, spying, or intelligence gathering is the act of obtaining secret or confidential information (intelligence) from non-disclosed sources or divulging of the same without the permission of the holder of the information for a tangibl ...
and
sedition
Sedition is overt conduct, such as speech and organization, that tends toward rebellion against the established order. Sedition often includes subversion of a constitution and incitement of discontent toward, or insurrection against, estab ...
has led many governments to classify it as a weapon and to limit or even prohibit its use and export.
In some jurisdictions where the use of cryptography is legal, laws permit investigators to
compel the disclosure of
encryption keys for documents relevant to an investigation.
Cryptography also plays a major role in
digital rights management
Digital rights management (DRM) is the management of legal access to digital content. Various tools or technological protection measures (TPM) such as access control technologies can restrict the use of proprietary hardware and copyrighted works. ...
and
copyright infringement
Copyright infringement (at times referred to as piracy) is the use of works protected by copyright without permission for a usage where such permission is required, thereby infringing certain exclusive rights granted to the copyright holder, s ...
disputes in regard to
digital media
Digital media is any communication media that operate in conjunction with various encoded machine-readable data formats. Digital media can be created, viewed, distributed, modified, listened to, and preserved on a digital electronics device. ' ...
.
Terminology
![Caesar cipher left shift of 3](https://upload.wikimedia.org/wikipedia/commons/4/4a/Caesar_cipher_left_shift_of_3.svg)
The first use of the term "
cryptograph
Cryptograph was a limited Swedish company developing and selling crypto machines, founded on 21 July 1916 and liquidated in 1930. It was probably the first company in the world to focus entirely on the cryptographic market.
In December 1914, tw ...
" (as opposed to "
cryptogram
A cryptogram is a type of puzzle that consists of a short piece of encrypted text. Generally the cipher used to encrypt the text is simple enough that the cryptogram can be solved by hand. Substitution ciphers where each letter is replaced by ...
") dates back to the 19th century—originating from "
The Gold-Bug
"The Gold-Bug" is a short story by American writer Edgar Allan Poe published in 1843. The plot follows William Legrand, who was bitten by a gold-colored bug. His servant Jupiter fears that Legrand is going insane and goes to Legrand's friend, an ...
," a story by
Edgar Allan Poe
Edgar Allan Poe (; Edgar Poe; January 19, 1809 – October 7, 1849) was an American writer, poet, editor, and literary critic. Poe is best known for his poetry and short stories, particularly his tales of mystery and the macabre. He is wide ...
.
Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (called
plaintext
In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted.
Overview
With the advent of comp ...
) into an unintelligible form (called
ciphertext
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher. Ciphertext is also known as encrypted or encoded information because it contains a form of the original plaintext ...
).
Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A
cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
(or cypher) is a pair of algorithms that carry out 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 string of characters (ideally short so it can be remembered by the user), which is needed to decrypt the ciphertext. In formal mathematical terms, a "
cryptosystem
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption).
Typically, a cryptosystem consists of three algorithms: one for key generation, one for ...
" is the ordered list of elements of finite possible plaintexts, finite possible cyphertexts, finite possible keys, and the encryption and decryption algorithms that 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. Historically, ciphers were often used directly for encryption or decryption without additional procedures such as
authentication
Authentication (from ''authentikos'', "real, genuine", from αὐθέντης ''authentes'', "author") is the act of proving an assertion, such as the identity of a computer system user. In contrast with identification, the act of indicati ...
or integrity checks.
There are two main types of cryptosystems:
symmetric
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definiti ...
and
asymmetric. In symmetric systems, the only ones known until the 1970s, the same secret key encrypts and decrypts a message. Data manipulation in symmetric systems is significantly faster than in asymmetric systems. Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. The advantage of asymmetric systems is that the public key can be freely published, allowing parties to establish secure communication without having a shared secret key. In practice, asymmetric systems are used to first exchange a secret key, and then secure communication proceeds via a more efficient symmetric system using that key.
Examples of asymmetric systems include
Diffie–Hellman key exchange
Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include:
* Diffie–Hellman–Merkle key exchange
* Diffie–Hellman key agreement
* Diffie–Hellman key establishment
* Diffie–Hellman key negotiation
* Exponential key exc ...
, RSA (
Rivest–Shamir–Adleman
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly ...
), ECC (
Elliptic Curve Cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide e ...
), and
Post-quantum cryptography
In cryptography, post-quantum cryptography (sometimes referred to as quantum-proof, quantum-safe or quantum-resistant) refers to cryptographic algorithms (usually public-key algorithms) that are thought to be secure against a cryptanalytic attack ...
. Secure symmetric algorithms include the commonly used AES (
Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant ...
) which replaced the older DES (
Data Encryption Standard
The Data Encryption Standard (DES ) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cry ...
).
Insecure symmetric algorithms include children's language tangling schemes such as
Pig Latin
Pig Latin is a language game or argot in which words in English are altered, usually by adding a fabricated suffix or by moving the onset or initial consonant or consonant cluster of a word to the end of the word and adding a vocalic syllable ...
or other
cant
Cant, CANT, canting, or canted may refer to:
Language
* Cant (language), a secret language
* Beurla Reagaird, a language of the Scottish Highland Travellers
* Scottish Cant, a language of the Scottish Lowland Travellers
* Shelta or the Cant, a la ...
, and all historical cryptographic schemes, however seriously intended, prior to the invention of the
one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...
early in the 20th century.
In
colloquial
Colloquialism (), also called colloquial language, everyday language or general parlance, is the linguistic style used for casual (informal) communication. It is the most common functional style of speech, the idiom normally employed in conver ...
use, the term "
code
In communications and information processing, code is a system of rules to convert information—such as a letter, word, sound, image, or gesture—into another form, sometimes shortened or secret, for communication through a communication ...
" is often used to mean any method of encryption or concealment of meaning. However, in cryptography, code has a more specific meaning: the replacement of a unit of plaintext (i.e., a meaningful word or phrase) with a
code word
In communication, a code word is an element of a standardized code or protocol. Each code word is assembled in accordance with the specific rules of the code and assigned a unique meaning. Code words are typically used for reasons of reliability, ...
(for example, "wallaby" replaces "attack at dawn"). A cypher, in contrast, is a scheme for changing or substituting an element below such a level (a letter, a syllable, or a pair of letters, etc.) in order to produce a cyphertext.
Cryptanalysis
Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic sec ...
is 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 "cryptography" and "cryptology" interchangeably in English, while others (including US military practice generally) use "cryptography" to refer specifically to the use and practice of cryptographic techniques and "cryptology" to refer to the combined study of cryptography and cryptanalysis.
Oded Goldreich
Oded Goldreich ( he, עודד גולדרייך; b. 1957) is a professor of Computer Science at the Faculty of Mathematics and Computer Science of Weizmann Institute of Science, Israel. His research interests lie within the theory of computation ...
, ''Foundations of Cryptography, Volume 1: Basic Tools'', Cambridge University Press, 2001, English is more flexible than several other languages in which "cryptology" (done by cryptologists) is always used in the second sense above. advises that
steganography
Steganography ( ) is the practice of representing information within another message or physical object, in such a manner that the presence of the information is not evident to human inspection. In computing/electronic contexts, a computer file, ...
is sometimes included in cryptology.
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
Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion of
messages from 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
secrecy
Secrecy is the practice of hiding information from certain individuals or groups who do not have the "need to know", perhaps while sharing it with other individuals. That which is kept hidden is known as the secret.
Secrecy is often controvers ...
in
communications
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
, such as those of
spies
Spies most commonly refers to people who engage in spying, espionage or clandestine operations.
Spies or The Spies may also refer to:
* Spies (surname), a German surname
* Spies (band), a jazz fusion band
* Spies (song), "Spies" (song), a song by ...
, military leaders, and
diplomat
A diplomat (from grc, δίπλωμα; romanized ''diploma'') is a person appointed by a state or an intergovernmental institution such as the United Nations or the European Union to conduct diplomacy with one or more other states or internati ...
s. In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication,
digital signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created b ...
s,
interactive proofs and
secure computation, among others.
Classic cryptography
![Skytala&EmptyStrip-Shaded](https://upload.wikimedia.org/wikipedia/commons/b/b2/Skytala%26EmptyStrip-Shaded.png)
The main classical cipher types are
transposition cipher
In cryptography, a transposition cipher is a method of encryption which scrambles the positions of characters (''transposition'') without changing the characters themselves. Transposition ciphers reorder units of plaintext (typically characters or ...
s, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and
substitution cipher
In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, trip ...
s, which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the
Latin alphabet
The Latin alphabet or Roman alphabet is the collection of letters originally used by the ancient Romans to write the Latin language. Largely unaltered with the exception of extensions (such as diacritics), it used to write English and the o ...
). Simple versions of either have never offered much confidentiality from enterprising opponents. An early substitution cipher was the
Caesar cipher, in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet.
Suetonius
Gaius Suetonius Tranquillus (), commonly referred to as Suetonius ( ; c. AD 69 – after AD 122), was a Roman historian who wrote during the early Imperial era of the Roman Empire.
His most important surviving work is a set of biographies ...
reports that
Julius Caesar
Gaius Julius Caesar (; ; 12 July 100 BC – 15 March 44 BC), was a Roman general and statesman. A member of the First Triumvirate, Caesar led the Roman armies in the Gallic Wars before defeating his political rival Pompey in a civil war, and ...
used it with a shift of three to communicate with his generals.
Atbash is an example of an early Hebrew cipher. The earliest known use of cryptography is some carved ciphertext on stone in
Egypt
Egypt ( ar, مصر , ), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and southwest corner of Asia via a land bridge formed by the Sinai Peninsula. It is bordered by the Mediter ...
(ca 1900 BCE), but this may have been done for the amusement of literate observers rather than as a way of concealing information.
The
Greeks of Classical times are said to have known of ciphers (e.g., the
scytale
In cryptography, a scytale (; also transliterated skytale, grc, σκυτάλη ''skutálē'' "baton, cylinder", also ''skútalon'') is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment wound aro ...
transposition cipher claimed to have been used by the
Sparta
Sparta ( Doric Greek: Σπάρτα, ''Spártā''; Attic Greek: Σπάρτη, ''Spártē'') was a prominent city-state in Laconia, in ancient Greece. In antiquity, the city-state was known as Lacedaemon (, ), while the name Sparta referre ...
n military).
Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from
Herodotus
Herodotus ( ; grc, , }; BC) was an ancient Greek historian and geographer from the Greek city of Halicarnassus, part of the Persian Empire (now Bodrum, Turkey) and a later citizen of Thurii in modern Calabria ( Italy). He is known f ...
, was a message tattooed on a slave's shaved head and concealed under the regrown hair.
More modern examples of steganography include the use of
invisible ink
Invisible ink, also known as security ink or sympathetic ink, is a substance used for writing, which is invisible either on application or soon thereafter, and can later be made visible by some means, such as heat or ultraviolet light. Invisible ...
,
microdot
A microdot is text or an image substantially reduced in size to prevent detection by unintended recipients. Microdots are normally circular and around in diameter but can be made into different shapes and sizes and made from various materials su ...
s, and
digital watermark
A digital watermark is a kind of marker covertly embedded in a noise-tolerant signal such as audio, video or image data. It is typically used to identify ownership of the copyright of such signal. "Watermarking" is the process of hiding digital inf ...
s to conceal information.
In India, the 2000-year-old
Kamasutra
The ''Kama Sutra'' (; sa, कामसूत्र, , ; ) is an ancient Indian Sanskrit text on sexuality, eroticism and emotional fulfillment in life. Attributed to Vātsyāyana, the ''Kama Sutra'' is neither exclusively nor predominantly ...
of
Vātsyāyana
Vātsyāyana was an ancient Indian philosopher, known for authoring the ''Kama Sutra''. He was a brahmin, and lived in India during the second or third century CE, probably in Pataliputra (modern day Patna in Bihar).
He is not to be confused w ...
speaks of two different kinds of ciphers called Kautiliyam and Mulavediya. In the Kautiliyam, the cipher letter substitutions are based on phonetic relations, such as vowels becoming consonants. In the Mulavediya, the cipher alphabet consists of pairing letters and using the reciprocal ones.
In
Sassanid Persia
The Sasanian () or Sassanid Empire, officially known as the Empire of Iranians (, ) and also referred to by historians as the Neo-Persian Empire, was the last Iranian empire before the early Muslim conquests of the 7th-8th centuries AD. Named ...
, there were two secret scripts, according to the Muslim author
Ibn al-Nadim
Abū al-Faraj Muḥammad ibn Isḥāq al-Nadīm ( ar, ابو الفرج محمد بن إسحاق النديم), also ibn Abī Ya'qūb Isḥāq ibn Muḥammad ibn Isḥāq al-Warrāq, and commonly known by the ''nasab'' (patronymic) Ibn al-Nadīm ...
: the ''šāh-dabīrīya'' (literally "King's script") which was used for official correspondence, and the ''rāz-saharīya'' which was used to communicate secret messages with other countries.
David Kahn notes in ''
The Codebreakers
''The Codebreakers – The Story of Secret Writing'' () is a book by David Kahn, published in 1967, comprehensively chronicling the history of cryptography from ancient Egypt to the time of its writing. The United States government attempted to h ...
'' that modern cryptology originated among the
Arabs
The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Wester ...
, the first people to systematically document cryptanalytic methods.
Al-Khalil
Hebron ( ar, الخليل or ; he, חֶבְרוֹן ) is a Palestinian. city in the southern West Bank, south of Jerusalem. Nestled in the Judaean Mountains, it lies above sea level. The second-largest city in the West Bank (after East J ...
(717–786) wrote the ''Book of Cryptographic Messages'', which contains the first use of
permutations and combinations to list all possible
Arabic
Arabic (, ' ; , ' or ) is a Semitic languages, Semitic language spoken primarily across the Arab world.Semitic languages: an international handbook / edited by Stefan Weninger; in collaboration with Geoffrey Khan, Michael P. Streck, Janet C ...
words with and without vowels.
![Al-kindi cryptographic](https://upload.wikimedia.org/wikipedia/commons/7/76/Al-kindi_cryptographic.png)
Ciphertexts produced by a
classical cipher
In cryptography, a classical cipher is a type of cipher that was used historically but for the most part, has fallen into disuse. In contrast to modern cryptographic algorithms, most classical ciphers can be practically computed and solved by hand. ...
(and some modern ciphers) will reveal statistical information about the plaintext, and that information can often be used to break the cipher. After the discovery of
frequency analysis
In cryptanalysis, frequency analysis (also known as counting letters) is the study of the frequency of letters or groups of letters in a ciphertext. The method is used as an aid to breaking classical ciphers.
Frequency analysis is based on t ...
, perhaps by the
Arab mathematician and
polymath
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
Al-Kindi
Abū Yūsuf Yaʻqūb ibn ʼIsḥāq aṣ-Ṣabbāḥ al-Kindī (; ar, أبو يوسف يعقوب بن إسحاق الصبّاح الكندي; la, Alkindus; c. 801–873 AD) was an Arab Muslim philosopher, polymath, mathematician, physician ...
(also known as ''Alkindus'') in the 9th century,
nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as
puzzle
A puzzle is a game, Problem solving, problem, or toy that tests a person's ingenuity or knowledge. In a puzzle, the solver is expected to put pieces together (Disentanglement puzzle, or take them apart) in a logical way, in order to arrive at th ...
s (see
cryptogram
A cryptogram is a type of puzzle that consists of a short piece of encrypted text. Generally the cipher used to encrypt the text is simple enough that the cryptogram can be solved by hand. Substitution ciphers where each letter is replaced by ...
). Al-Kindi wrote a book on cryptography entitled ''Risalah fi Istikhraj al-Mu'amma'' (''Manuscript for the Deciphering Cryptographic Messages''), which described the first known use of frequency analysis cryptanalysis techniques.
![Encoded letter of Gabriel Luetz d Aramon after 1546 with partial deciphering](https://upload.wikimedia.org/wikipedia/commons/b/b8/Encoded_letter_of_Gabriel_Luetz_d_Aramon_after_1546_with_partial_deciphering.jpg)
Language letter frequencies may offer little help for some extended historical encryption techniques such as
homophonic cipher
In cryptography, a substitution cipher is a method of encrypting in which units of plaintext are replaced with the ciphertext, in a defined manner, with the help of a key; the "units" may be single letters (the most common), pairs of letters, trip ...
that tend to flatten the frequency distribution. For those ciphers, language letter group (or n-gram) frequencies may provide an attack.
Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of the polyalphabetic cipher, most clearly by
Leon Battista Alberti
Leon Battista Alberti (; 14 February 1404 – 25 April 1472) was an Italian Renaissance humanist author, artist, architect, poet, priest, linguist, philosopher, and cryptographer; he epitomised the nature of those identified now as polymaths. H ...
around the year 1467, though there is some indication that it was already known to Al-Kindi.
[ Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter at the limit). He also invented what was probably the first automatic cipher device, a wheel that implemented a partial realization of his invention. In the ]Vigenère cipher
The Vigenère cipher () is a method of encryption, encrypting alphabetic text by using a series of interwoven Caesar ciphers, based on the letters of a keyword. It employs a form of polyalphabetic cipher, polyalphabetic substitution.
First desc ...
, a polyalphabetic cipher, encryption uses a ''key word'', which controls letter substitution depending on which letter of the key word is used. In the mid-19th century Charles Babbage
Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer.
Babbage is considered ...
showed that the Vigenère cipher was vulnerable to Kasiski examination
In cryptanalysis, Kasiski examination (also referred to as Kasiski's test or Kasiski's method) is a method of attacking polyalphabetic substitution ciphers, such as the Vigenère cipher. It was first published by Friedrich Kasiski in 1863, but se ...
, but this was first published about ten years later by Friedrich Kasiski
Major Friedrich Wilhelm Kasiski (29 November 1805 – 22 May 1881) was a German infantry officer, cryptographer and archeologist. Kasiski was born in Schlochau, Kingdom of Prussia (now Człuchów, Poland).
Military service
Kasiski enlisted in ...
.
Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as many a would-be cryptanalyst was unaware of the technique. Breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved, thus making espionage, bribery, burglary, defection, etc., more attractive approaches to the cryptanalytically uninformed. It was finally explicitly recognized in the 19th century that secrecy of a cipher's algorithm is not a sensible nor practical safeguard of message security; in fact, it was further realized that any adequate cryptographic scheme (including ciphers) should remain secure even if the adversary fully understands the cipher algorithm itself. Security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack. This fundamental principle was first explicitly stated in 1883 by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle
Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be s ...
; alternatively and more bluntly, it was restated by Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory".
As a 21-year-o ...
, the inventor of information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
and the fundamentals of theoretical cryptography, as ''Shannon's Maxim''—'the enemy knows the system'.
Different physical devices and aids have been used to assist with ciphers. One of the earliest may have been the scytale of ancient Greece, a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the cipher grille, which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk
A cipher disk is an enciphering and deciphering tool developed in 1470 by the Italian architect and author Leon Battista Alberti. He constructed a device, (eponymously called the Alberti cipher disk) consisting of two concentric circular plate ...
, Johannes Trithemius
Johannes Trithemius (; 1 February 1462 – 13 December 1516), born Johann Heidenberg, was a German Benedictine abbot and a polymath who was active in the German Renaissance as a lexicographer, chronicler, cryptographer, and occultist. He is consi ...
' tabula recta
In cryptography, the ''tabula recta'' (from Latin ''tabula rēcta'') is a square table of alphabets, each row of which is made by shifting the previous one to the left. The term was invented by the German author and monk Johannes TrithemiusSal ...
scheme, and Thomas Jefferson
Thomas Jefferson (April 13, 1743 – July 4, 1826) was an American statesman, diplomat, lawyer, architect, philosopher, and Founding Fathers of the United States, Founding Father who served as the third president of the United States from 18 ...
's wheel cypher (not publicly known, and reinvented independently by Bazeries around 1900). Many mechanical encryption/decryption devices were invented early in the 20th century, and several patented, among them rotor machine
In cryptography, a rotor machine is an electro-mechanical stream cipher device used for encrypting and decrypting messages. Rotor machines were the cryptographic state-of-the-art for much of the 20th century; they were in widespread use in the 19 ...
s—famously including the Enigma machine used by the German government and military from the late 1920s and during World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
. The ciphers implemented by better quality examples of these machine designs brought about a substantial increase in cryptanalytic difficulty after WWI.
Early computer-era cryptography
Cryptanalysis of the new mechanical ciphering devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park
Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
during WWII spurred the development of more efficient means for carrying out repetitious tasks, such as military code breaking (decryption). This culminated in the development of the Colossus
Colossus, Colossos, or the plural Colossi or Colossuses, may refer to:
Statues
* Any exceptionally large statue
** List of tallest statues
** :Colossal statues
* ''Colossus of Barletta'', a bronze statue of an unidentified Roman emperor
* ''Col ...
, the world's first fully electronic, digital, programmable computer, which assisted in the decryption of ciphers generated by the German Army's Lorenz SZ40/42 machine.
Extensive open academic research into cryptography is relatively recent, beginning in the mid-1970s. In the early 1970s IBM personnel designed the Data Encryption Standard (DES) algorithm that became the first federal government cryptography standard in the United States. In 1976 Whitfield Diffie
Bailey Whitfield 'Whit' Diffie (born June 5, 1944), ForMemRS, is an American cryptographer and mathematician and one of the pioneers of public-key cryptography along with Martin Hellman and Ralph Merkle. Diffie and Hellman's 1976 paper ''New Dire ...
and Martin Hellman
Martin Edward Hellman (born October 2, 1945) is an American cryptologist and mathematician, best known for his involvement with public key cryptography in cooperation with Whitfield Diffie and Ralph Merkle. Hellman is a longtime contributor to th ...
published the Diffie–Hellman key exchange algorithm. In 1977 the RSA algorithm
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly ...
was published in Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...
's ''Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
'' column. Since then, cryptography has become a widely used tool in communications, computer network
A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are ...
s, and computer security
Computer security, cybersecurity (cyber security), or information technology security (IT security) is the protection of computer systems and networks from attack by malicious actors that may result in unauthorized information disclosure, the ...
generally.
Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are suf ...
or the discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b' ...
problems, so there are deep connections with abstract mathematics. There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...
is 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 RSA is 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 Michael O. Rabin
Michael Oser Rabin ( he, מִיכָאֵל עוזר רַבִּין; born September 1, 1931) is an Israeli mathematician and computer scientist and a recipient of the Turing Award.
Biography Early life and education
Rabin was born in 1931 in ...
that are provably secure provided factoring ''n = pq'' is impossible; it is quite unusable in practice. The discrete logarithm problem
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b'' ...
is 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.[''Cryptography: Theory and Practice'', Third Edition (Discrete Mathematics and Its Applications), 2005, by Douglas R. Stinson, Chapman and Hall/CRC]
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 attack
In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct ...
s, so when specifying key length
In cryptography, key size, key length, or key space refer to the number of bits in a key used by a cryptographic algorithm (such as a cipher).
Key length defines the upper-bound on an algorithm's security (i.e. a logarithmic measure of the fastest ...
s, the required key lengths are similarly advancing. The potential impact of quantum computing
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
are already being considered by some cryptographic system designers developing 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.
Modern cryptography
Prior to the early 20th century, cryptography was mainly concerned with linguistic
Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
and lexicographic
Lexicography is the study of lexicons, and is divided into two separate academic disciplines. It is the art of compiling dictionaries.
* Practical lexicography is the art or craft of compiling, writing and editing dictionaries.
* Theoretica ...
patterns. Since then cryptography has broadened in scope, and now makes extensive use of mathematical subdisciplines, including information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
, computational complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...
, statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...
, abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''a ...
, number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
, and finite mathematics. Cryptography is also a branch of engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
, but an unusual one since it deals with active, intelligent, and malevolent opposition; 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 quantum physics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...
.
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 binary
Binary may refer to:
Science and technology Mathematics
* Binary number, a representation of numbers using only two digits (0 and 1)
* Binary function, a function that takes two arguments
* Binary operation, a mathematical operation that t ...
bit
The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...
sequences (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.
Modern cryptography
Symmetric-key cryptography
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 ciphers are implemented as either block ciphers or stream ciphers
stream cipher is a symmetric key cipher where plaintext digits are combined with a pseudorandom cipher digit stream (keystream). In a stream cipher, each plaintext digit is encrypted one at a time with the corresponding digit of the keystream, ...
. A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher.
The Data Encryption Standard
The Data Encryption Standard (DES ) is a symmetric-key algorithm for the encryption of digital data. Although its short key length of 56 bits makes it too insecure for modern applications, it has been highly influential in the advancement of cry ...
(DES) and the Advanced Encryption Standard
The Advanced Encryption Standard (AES), also known by its original name Rijndael (), is a specification for the encryption of electronic data established by the U.S. National Institute of Standards and Technology (NIST) in 2001.
AES is a variant ...
(AES) are block cipher designs that have been designated cryptography standards
There are a number of standards related to cryptography. Standard algorithms and protocols provide a focus for study; standards for popular applications attract a large amount of cryptanalysis.
Encryption standards
* Data Encryption Standard (DE ...
by the US government (though DES's designation was finally withdrawn after the AES was adopted). Despite its deprecation as an official standard, DES (especially its still-approved and much more secure triple-DES
In cryptography, Triple DES (3DES or TDES), officially the Triple Data Encryption Algorithm (TDEA or Triple DEA), is a Symmetric-key algorithm, symmetric-key block cipher, which applies the Data Encryption Standard, DES cipher algorithm three ti ...
variant) remains quite popular; it is used across a wide range of applications, from ATM encryption to e-mail privacy
Email privacy is a broad topic dealing with issues of unauthorized access to, and inspection of, electronic mail, or unauthorized tracking spy pixel, when a user reads an email. This unauthorized access can happen while an email is in transit, as ...
and secure remote access. 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
In cryptography, FEAL (the Fast data Encipherment ALgorithm) is a block cipher proposed as an alternative to the Data Encryption Standard (DES), and designed to be much faster in software. The Feistel based algorithm was first published in 1987 ...
.
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 cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...
. 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. RC4
In cryptography, RC4 (Rivest Cipher 4, also known as ARC4 or ARCFOUR, meaning Alleged RC4, see below) is a stream cipher. While it is remarkable for its simplicity and speed in software, multiple vulnerabilities have been discovered in RC4, ren ...
is a widely used stream cipher. Block ciphers can be used as stream ciphers by generating blocks of a keystream (in place of a Pseudorandom number generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generate ...
) and applying an XOR
Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR ( or ), EOR, EXOR, , ...
operation to each bit of the plaintext with each bit of the keystream.
Message authentication code
In cryptography, a message authentication code (MAC), sometimes known as a ''tag'', is a short piece of information used for authenticating a message. In other words, to confirm that the message came from the stated sender (its authenticity) and ...
s (MACs) are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt; this additional complication blocks an attack scheme against bare digest algorithms, and so has been thought worth the effort. Cryptographic hash functions
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography:
* the probability of a particular n-bit output ...
are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed-length 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. MD4
The MD4 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1990. The digest length is 128 bits. The algorithm has influenced later designs, such as the MD5, SHA-1 and RIPEMD algorithms. The initialism "MD" s ...
is a long-used hash function that is now broken; MD5, a strengthened variant of MD4, is also widely used but broken in practice. The US National Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collecti ...
developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1
In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecima ...
is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression ...
family 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 NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
's overall hash algorithm toolkit."
Thus, a hash function design competition was meant to select a new U.S. national standard, to be called SHA-3
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...
, by 2012. The competition ended on October 2, 2012, when the NIST announced that Keccak
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...
would be the new SHA-3 hash algorithm. 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.
Public-key cryptography
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 management
Key management refers to management of cryptographic keys in a cryptosystem. This includes dealing with the generation, exchange, storage, use, crypto-shredding (destruction) and replacement of keys. It includes cryptographic protocol design, ...
necessary 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 square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...
of the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret.
In a groundbreaking 1976 paper, Whitfield Diffie and Martin Hellman proposed the notion of ''public-key'' (also, more generally, called ''asymmetric key'') cryptography in which two different but mathematically related keys are used—a ''public'' key and a ''private'' key. A public key system is so constructed that calculation of one key (the 'private key') is computationally infeasible from the other (the 'public key'), even though they are necessarily related. Instead, both keys are generated secretly, as an interrelated pair.Ralph Merkle
Ralph C. Merkle (born February 2, 1952) is a computer scientist and mathematician. He is one of the inventors of public-key cryptography, the inventor of cryptographic hashing, and more recently a researcher and speaker on cryonics.
Contribution ...
was working on similar ideas at the time and encountered publication delays, and Hellman has suggested that the term used should be Diffie–Hellman–Merkle aysmmetric key cryptography. The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".
In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. In a public-key encryption system, the ''public key'' is used for encryption, while the ''private'' or ''secret key'' is used for decryption. While Diffie and Hellman could not find such a system, they showed that public-key cryptography was indeed possible by presenting the Diffie–Hellman key exchange
Diffie–Hellman key exchangeSynonyms of Diffie–Hellman key exchange include:
* Diffie–Hellman–Merkle key exchange
* Diffie–Hellman key agreement
* Diffie–Hellman key establishment
* Diffie–Hellman key negotiation
* Exponential key exc ...
protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key.
The X.509
In cryptography, X.509 is an International Telecommunication Union (ITU) standard defining the format of public key certificates. X.509 certificates are used in many Internet protocols, including TLS/SSL, which is the basis for HTTPS, the secu ...
standard defines the most commonly used format for public key certificates
In cryptography, a public key certificate, also known as a digital certificate or identity certificate, is an electronic document used to prove the validity of a public key. The certificate includes information about the key, information about the ...
.
Diffie and Hellman's publication sparked widespread academic efforts in finding a practical public-key encryption system. This race was finally won in 1978 by Ronald Rivest
Ronald Linn Rivest (; born May 6, 1947) is a cryptographer and an Institute Professor at MIT. He is a member of MIT's Department of Electrical Engineering and Computer Science (EECS) and a member of MIT's Computer Science and Artificial Int ...
, Adi Shamir
Adi Shamir ( he, עדי שמיר; born July 6, 1952) is an Israeli cryptographer. He is a co-inventor of the Rivest–Shamir–Adleman (RSA) algorithm (along with Ron Rivest and Len Adleman), a co-inventor of the Feige–Fiat–Shamir identificat ...
, and Len Adleman
Leonard Adleman (born December 31, 1945) is an American computer scientist. He is one of the creators of the RSA encryption algorithm, for which he received the 2002 Turing Award, often called the Nobel prize of Computer science. He is also kno ...
, whose solution has since become known as the RSA algorithm
RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonard Adleman, who publicly ...
.
Previously released as an MIT
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...
"Technical Memo" in April 1977, and published in Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis ...
's ''Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
'' Mathematical recreations
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limite ...
column
The Diffie–Hellman and RSA algorithms, in addition to being the first publicly known examples of high-quality public-key algorithms, have been among the most widely used. Other asymmetric-key algorithms include the Cramer–Shoup cryptosystem, ElGamal encryption
In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985. ElGamal encryption is used in th ...
, and various elliptic curve techniques.
A document published in 1997 by the Government Communications Headquarters (GCHQ
Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the Unit ...
), a British intelligence organization, revealed that cryptographers at GCHQ had anticipated several academic developments. Reportedly, around 1970, James H. Ellis had conceived the principles of asymmetric key cryptography. In 1973, Clifford Cocks
Clifford Christopher Cocks (born 28 December 1950) is a British mathematician and cryptographer.
In 1973, while working at the United Kingdom Government Communications Headquarters (GCHQ), he invented a public-key cryptography algorithm equiv ...
invented a solution that was very similar in design rationale to RSA. In 1974, Malcolm J. Williamson is claimed to have developed the Diffie–Hellman key exchange.
Public-key cryptography is also used for implementing digital signature
A digital signature is a mathematical scheme for verifying the authenticity of digital messages or documents. A valid digital signature, where the prerequisites are satisfied, gives a recipient very high confidence that the message was created b ...
schemes. A digital signature is reminiscent of an ordinary signature
A signature (; from la, signare, "to sign") is a handwritten (and often stylized) depiction of someone's name, nickname, or even a simple "X" or other mark that a person writes on documents as a proof of identity and intent. The writer of a ...
; they both have the characteristic of being easy for a user to produce, but difficult for anyone else to forge
A forge is a type of hearth used for heating metals, or the workplace (smithy) where such a hearth is located. The forge is used by the smith to heat a piece of metal to a temperature at which it becomes easier to shape by forging, or to th ...
. Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for ''signing'', in which a secret key is used to process the message (or a hash of the message, or both), and one for ''verification'', in which the matching public key is used with the message to check the validity of the signature. RSA and DSA are two of the most popular digital signature schemes. Digital signatures are central to the operation of public key infrastructure
A public key infrastructure (PKI) is a set of roles, policies, hardware, software and procedures needed to create, manage, distribute, use, store and revoke digital certificates and manage public-key encryption. The purpose of a PKI is to facilit ...
s and many network security schemes (e.g., SSL/TLS
Transport Layer Security (TLS) is a cryptographic protocol designed to provide communications security over a computer network. The protocol is widely used in applications such as email, instant messaging, and voice over IP, but its use in securi ...
, many VPN
A virtual private network (VPN) extends a private network across a public network and enables users to send and receive data across shared or public networks as if their computing devices were directly connected to the private network. The be ...
s, etc.).
Public-key algorithms are most often based on the computational complexity
In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...
of "hard" problems, often from number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
. For example, the hardness of RSA is related to the integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are suf ...
problem, while Diffie–Hellman and DSA are related to the discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b' ...
problem. The security of elliptic curve cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide e ...
is based on number theoretic problems involving elliptic curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...
s. Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a sy ...
multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonly hybrid cryptosystems, in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm. Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed.
Cryptographic hash functions
Cryptographic hash functions are cryptographic algorithms that generate and use keys to encrypt data, and such functions may be viewed as keys themselves. They take a message of any length as input, and output a short, fixed-length 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. MD4
The MD4 Message-Digest Algorithm is a cryptographic hash function developed by Ronald Rivest in 1990. The digest length is 128 bits. The algorithm has influenced later designs, such as the MD5, SHA-1 and RIPEMD algorithms. The initialism "MD" s ...
is a long-used hash function that is now broken; MD5, a strengthened variant of MD4, is also widely used but broken in practice. The US National Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collecti ...
developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1
In cryptography, SHA-1 (Secure Hash Algorithm 1) is a cryptographically broken but still widely used hash function which takes an input and produces a 160-bit (20-byte) hash value known as a message digest – typically rendered as 40 hexadecima ...
is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression ...
family 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 NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical sci ...
's overall hash algorithm toolkit."
Thus, a hash function design competition was meant to select a new U.S. national standard, to be called SHA-3
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...
, by 2012. The competition ended on October 2, 2012, when the NIST announced that Keccak
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like struct ...
would be the new SHA-3 hash algorithm. 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.
Cryptanalysis
The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion.
It is a common misconception that every encryption method can be broken. In connection with his WWII work at Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial research and scientific development company owned by mult ...
, Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory".
As a 21-year-o ...
proved that the one-time pad
In cryptography, the one-time pad (OTP) is an encryption technique that cannot be cracked, but requires the use of a single-use pre-shared key that is not smaller than the message being sent. In this technique, a plaintext is paired with a ran ...
cipher is unbreakable, provided the key material is truly random
In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...
, never reused, kept secret from all possible attackers, and of equal or greater length than the message. Most cipher
In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s, apart from the one-time pad, can be broken with enough computational effort by brute force attack
In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct ...
, but the amount of effort needed may be exponentially
Exponential may refer to any of several mathematical topics related to exponentiation, including:
*Exponential function, also:
**Matrix exponential, the matrix analogue to the above
* Exponential decay, decrease at a rate proportional to value
*Exp ...
dependent on the key size, as compared to the effort needed to make use of the cipher. In such cases, effective security could be achieved if it is proven that the effort required (i.e., "work factor", in Shannon's terms) is beyond the ability of any adversary. This means it must be shown that no efficient method (as opposed to the time-consuming brute force method) can be found to break the cipher. Since no such proof has been found to date, the one-time-pad remains the only theoretically unbreakable cipher. Although well-implemented one-time-pad encryption cannot be broken, traffic analysis is still possible.
There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways. A common distinction turns on what Eve (an attacker) knows and what capabilities are available. In a ciphertext-only attack
In cryptography, a ciphertext-only attack (COA) or known ciphertext attack is an attack model for cryptanalysis where the attacker is assumed to have access only to a set of ciphertexts. While the attacker has no channel providing access to the pl ...
, Eve has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack
The known-plaintext attack (KPA) is an attack model for cryptanalysis where the attacker has access to both the plaintext (called a crib), and its encrypted version (ciphertext). These can be used to reveal further secret information such as secr ...
, Eve has access to a ciphertext and its corresponding plaintext (or to many such pairs). In a chosen-plaintext attack
A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts.Ross Anderson, ''Security Engineering: A Guide to Building Dependable Distributed Systems''. ...
, Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening
Gardening is the practice of growing and cultivating plants as part of horticulture. In gardens, ornamental plants are often grown for their flowers, foliage, or overall appearance; useful plants, such as root vegetables, leaf vegetables, fruits ...
, used by the British during WWII. In a chosen-ciphertext attack
A chosen-ciphertext attack (CCA) is an attack model for cryptanalysis where the cryptanalyst can gather information by obtaining the decryptions of chosen ciphertexts. From these pieces of information the adversary can attempt to recover the hidden ...
, Eve may be able to ''choose'' ciphertexts and learn their corresponding plaintexts. Finally in a man-in-the-middle
In cryptography and computer security, a man-in-the-middle, monster-in-the-middle, machine-in-the-middle, monkey-in-the-middle, meddler-in-the-middle, manipulator-in-the-middle (MITM), person-in-the-middle (PITM) or adversary-in-the-middle (AiTM) ...
attack Eve gets in between Alice (the sender) and Bob (the recipient), accesses and modifies the traffic and then forwards it to the recipient. Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols
Protocol may refer to:
Sociology and politics
* Protocol (politics), a formal agreement between nation states
* Protocol (diplomacy), the etiquette of diplomacy and affairs of state
* Etiquette, a code of personal behavior
Science and technology
...
involved).
Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher. For example, a simple brute force attack against DES requires one known plaintext and 255 decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even that the key sought will have been found. But this may not be enough assurance; a linear cryptanalysis
In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most ...
attack against DES requires 243 known plaintexts (with their corresponding ciphertexts) and approximately 243 DES operations. This is a considerable improvement over brute force attacks.
Public-key algorithms are based on the computational difficulty of various problems. The most famous of these are the difficulty of integer factorization
In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization.
When the numbers are suf ...
of semiprime
In mathematics, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other, so the semiprimes include the squares of prime numbers.
Because there are infinitely many prime nu ...
s and the difficulty of calculating discrete logarithm
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b'k'' can be defined for all integers ''k'', and the discrete logarithm log''b' ...
s, both of which are not yet proven to be solvable in polynomial time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by ...
(P) using only a classical Turing-complete
In computability theory, a system of data-manipulation rules (such as a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Tur ...
computer. Much public-key cryptanalysis concerns designing algorithms in P that can solve these problems, or using other technologies, such as quantum computers
Quantum computing is a type of computation whose operations can harness the phenomena of quantum mechanics, such as superposition, interference, and entanglement. Devices that perform quantum computations are known as quantum computers. Though ...
. For instance, the best-known algorithms for solving the elliptic curve-based version of discrete logarithm are much more time-consuming than the best-known algorithms for factoring, at least for problems of more or less equivalent size. Thus, to achieve an equivalent strength of encryption, techniques that depend upon the difficulty of factoring large composite numbers, such as the RSA cryptosystem, require larger keys than elliptic curve techniques. For this reason, public-key cryptosystems based on elliptic curves have become popular since their invention in the mid-1990s.
While pure cryptanalysis uses weaknesses in the algorithms themselves, other attacks on cryptosystems are based on actual use of the algorithms in real devices, and are called ''side-channel attack
In computer security, a side-channel attack is any attack based on extra information that can be gathered because of the fundamental way a computer protocol or algorithm is implemented, rather than flaws in the design of the protocol or algorit ...
s''. If a cryptanalyst has access to, for example, the amount of time the device took to encrypt a number of plaintexts or report an error in a password or PIN character, he may be able to use a timing attack
In cryptography, a timing attack is a side-channel attack in which the attacker attempts to compromise a cryptosystem by analyzing the time taken to execute cryptographic algorithms. Every logical operation in a computer takes time to execute, and ...
to break a cipher that is otherwise resistant to analysis. An attacker might also study the pattern and length of messages to derive valuable information; this is known as traffic analysis
Traffic analysis is the process of intercepting and examining messages in order to deduce information from patterns in communication, it can be performed even when the messages are encrypted. In general, the greater the number of messages observed ...
and can be quite useful to an alert adversary. Poor administration of a cryptosystem, such as permitting too short keys, will make any system vulnerable, regardless of other virtues. Social engineering and other attacks against humans (e.g., bribery
Bribery is the Offer and acceptance, offering, Gift, giving, Offer and acceptance, receiving, or Solicitation, soliciting of any item of value to influence the actions of an official, or other person, in charge of a public or legal duty. With reg ...
, extortion
Extortion is the practice of obtaining benefit through coercion. In most jurisdictions it is likely to constitute a criminal offence; the bulk of this article deals with such cases. Robbery is the simplest and most common form of extortion, ...
, blackmail
Blackmail is an act of coercion using the threat of revealing or publicizing either substantially true or false information about a person or people unless certain demands are met. It is often damaging information, and it may be revealed to fa ...
, espionage
Espionage, spying, or intelligence gathering is the act of obtaining secret or confidential information (intelligence) from non-disclosed sources or divulging of the same without the permission of the holder of the information for a tangibl ...
, torture
Torture is the deliberate infliction of severe pain or suffering on a person for reasons such as punishment, extracting a confession, interrogation for information, or intimidating third parties. Some definitions are restricted to acts c ...
, ...) are usually employed due to being more cost-effective and feasible to perform in a reasonable amount of time compared to pure cryptanalysis by a high margin.
Cryptographic primitives
Much of the theoretical work in cryptography concerns cryptographic ''primitives''—algorithms with basic cryptographic properties—and their relationship to other cryptographic problems. More complicated cryptographic tools are then built from these basic primitives. These primitives provide fundamental properties, which are used to develop more complex tools called ''cryptosystems'' or ''cryptographic protocols'', which guarantee one or more high-level security properties. Note, however, that the distinction between cryptographic ''primitives'' and cryptosystems, is quite arbitrary; for example, the RSA algorithm is sometimes considered a cryptosystem, and sometimes a primitive. Typical examples of cryptographic primitives include pseudorandom function
In cryptography, a pseudorandom function family, abbreviated PRF, is a collection of efficiently-computable functions which emulate a random oracle in the following way: no efficient algorithm can distinguish (with significant advantage) betwee ...
s, one-way function
In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, spe ...
s, etc.
Cryptosystems
One or more cryptographic primitives are often used to develop a more complex algorithm, called a cryptographic system, or ''cryptosystem''. Cryptosystems (e.g., El-Gamal encryption) are designed to provide particular functionality (e.g., public key encryption) while guaranteeing certain security properties (e.g., chosen-plaintext attack (CPA) security in the random oracle model
In cryptography, a random oracle is an oracle (a theoretical black box) that responds to every ''unique query'' with a (truly) random response chosen uniformly from its output domain. If a query is repeated, it responds the same way every time t ...
). Cryptosystems use the properties of the underlying cryptographic primitives to support the system's security properties. As the distinction between primitives and cryptosystems is somewhat arbitrary, a sophisticated cryptosystem can be derived from a combination of several more primitive cryptosystems. In many cases, the cryptosystem's structure involves back and forth communication among two or more parties in space (e.g., between the sender of a secure message and its receiver) or across time (e.g., cryptographically protected backup
In information technology, a backup, or data backup is a copy of computer data taken and stored elsewhere so that it may be used to restore the original after a data loss event. The verb form, referring to the process of doing so, is "back up", w ...
data). Such cryptosystems are sometimes called ''cryptographic protocols''.
Some widely known cryptosystems include RSA, Schnorr signature, ElGamal encryption
In cryptography, the ElGamal encryption system is an asymmetric key encryption algorithm for public-key cryptography which is based on the Diffie–Hellman key exchange. It was described by Taher Elgamal in 1985. ElGamal encryption is used in th ...
, and Pretty Good Privacy (PGP). More complex cryptosystems include electronic cash systems, signcryption systems, etc. Some more 'theoretical' cryptosystems include interactive proof systems, (like zero-knowledge proofs), systems for secret sharing, etc.
Lightweight cryptography
Lightweight cryptography (LWC) concerns cryptographic algorithms developed for a strictly constrained environment. The growth of Internet of things, Internet of Things (IoT) has spiked research into the development of lightweight algorithms that are better suited for the environment. An IoT environment requires strict constraints on power consumption, processing power, and security. Algorithms such as PRESENT, Advanced Encryption Standard, AES, and Speck (cipher), SPECK are examples of the many LWC algorithms that have been developed to achieve the standard set by the National Institute of Standards and Technology.
Applications
General
Cryptography is widely used on the internet to help protect user-data and prevent eavesdropping. To ensure secrecy during transmission, many systems use private key cryptography to protect transmitted information. With public-key systems, one can maintain secrecy without a master key or a large number of keys. But, some algorithms like BitLocker, Bitlocker and VeraCrypt, Veracrypt are generally not private-public key cryptography. Such as Veracrypt, it uses a password hash to generate the single private key. However, it can be configured to run in public-private key systems. The C++ opensource encryption library OpenSSL provides Free and open-source software, free and opensource encryption software and tools. The most commonly used encryption cipher suit is Advanced Encryption Standard, AES, as it has hardware acceleration for all x86 based processors that has AES instruction set, AES-NI. A close contender is ChaCha20-Poly1305, which is a stream cipher, however it is commonly used for mobile devices as they are ARM architecture family, ARM based which does not feature AES-NI instruction set extension.
Cybersecurity
Cryptography can be used to secure communications by encrypting them. Websites use encryption via HTTPS. "End-to-end" encryption, where only sender and receiver can read messages, is implemented for email in Pretty Good Privacy and for secure messaging in general in WhatsApp, Signal (software), Signal and Telegram (software), Telegram.
Operating systems use encryption to keep passwords secret, conceal parts of the system, and ensure that software updates are truly from the system maker. Instead of storing plaintext passwords, computer systems store hashes thereof; then, when a user logs in, the system passes the given password through a cryptographic hash function and compares it to the hashed value on file. In this manner, neither the system nor an attacker has at any point access to the password in plaintext.
Encryption is sometimes used to encrypt one's entire drive. For example, University College London has implemented BitLocker (a program by Microsoft) to render drive data opaque without users logging in.
Cryptocurrencies and cryptoeconomics
Cryptographic techniques enable cryptocurrency technologies, such as Distributed Ledger Technology, distributed ledger technologies (e.g., Blockchain, blockchains), which finance cryptoeconomics applications such as Decentralized finance, decentralized finance (DeFi). Key cryptographic techniques that enable cryptocurrencies and cryptoeconomics include, but are not limited to: cryptographic keys, Cryptographic hash function, cryptographic hash functions, Public key encryption, asymmetric (public key) encryption, Multi-factor authentication, Multi-Factor Authentication (MFA), End-to-end encryption, End-to-End Encryption (E2EE), and Zero-knowledge proof, Zero Knowledge Proofs (ZKP).
Legal issues
Prohibitions
Cryptography has long been of interest to intelligence gathering and law enforcement agency, law enforcement agencies. Secret communications may be criminal or even treasonous . Because of its facilitation of privacy, and the diminution of privacy attendant on its prohibition, cryptography is also of considerable interest to civil rights supporters. Accordingly, there has been a history of controversial legal issues surrounding cryptography, especially since the advent of inexpensive computers has made widespread access to high-quality cryptography possible.
In some countries, even the domestic use of cryptography is, or has been, restricted. Until 1999, France significantly restricted the use of cryptography domestically, though it has since relaxed many of these rules. In People's Republic of China, China and Islamic Republic of Iran, Iran, a license is still required to use cryptography. Many countries have tight restrictions on the use of cryptography. Among the more restrictive are laws in Belarus, Kazakhstan, Mongolia, Pakistan, Singapore, Tunisia, and Vietnam.
In the United States, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography. One particularly important issue has been the export of cryptography and cryptographic software and hardware. Probably because of the importance of cryptanalysis in World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
and an expectation that cryptography would continue to be important for national security, many Western governments have, at some point, strictly regulated export of cryptography. After World War II, it was illegal in the US to sell or distribute encryption technology overseas; in fact, encryption was designated as auxiliary military equipment and put on the United States Munitions List.
Until the development of the personal computer, asymmetric key algorithms (i.e., public key techniques), and the Internet, this was not especially problematic. However, as the Internet grew and computers became more widely available, high-quality encryption techniques became well known around the globe.
Export controls
In the 1990s, there were several challenges to US export regulation of cryptography. After the source code for Philip Zimmermann's Pretty Good Privacy (PGP) encryption program found its way onto the Internet in June 1991, a complaint by RSA Security (then called RSA Data Security, Inc.) resulted in a lengthy criminal investigation of Zimmermann by the US Customs Service and the Federal Bureau of Investigation, FBI, though no charges were ever filed. Daniel J. Bernstein, then a graduate student at UC Berkeley, brought a lawsuit against the US government challenging some aspects of the restrictions based on 1st Amendment, free speech grounds. The 1995 case ''Bernstein v. United States'' ultimately resulted in a 1999 decision that printed source code for cryptographic algorithms and systems was protected as freedom of speech, free speech by the United States Constitution.
In 1996, thirty-nine countries signed the Wassenaar Arrangement, an arms control treaty that deals with the export of arms and "dual-use" technologies such as cryptography. The treaty stipulated that the use of cryptography with short key-lengths (56-bit for symmetric encryption, 512-bit for RSA) would no longer be export-controlled. Cryptography exports from the US became less strictly regulated as a consequence of a major relaxation in 2000; there are no longer very many restrictions on key sizes in US-Export of cryptography, exported mass-market software. Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browsers such as Firefox or Internet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security). The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME. Many Internet users don't realize that their basic application software contains such extensive cryptosystem
In cryptography, a cryptosystem is a suite of cryptographic algorithms needed to implement a particular security service, such as confidentiality (encryption).
Typically, a cryptosystem consists of three algorithms: one for key generation, one for ...
s. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally don't find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.
NSA involvement
Another contentious issue connected to cryptography in the United States is the influence of the National Security Agency
The National Security Agency (NSA) is a national-level intelligence agency of the United States Department of Defense, under the authority of the Director of National Intelligence (DNI). The NSA is responsible for global monitoring, collecti ...
on cipher development and policy. The NSA was involved with the design of Data Encryption Standard, DES during its development at IBM and its consideration by the National Bureau of Standards as a possible Federal Standard for cryptography. DES was designed to be resistant to differential cryptanalysis, a powerful and general cryptanalytic technique known to the NSA and IBM, that became publicly known only when it was rediscovered in the late 1980s. According to Steven Levy, IBM discovered differential cryptanalysis, but kept the technique secret at the NSA's request. The technique became publicly known only when Biham and Shamir re-discovered and announced it some years later. The entire affair illustrates the difficulty of determining what resources and knowledge an attacker might actually have.
Another instance of the NSA's involvement was the 1993 Clipper chip affair, an encryption microchip intended to be part of the Capstone (cryptography), Capstone cryptography-control initiative. Clipper was widely criticized by cryptographers for two reasons. The cipher algorithm (called Skipjack (cipher), Skipjack) was then classified (declassified in 1998, long after the Clipper initiative lapsed). The classified cipher caused concerns that the NSA had deliberately made the cipher weak in order to assist its intelligence efforts. The whole initiative was also criticized based on its violation of Kerckhoffs's Principle
Kerckhoffs's principle (also called Kerckhoffs's desideratum, assumption, axiom, doctrine or law) of cryptography was stated by Dutch-born cryptographer Auguste Kerckhoffs in the 19th century. The principle holds that a cryptosystem should be s ...
, as the scheme included a special key escrow, escrow key held by the government for use by law enforcement (i.e. Telephone tapping, wiretapping).
Digital rights management
Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of copyrighted material, being widely implemented and deployed at the behest of some copyright holders. In 1998, U.S. President Bill Clinton signed the Digital Millennium Copyright Act (DMCA), which criminalized all production, dissemination, and use of certain cryptanalytic techniques and technology (now known or later discovered); specifically, those that could be used to circumvent DRM technological schemes. This had a noticeable impact on the cryptography research community since an argument can be made that any cryptanalytic research violated the DMCA. Similar statutes have since been enacted in several countries and regions, including the implementation in the Directive on the harmonisation of certain aspects of copyright and related rights in the information society, EU Copyright Directive. Similar restrictions are called for by treaties signed by World Intellectual Property Organization member-states.
The United States Department of Justice and Federal Bureau of Investigation, FBI have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one. Niels Ferguson, a well-respected cryptography researcher, has publicly stated that he will not release some of his research into an Intel Corporation, Intel security design for fear of prosecution under the DMCA. Cryptologist Bruce Schneier has argued that the DMCA encourages vendor lock-in, while inhibiting actual measures toward cyber-security. Both Alan Cox (computer programmer), Alan Cox (longtime Linux kernel developer) and Edward Felten (and some of his students at Princeton) have encountered problems related to the Act. Dmitry Sklyarov was arrested during a visit to the US from Russia, and jailed for five months pending trial for alleged violations of the DMCA arising from work he had done in Russia, where the work was legal. In 2007, the cryptographic keys responsible for Blu-ray and HD DVD content scrambling were AACS encryption key controversy, discovered and released onto the Internet. In both cases, the MPAA, Motion Picture Association of America sent out numerous DMCA takedown notices, and there was a massive Internet backlash triggered by the perceived impact of such notices on fair use and free speech.
Forced disclosure of encryption keys
In the United Kingdom, the Regulation of Investigatory Powers Act 2000, Regulation of Investigatory Powers Act gives UK police the powers to force suspects to decrypt files or hand over passwords that protect encryption keys. Failure to comply is an offense in its own right, punishable on conviction by a two-year jail sentence or up to five years in cases involving national security. Successful prosecutions have occurred under the Act; the first, in 2009, resulted in a term of 13 months' imprisonment. Similar forced disclosure laws in Australia, Finland, France, and India compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation.
In the United States, the federal criminal case of ''United States v. Fricosu'' addressed whether a search warrant can compel a person to reveal an encryption
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decip ...
passphrase or password. The Electronic Frontier Foundation (EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment to the United States Constitution, Fifth Amendment. In 2012, the court ruled that under the All Writs Act, the defendant was required to produce an unencrypted hard drive for the court.
In many jurisdictions, the legal status of forced disclosure remains unclear.
The 2016 FBI–Apple encryption dispute concerns the ability of courts in the United States to compel manufacturers' assistance in unlocking cell phones whose contents are cryptographically protected.
As a potential counter-measure to forced disclosure some cryptographic software supports plausible deniability, where the encrypted data is indistinguishable from unused random data (for example such as that of a Data remanence, drive which has been securely wiped).
See also
* Collision attack
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* Secure cryptoprocessor
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* – first cryptography chart
* World Wide Web Consortium's
References
Further reading
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* Excellent coverage of many classical ciphers and cryptography concepts and of the "modern" DES and RSA systems.
* ''Cryptography and Mathematics'' by Bernhard Esslinger, 200 pages, part of the free open-source package CrypTool, . CrypTool is the most widespread e-learning program about cryptography and cryptanalysis, open source.
* ''In Code: A Mathematical Journey'' by Sarah Flannery (with David Flannery). Popular account of Sarah's award-winning project on public-key cryptography, co-written with her father.
* James Gannon (author), James Gannon, ''Stealing Secrets, Telling Lies: How Spies and Codebreakers Helped Shape the Twentieth Century'', Washington, D.C., Brassey's, 2001, .
* Oded Goldreich
Oded Goldreich ( he, עודד גולדרייך; b. 1957) is a professor of Computer Science at the Faculty of Mathematics and Computer Science of Weizmann Institute of Science, Israel. His research interests lie within the theory of computation ...
''Foundations of Cryptography''
in two volumes, Cambridge University Press, 2001 and 2004.
* ''Alvin's Secret Code'' by Clifford B. Hicks (children's novel that introduces some basic cryptography and cryptanalysis).
*
Introduction to Modern Cryptography
' by Jonathan Katz and Yehuda Lindell.
* Ibrahim A. Al-Kadi, "The Origins of Cryptology: the Arab Contributions," Cryptologia, vol. 16, no. 2 (April 1992), pp. 97–126.
Jan Pelzl
''Understanding Cryptography, A Textbook for Students and Practitioners''.
Springer, 2009. (Slides, online cryptography lectures and other information are available on the companion web site.) Very accessible introduction to practical cryptography for non-mathematicians.
* , giving an overview of international law issues regarding cryptography.
* ''Introduction to Modern Cryptography'' by Phillip Rogaway and Mihir Bellare, a mathematical introduction to theoretical cryptography including reduction-based security proofs
PDF download
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* Tenzer, Theo (2021): ''SUPER SECRETO – The Third Epoch of Cryptography: Multiple, exponential, quantum-secure and above all, simple and practical Encryption for Everyone'', Norderstedt, .
* Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) ''Max Planck Encyclopedia of Public International Law'' (Oxford University Press 2009).
External links
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Cryptography Works - web information portal
Crypto Glossary and Dictionary of Technical Cryptography
A Course in Cryptography
by Raphael Pass & Abhi Shelat – offered at Cornell in the form of lecture notes.
* For more on the use of cryptographic elements in fiction, see:
at the Library of Congress has early editions of works of seventeenth-century English literature, publications relating to cryptography.
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Cryptography,
Applied mathematics
Banking technology
Formal sciences