Cryptography

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Cryptography, or cryptology (from

The growth of cryptographic technology has raised a number of legal issues in the Information Age. Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export.^[7] 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.^[8][9] Cryptography also plays a major role in digital rights management and copyright infringement disputes with regard to digital media.^[10]

The first use of the term "cryptograph" (as opposed to "cryptogram") dates back to the 19th century—originating from "The Gold-Bug", a story by Edgar Allan Poe.^[11][12]

Until modern times, cryptography referred almost exclusively to "encryption", which is the process of converting ordinary information (called plaintext) into an unintelligible form (called ciphertext).^[13] Decryption is the reverse, in other words, moving from the unintelligible ciphertext back to plaintext. A cipher (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" 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 or integrity checks.

There are two main types of cryptosystems:

Cryptanalysis 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,

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. Cryptolingusitics is especially used in military intelligence applications for deciphering foreign communications.^[20][21]

Before the modern era, cryptography focused on message confidentiality (i.e., encryption)—conversion of

The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and substitution ciphers, 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).^[22] 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 reports that Julius Caesar 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 (c. 1900 BCE), but this may have been done for the amusement of literate observers rather than as a way of concealing information.

The

In India, the 2000-year-old

David Kahn notes in The Codebreakers that modern cryptology originated among the Arabs, the first people to systematically document cryptanalytic methods.^[25] Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains the first use of permutations and combinations to list all possible Arabic words with and without vowels.^[26]

Ciphertexts produced by a

Language letter frequencies may offer little help for some extended historical encryption techniques such as homophonic cipher 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

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.^[33]

Symmetric key ciphers are implemented as either

The

Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the one-time pad. In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material. RC4 is a widely used stream cipher.^[5] Block ciphers can be used as stream ciphers by generating blocks of a keystream (in place of a Pseudorandom number generator) and applying an XOR operation to each bit of the plaintext with each bit of the keystream.^[43]

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 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 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.^[47] 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.^[48] The historian David Kahn described public-key cryptography as "the most revolutionary new concept in the field since polyalphabetic substitution emerged in the Renaissance".^[49]

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 protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key.^[33] The

A document published in 1997 by the Government Communications Headquarters (GCHQ), a British intelligence organization, revealed that cryptographers at GCHQ had anticipated several academic developments.^[52] Reportedly, around 1970, James H. Ellis had conceived the principles of asymmetric key cryptography. In 1973, Clifford Cocks invented a solution that was very similar in design rationale to RSA.^[52][53] In 1974, Malcolm J. Williamson is claimed to have developed the Diffie–Hellman key exchange.^[54]

Public-key cryptography is also used for implementing

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, Eve has access only to the ciphertext (good modern cryptosystems are usually effectively immune to ciphertext-only attacks). In a known-plaintext attack, Eve has access to a ciphertext and its corresponding plaintext (or to many such pairs). In a chosen-plaintext attack, Eve may choose a plaintext and learn its corresponding ciphertext (perhaps many times); an example is gardening, used by the British during WWII. In a chosen-ciphertext attack, Eve may be able to choose ciphertexts and learn their corresponding plaintexts.^[5] Finally in a man-in-the-middle attack Eve gets in between Alice (the sender) and Bob (the recipient), accesses and modifies the traffic and then forward it to the recipient.^[56] Also important, often overwhelmingly so, are mistakes (generally in the design or use of one of the protocols 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 attack against DES requires 2⁴³ known plaintexts (with their corresponding ciphertexts) and approximately 2⁴³ DES operations.^[57] 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

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

or torture) 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

pseudorandom functions, one-way functions

, etc.

Cryptosystems

Main article: List of cryptosystems

One or more cryptographic primitives are often used to develop a more complex algorithm, called a cryptographic system, or cryptosystem. Cryptosystems (e.g.,

random oracle model). 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 data). Such cryptosystems are sometimes called cryptographic protocols

.

Some widely known cryptosystems include RSA, Schnorr signature, ElGamal encryption, and Pretty Good Privacy (PGP). More complex cryptosystems include electronic cash^[59] systems, signcryption systems, etc. Some more 'theoretical'^{[clarification needed]} cryptosystems include interactive proof systems,^[60] (like zero-knowledge proofs)^[61] and systems for secret sharing.^[62][63]

Lightweight cryptography

Lightweight cryptography (LWC) concerns cryptographic algorithms developed for a strictly constrained environment. The growth of 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.^[64] Algorithms such as PRESENT, AES, and 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.^[65]

Applications

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Main category: Applications of cryptography

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.^[66] But, some algorithms like BitLocker and VeraCrypt are generally not private-public key cryptography. For example, Veracrypt 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 opensource encryption software and tools. The most commonly used encryption cipher suit is AES,^[67] as it has hardware acceleration for all x86 based processors that has 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 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

Signal and Telegram.^[68]

Operating systems use encryption to keep passwords secret, conceal parts of the system, and ensure that software updates are truly from the system maker.[68] 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.^[68]

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.^[68]

Cryptocurrencies and cryptoeconomics

Cryptographic techniques enable

asymmetric (public key) encryption, Multi-Factor Authentication (MFA), End-to-End Encryption (E2EE), and Zero Knowledge Proofs (ZKP)

.

Legal issues

See also:

Cryptography laws in different nations

Prohibitions

Cryptography has long been of interest to intelligence gathering and law enforcement agencies.^[9] Secret communications may be criminal or even treasonous.^{[citation needed]} 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

Iran, a license is still required to use cryptography.^[7] 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.^[69]

In the United States, cryptography is legal for domestic use, but there has been much conflict over legal issues related to cryptography.[9] 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 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.^[70] 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

Main article: Export of cryptography

In the 1990s, there were several challenges to US export regulation of cryptography. After the

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 free speech by the United States Constitution.^[73]

In 1996, thirty-nine countries signed the

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 do not realize that their basic application software contains such extensive cryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally do not 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.^{[citation needed}

]

NSA involvement

See also: Clipper chip

Another contentious issue connected to cryptography in the United States is the influence of the

National Bureau of Standards as a possible Federal Standard for cryptography.^[76] DES was designed to be resistant to differential cryptanalysis,^[77] 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.^[78] According to Steven Levy, IBM discovered differential cryptanalysis,^[72]

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

wiretapping).^[72]

Digital rights management

Main article: Digital rights management

Cryptography is central to digital rights management (DRM), a group of techniques for technologically controlling use of

EU Copyright Directive. Similar restrictions are called for by treaties signed by World Intellectual Property Organization

member-states.

The

free speech

.

Forced disclosure of encryption keys

Main article: Key disclosure law

In the United Kingdom, the 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.^[8] Successful prosecutions have occurred under the Act; the first, in 2009,^[82] resulted in a term of 13 months' imprisonment.^[83] 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 passphrase or password.^[84] The Electronic Frontier Foundation (EFF) argued that this is a violation of the protection from self-incrimination given by the Fifth Amendment.^[85] In 2012, the court ruled that under the All Writs Act, the defendant was required to produce an unencrypted hard drive for the court.^[86]

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 drive which has been securely wiped).

See also

• Collision attack
• Comparison of cryptography libraries
• Cryptovirology – Securing and encrypting virology
• Crypto Wars – Attempts to limit access to strong cryptography
• Encyclopedia of Cryptography and Security – Book by Technische Universiteit Eindhoven
• Global surveillance – Mass surveillance across national borders
• Indistinguishability obfuscation – Type of cryptographic software obfuscation
• Information theory – Scientific study of digital information
• Outline of cryptography
  • List of cryptographers
  • List of multiple discoveries
  • List of unsolved problems in computer science – List of unsolved computational problems
• Pre-shared key – Method to set encryption keys
• Secure cryptoprocessor
• Strong cryptography – Term applied to cryptographic systems that are highly resistant to cryptanalysis
• Syllabical and Steganographical Table – Eighteenth-century work believed to be the first cryptography chart – first cryptography chart
• World Wide Web Consortium's Web Cryptography API – World Wide Web Consortium cryptography standard

References

Further reading

Further information:

Books on cryptography

• Arbib, Jonathan; Dwyer, John (2011). Discrete Mathematics for Cryptography. Algana Publishing.
  ISBN 978-1-907934-01-8
  .
• Becket, B (1988). Introduction to Cryptology. Blackwell Scientific Publications.
  OCLC 16832704
  . Excellent coverage of many classical ciphers and cryptography concepts and of the "modern" DES and RSA systems.
• Esslinger, Bernhard; et al. The CrypTool Script (PDF) (10th ed.). Archived from the original (PDF) on 22 July 2011. Retrieved 23 December 2013. 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.
• ISBN 1-57488-367-4
  .
• Oded Goldreich, Foundations of Cryptography Archived 9 August 2016 at the Wayback Machine, 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 Archived 16 October 2009 at the Wayback Machine 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.
• Christof Paar, Jan Pelzl, Understanding Cryptography, A Textbook for Students and Practitioners. Archived 31 October 2020 at the Wayback Machine 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.
• "Max Planck Encyclopedia of Public International Law". Archived from the original on 1 May 2018. Retrieved 15 December 2021., 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 Archived 24 September 2009 at the Wayback Machine.
• ISBN 978-0-13-335469-0
  .
• Tenzer, Theo (2021): Super Secreto – The Third Epoch of Cryptography: Multiple, exponential, quantum-secure and above all, simple and practical Encryption for Everyone, Norderstedt,
  ISBN 978-3755761174
  .
• Johann-Christoph Woltag, 'Coded Communications (Encryption)' in Rüdiger Wolfrum (ed) Max Planck Encyclopedia of Public International Law (Oxford University Press 2009).

External links

Wikiquote has quotations related to Cryptography.

Wikibooks has more on the topic of: Cryptography

At Wikiversity, you can learn more and teach others about Cryptography at the Department of Cryptography

Wikisource has the text of the 1911 Encyclopædia Britannica article "Cryptography".

Library resources about
Cryptography

---

• Online books
• Resources in your library
• Resources in other libraries

• The dictionary definition of cryptography at Wiktionary
• Media related to Cryptography at Wikimedia Commons
• Cryptography on In Our Time at the BBC
• Crypto Glossary and Dictionary of Technical Cryptography Archived 4 July 2022 at the Wayback Machine
• 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: Dooley, John F. (23 August 2012). "Cryptology in Fiction". Archived from the original on 29 July 2020. Retrieved 20 February 2015.
• The George Fabyan Collection at the Library of Congress has early editions of works of seventeenth-century English literature, publications relating to cryptography.