Cryptography

[3] Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others.

[5] Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications.

Cryptography prior to the modern age was effectively synonymous with encryption, converting readable information (plaintext) to unintelligible nonsense text (ciphertext), which can only be read by reversing the process (decryption).

Theoretical advances (e.g., improvements in integer factorization algorithms) and faster computing technology require these designs to be continually reevaluated and, if necessary, adapted.

In recent decades, the field has expanded beyond confidentiality concerns to include techniques for message integrity checking, sender/receiver identity authentication, digital signatures, interactive proofs and secure computation, among others.

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.

[25] David Kahn notes in The Codebreakers that modern cryptology originated among the Arabs, the first people to systematically document cryptanalytic methods.

The Arab mathematician and polymath 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.

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.

Many mechanical encryption/decryption devices were invented early in the 20th century, and several patented, among them rotor machines—famously including the Enigma machine used by the German government and military from the late 1920s and during World War II.

In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitive tasks, such as military code breaking (decryption).

This culminated in the development of the Colossus, 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.

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.

There are systems similar to RSA, such as one by Michael O. Rabin that are provably secure provided factoring n = pq is impossible; it is quite unusable in practice.

Many computer ciphers can be characterized by their operation on binary bit sequences (sometimes in groups or blocks), unlike classical and mechanical schemes, which generally manipulate traditional characters (i.e., letters and digits) directly.

Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes.

In connection with his WWII work at Bell Labs, Claude Shannon proved that the one-time pad cipher is unbreakable, provided the key material is truly random, never reused, kept secret from all possible attackers, and of equal or greater length than the message.

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 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).

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.

For example, University College London has implemented BitLocker (a program by Microsoft) to render drive data opaque without users logging in.

[77][78] 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 free speech grounds.

[80] Cryptography exports from the US became less strictly regulated as a consequence of a major relaxation in 2000;[81] there are no longer very many restrictions on key sizes in US-exported mass-market software.

[citation needed] Another contentious issue connected to cryptography in the United States is the influence of the National Security Agency on cipher development and policy.

[82] DES was designed to be resistant to differential cryptanalysis,[83] 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.

The whole initiative was also criticized based on its violation of Kerckhoffs's Principle, as the scheme included a special escrow key held by the government for use by law enforcement (i.e.

The United States Department of Justice and FBI have not enforced the DMCA as rigorously as had been feared by some, but the law, nonetheless, remains a controversial one.

[87] Both Alan Cox (longtime Linux kernel developer) and Edward Felten (and some of his students at Princeton) have encountered problems related to the Act.

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.

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.

Lorenz cipher machine with twelve rotors mechanism
Lorenz cipher machine, used in World War II to encrypt communications of the German High Command .
diagram showing shift three alphabetic cypher D becomes A and E becomes B
Alphabet shift ciphers are believed to have been used by Julius Caesar over 2,000 years ago. [ 6 ] This is an example with k = 3 . In other words, the letters in the alphabet are shifted three in one direction to encrypt and three in the other direction to decrypt.
Skytala stick with strip of paper wound around in spiral
Reconstructed ancient Greek scytale , an early cipher device
Arabic text of a book by Al-Kindi
First page of a book by Al-Kindi which discusses encryption of messages
book sized metal machine with large dial left page and nineteen small dials right page
16th-century book-shaped French cipher machine, with arms of Henri II of France
manuscript from Gabriel de Luetz d'Aramon in bound volume
Enciphered letter from Gabriel de Luetz d'Aramon , French Ambassador to the Ottoman Empire , after 1546, with partial decipherment
Diagram showing an encrypt and decrypt process with a key
Symmetric-key cryptography, where a single key is used for both encryption and decryption
logic diagram showing International Data Encryption Algorithm cypher process
One round (out of 8.5) of the IDEA cipher, used in most versions of PGP and OpenPGP compatible software for time-efficient encryption of messages
diagram of Public-key cryptography showing public key and private key
Public-key cryptography, where different keys are used for encryption and decryption.
headshots of Whitfield Diffie and Martin Hellman
Whitfield Diffie and Martin Hellman , authors of the first published paper on public-key cryptography.
In this example the message is only signed and not encrypted. 1) Alice signs a message with her private key. 2) Bob can verify that Alice sent the message and that the message has not been modified.
Enigma machine typewriter keypad over many rotors in a wood box
Variants of the Enigma machine , used by Germany's military and civil authorities from the late 1920s through World War II , implemented a complex electro-mechanical polyalphabetic cipher . Breaking and reading of the Enigma cipher at Poland's Cipher Bureau , for 7 years before the war, and subsequent decryption at Bletchley Park , was important to Allied victory. [ 13 ]
NSA headquarters in Fort Meade, Maryland