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Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classical cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids. In the early 20th century, the invention of complex mechanical and electromechanical machines, such as the Enigma rotor machine, provided more sophisticated and efficient means of encryption; and the subsequent introduction of electronics and computing has allowed elaborate schemes of still greater complexity, most of which are entirely unsuited to pen and paper. The development of cryptography has been paralleled by the development of cryptanalysis — the "breaking" of codes and ciphers. The discovery and application, early on, of frequency analysis to the reading of encrypted communications has, on occasion, altered the course of history. Thus the Zimmermann Telegram triggered the United States' entry into World War I; and Allies reading of Nazi Germany's ciphers shortened World War II, in some evaluations by as much as two years. Until the 1960s, secure cryptography was largely the preserve of governments. Two events have since brought it squarely into the public domain: the creation of a public encryption standard (DES), and the invention of public key cryptography.

The earliest known use of cryptography is found in non standard hieroglyphs carved into the wall of a tomb from the Old Kingdom of Egypt circa 1900 BC. These are not thought to be serious attempts at secret communications, however, but rather to have been attempts at mystery, intrigue, or even amusement for literate onlookers. Some clay tablets from Mesopotamia somewhat later are clearly meant to protect information—one dated near 1500 BC was found to encrypt a craftsman's recipe for pottery glaze, presumably commercially valuable. Furthermore, Hebrew scholars made use of simple monoalphabetic substitution ciphers (such as the Atbash cipher) beginning perhaps around 600 to 500 BC. In India around 400 BC to 200 AD, Mlecchita vikalpa or "the art of understanding writing in cypher, and the writing of words in a peculiar way" was documented in the Kama Sutra for the purpose of communication between lovers. This was also likely a simple substitution cipher. Parts of the Egyptian demotic Greek Magical Papyri were written in a cypher script. The ancient Greeks are said to have known of ciphers. The scytale transposition cipher was used by the Spartan military, Herodotus tells us of secret messages physically concealed beneath wax on wooden tablets or as a tattoo on a slave's head concealed by regrown hair, although these are not properly examples of cryptography per se as the message, once known, is directly readable; this is known as steganography. Another Greek method was developed by Polybius (now called the "Polybius Square").

David Kahn notes in The Codebreakers that modern cryptology originated among the Arabs, the first people to systematically document cryptanalytic methods. 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. The invention of the frequency analysis technique for breaking monoalphabetic substitution ciphers, by Al Kindi, an Arab mathematician, sometime around AD 800, proved to be the single most significant cryptanalytic advance until World War II. Al Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which he described the first cryptanalytic techniques, including some for polyalphabetic ciphers, cipher classification, Arabic phonetics and syntax, and most importantly, gave the first descriptions on frequency analysis. He also covered methods of encipherments, cryptanalysis of certain encipherments, and statistical analysis of letters and letter combinations in Arabic. An important contribution of Ibn Adlan (1187–1268) was on sample size for use of frequency analysis. This period saw vital and significant cryptographic experimentation in the West. Ahmad al Qalqashandi (AD 1355–1418) wrote the Subh al a 'sha, a 14 volume encyclopedia which included a section on cryptology. This information was attributed to Ibn al Durayhim who lived from AD 1312 to 1361, but whose writings on cryptography have been lost. The list of ciphers in this work included both substitution and transposition, and for the first time, a cipher with multiple substitutions for each plaintext letter (later called homophonic substitution). Also traced to Ibn al Durayhim is an exposition on and a worked example of cryptanalysis, including the use of tables of letter frequencies and sets of letters which cannot occur together in one word. The earliest example of the homophonic substitution cipher is the one used by Duke of Mantua in the early 1400s. Homophonic cipher replaces each letter with multiple symbols depending on the letter frequency. The cipher is ahead of the time because it combines monoalphabetic and polyalphabetic features. Essentially all ciphers remained vulnerable to the cryptanalytic technique of frequency analysis until the development of the polyalphabetic cipher, and many remained so thereafter. The polyalphabetic cipher was most clearly explained by Leon Battista Alberti around AD 1467, for which he was called the "father of Western cryptology". In Europe, cryptography became (secretly) more important as a consequence of political competition and religious revolution. For instance, in Europe during and after the Renaissance, citizens of the various Italian states—the Papal States and the Roman Catholic Church included—were responsible for rapid proliferation of cryptographic techniques, few of which reflect understanding (or even knowledge) of Alberti's polyalphabetic advance. "Advanced ciphers", even after Alberti, were not as advanced as their inventors/developers/users claimed (and probably even they themselves believed). They were frequently broken. This over optimism may be inherent in cryptography, for it was then – and remains today – difficult in principle to know how vulnerable one's own system is. In the absence of knowledge, guesses and hopes are predictably common. Cryptography, cryptanalysis, and secret agent/courier betrayal featured in the Babington plot during the reign of Queen Elizabeth I which led to the execution of Mary, Queen of Scots. Robert Hooke suggested in the chapter Of Dr. Dee's Book of Spirits, that John Dee made use of Trithemian steganography, to conceal his communication with Queen Elizabeth I. The chief cryptographer of King Louis XIV of France was Antoine Rossignol; he and his family created what is known as the Great Cipher because it remained unsolved from its initial use until 1890, when French military cryptanalyst, Étienne Bazeries solved it. An encrypted message from the time of the Man in the Iron Mask (decrypted just prior to 1900 by Étienne Bazeries) has shed some, regrettably non definitive, light on the identity of that real, if legendary and unfortunate, prisoner. Outside of Europe, after the Mongols brought about the end of the Islamic Golden Age, cryptography remained comparatively undeveloped. Cryptography in Japan seems not to have been used until about 1510, and advanced techniques were not known until after the opening of the country to the West beginning in the 1860s.

Although cryptography has a long and complex history, it wasn't until the 19th century that it developed anything more than ad hoc approaches to either encryption or cryptanalysis (the science of finding weaknesses in crypto systems). Examples of the latter include Charles Babbage's Crimean War era work on mathematical cryptanalysis of polyalphabetic ciphers, redeveloped and published somewhat later by the Prussian Friedrich Kasiski. Understanding of cryptography at this time typically consisted of hard won rules of thumb; see, for example, Auguste Kerckhoffs' cryptographic writings in the latter 19th century. Edgar Allan Poe used systematic methods to solve ciphers in the 1840s. In particular he placed a notice of his abilities in the Philadelphia paper Alexander's Weekly (Express) Messenger, inviting submissions of ciphers, most of which he proceeded to solve. His success created a public stir for some months. He later wrote an essay on methods of cryptography which proved useful as an introduction for novice British cryptanalysts attempting to break German codes and ciphers during World War I, and a famous story, The Gold Bug, in which cryptanalysis was a prominent element. Cryptography, and its misuse, were involved in the execution of Mata Hari and in Dreyfus' conviction and imprisonment, both in the early 20th century. Cryptographers were also involved in exposing the machinations which had led to the Dreyfus affair; Mata Hari, in contrast, was shot. In World War I the Admiralty's Room 40 broke German naval codes and played an important role in several naval engagements during the war, notably in detecting major German sorties into the North Sea that led to the battles of Dogger Bank and Jutland as the British fleet was sent out to intercept them. However, its most important contribution was probably in decrypting the Zimmermann Telegram, a cable from the German Foreign Office sent via Washington to its ambassador Heinrich von Eckardt in Mexico which played a major part in bringing the United States into the war. In 1917, Gilbert Vernam proposed a teleprinter cipher in which a previously prepared key, kept on paper tape, is combined character by character with the plaintext message to produce the cyphertext. This led to the development of electromechanical devices as cipher machines, and to the only unbreakable cipher, the one time pad. During the 1920s, Polish naval officers assisted the Japanese military with code and cipher development. Mathematical methods proliferated in the period prior to World War II (notably in William F. Friedman's application of statistical techniques to cryptanalysis and cipher development and in Marian Rejewski's initial break into the German Army's version of the Enigma system in 1932).

By World War II, mechanical and electromechanical cipher machines were in wide use, although—where such machines were impractical—code books and manual systems continued in use. Great advances were made in both cipher design and cryptanalysis, all in secrecy. Information about this period has begun to be declassified as the official British 50 year secrecy period has come to an end, as US archives have slowly opened, and as assorted memoirs and articles have appeared.

The Germans made heavy use, in several variants, of an electromechanical rotor machine known as Enigma. Mathematician Marian Rejewski, at Poland's Cipher Bureau, in December 1932 deduced the detailed structure of the German Army Enigma, using mathematics and limited documentation supplied by Captain Gustave Bertrand of French military intelligence acquired from a German clerk. This was the greatest breakthrough in cryptanalysis in a thousand years and more, according to historian David Kahn. Rejewski and his mathematical Cipher Bureau colleagues, Jerzy Różycki and Henryk Zygalski, continued reading Enigma and keeping pace with the evolution of the German Army machine's components and encipherment procedures for some time. As the Poles' resources became strained by the changes being introduced by the Germans, and as war loomed, the Cipher Bureau, on the Polish General Staff's instructions, on 25 July 1939, at Warsaw, initiated French and British intelligence representatives into the secrets of Enigma decryption. Soon after the invasion of Poland by Germany on 1 September 1939, key Cipher Bureau personnel were evacuated southeastward; on 17 September, as the Soviet Union attacked Poland from the East, they crossed into Romania. From there they reached Paris, France; at PC Bruno, near Paris, they continued working toward breaking Enigma, collaborating with British cryptologists at Bletchley Park as the British got up to speed on their work breaking Enigma. In due course, the British cryptographerswhose ranks included many chess masters and mathematics dons such as Gordon Welchman, Max Newman, and Alan Turing (the conceptual founder of modern computing) made substantial breakthroughs in the scale and technology of Enigma decryption. German code breaking in World War II also had some success, most importantly by breaking the Naval Cipher No. 3. This enabled them to track and sink Atlantic convoys. It was only Ultra intelligence that finally persuaded the admiralty to change their codes in June 1943. This is surprising given the success of the British Room 40 code breakers in the previous world war. At the end of the War, on 19 April 1945, Britain's highest level civilian and military officials were told that they could never reveal that the German Enigma cipher had been broken because it would give the defeated enemy the chance to say they "were not well and fairly beaten". The German military also deployed several teleprinter stream ciphers. Bletchley Park called them the Fish ciphers; Max Newman and colleagues designed and deployed the Heath Robinson, and then the world's first programmable digital electronic computer, the Colossus, to help with their cryptanalysis. The German Foreign Office began to use the one time pad in 1919; some of this traffic was read in World War II partly as the result of recovery of some key material in South America that was discarded without sufficient care by a German courier. The Schlüsselgerät 41 was developed late in the war as a more secure replacement for Enigma, but only saw limited use.

A US Army group, the SIS, managed to break the highest security Japanese diplomatic cipher system (an electromechanical stepping switch machine called Purple by the Americans) in 1940, before the attack on Pearl Harbour. The locally developed Purple machine replaced the earlier "Red" machine used by the Japanese Foreign Ministry, and a related machine, the M 1, used by Naval attachés which was broken by the U. S. Navy's Agnes Driscoll. All the Japanese machine ciphers were broken, to one degree or another, by the Allies. The Japanese Navy and Army largely used code book systems, later with a separate numerical additive. US Navy cryptographers (with cooperation from British and Dutch cryptographers after 1940) broke into several Japanese Navy crypto systems. The break into one of them, JN 25, famously led to the US victory in the Battle of Midway; and to the publication of that fact in the Chicago Tribune shortly after the battle, though the Japanese seem not to have noticed for they kept using the JN 25 system.

The Americans referred to the intelligence resulting from cryptanalysis, perhaps especially that from the Purple machine, as 'Magic'. The British eventually settled on 'Ultra' for intelligence resulting from cryptanalysis, particularly that from message traffic protected by the various Enigmas. An earlier British term for Ultra had been 'Boniface' in an attempt to suggest, if betrayed, that it might have an individual agent as a source. Allied cipher machines used in World War II included the British TypeX and the American SIGABA; both were electromechanical rotor designs similar in spirit to the Enigma, albeit with major improvements. Neither is known to have been broken by anyone during the War. The Poles used the Lacida machine, but its security was found to be less than intended (by Polish Army cryptographers in the UK), and its use was discontinued. US troops in the field used the M 209 and the still less secure M 94 family machines. British SOE agents initially used 'poem ciphers' (memorized poems were the encryption/decryption keys), but later in the War, they began to switch to one time pads. The VIC cipher (used at least until 1957 in connection with Rudolf Abel's NY spy ring) was a very complex hand cipher, and is claimed to be the most complicated known to have been used by the Soviets, according to David Kahn in Kahn on Codes. For the decrypting of Soviet ciphers (particularly when one time pads were reused), see Venona project.

The second development, in 1976, was perhaps even more important, for it fundamentally changed the way cryptosystems might work. This was the publication of the paper New Directions in Cryptography by Whitfield Diffie and Martin Hellman. It introduced a radically new method of distributing cryptographic keys, which went far toward solving one of the fundamental problems of cryptography, key distribution, and has become known as Diffie–Hellman key exchange. The article also stimulated the almost immediate public development of a new class of enciphering algorithms, the asymmetric key algorithms. Prior to that time, all useful modern encryption algorithms had been symmetric key algorithms, in which the same cryptographic key is used with the underlying algorithm by both the sender and the recipient, who must both keep it secret. All of the electromechanical machines used in World War II were of this logical class, as were the Caesar and Atbash ciphers and essentially all cipher systems throughout history. The 'key' for a code is, of course, the codebook, which must likewise be distributed and kept secret, and so shares most of the same problems in practice. Of necessity, the key in every such system had to be exchanged between the communicating parties in some secure way prior to any use of the system (the term usually used is 'via a secure channel') such as a trustworthy courier with a briefcase handcuffed to a wrist, or face to face contact, or a loyal carrier pigeon. This requirement is never trivial and very rapidly becomes unmanageable as the number of participants increases, or when secure channels aren't available for key exchange, or when, as is sensible cryptographic practice, keys are frequently changed. In particular, if messages are meant to be secure from other users, a separate key is required for each possible pair of users. A system of this kind is known as a secret key, or symmetric key cryptosystem. D H key exchange (and succeeding improvements and variants) made operation of these systems much easier, and more secure, than had ever been possible before in all of history. In contrast, asymmetric key encryption uses a pair of mathematically related keys, each of which decrypts the encryption performed using the other. Some, but not all, of these algorithms have the additional property that one of the paired keys cannot be deduced from the other by any known method other than trial and error. An algorithm of this kind is known as a public key or asymmetric key system. Using such an algorithm, only one key pair is needed per user. By designating one key of the pair as private (always secret), and the other as public (often widely available), no secure channel is needed for key exchange. So long as the private key stays secret, the public key can be widely known for a very long time without compromising security, making it safe to reuse the same key pair indefinitely. For two users of an asymmetric key algorithm to communicate securely over an insecure channel, each user will need to know their own public and private keys as well as the other user's public key. Take this basic scenario: Alice and Bob each have a pair of keys they've been using for years with many other users. At the start of their message, they exchange public keys, unencrypted over an insecure line. Alice then encrypts a message using her private key, and then re encrypts that result using Bob's public key. The double encrypted message is then sent as digital data over a wire from Alice to Bob. Bob receives the bit stream and decrypts it using his own private key, and then decrypts that bit stream using Alice's public key. If the final result is recognizable as a message, Bob can be confident that the message actually came from someone who knows Alice's private key (presumably actually her if she's been careful with her private key), and that anyone eavesdropping on the channel will need Bob's private key in order to understand the message. Asymmetric algorithms rely for their effectiveness on a class of problems in mathematics called one way functions, which require relatively little computational power to execute, but vast amounts of power to reverse, if reversal is possible at all. A classic example of a one way function is multiplication of very large prime numbers. It's fairly quick to multiply two large primes, but very difficult to find the factors of the product of two large primes. Because of the mathematics of one way functions, most possible keys are bad choices as cryptographic keys; only a small fraction of the possible keys of a given length are suitable, and so asymmetric algorithms require very long keys to reach the same level of security provided by relatively shorter symmetric keys. The need to both generate the key pairs, and perform the encryption/decryption operations make asymmetric algorithms computationally expensive, compared to most symmetric algorithms. Since symmetric algorithms can often use any sequence of (random, or at least unpredictable) bits as a key, a disposable session key can be quickly generated for short term use. Consequently, it is common practice to use a long asymmetric key to exchange a disposable, much shorter (but just as strong) symmetric key. The slower asymmetric algorithm securely sends a symmetric session key, and the faster symmetric algorithm takes over for the remainder of the message. Asymmetric key cryptography, Diffie–Hellman key exchange, and the best known of the public key / private key algorithms (i. e., what is usually called the RSA algorithm), all seem to have been independently developed at a UK intelligence agency before the public announcement by Diffie and Hellman in 1976. GCHQ has released documents claiming they had developed public key cryptography before the publication of Diffie and Hellman's paper. Various classified papers were written at GCHQ during the 1960s and 1970s which eventually led to schemes essentially identical to RSA encryption and to Diffie–Hellman key exchange in 1973 and 1974. Some of these have now been published, and the inventors (James H. Ellis, Clifford Cocks, and Malcolm Williamson) have made public (some of) their work.

Hashing is a common technique used in cryptography to encode information quickly using typical algorithms. Generally, an algorithm is applied to a string of text, and the resulting string becomes the "hash value". This creates a "digital fingerprint" of the message, as the specific hash value is used to identify a specific message. The output from the algorithm is also referred to as a "message digest" or a "check sum". Hashing is good for determining if information has been changed in transmission. If the hash value is different upon reception than upon sending, there is evidence the message has been altered. Once the algorithm has been applied to the data to be hashed, the hash function produces a fixed length output. Essentially, anything passed through the hash function should resolve to the same length output as anything else passed through the same hash function. It is important to note that hashing is not the same as encrypting. Hashing is a one way operation that is used to transform data into the compressed message digest. Additionally, the integrity of the message can be measured with hashing. Conversely, encryption is a two way operation that is used to transform plaintext into cipher text and then vice versa. In encryption, the confidentiality of a message is guaranteed.