cryptology | Britannica.com Cryptology public-key cryptography Cryptology, science concerned with data communication and storage in secure and usually secret form. It encompasses both cryptography and cryptanalysis. The term cryptology is derived from the Greek kryptós (“hidden”) and lógos (“word”). Security obtains from legitimate users being able to transform information by virtue of a secret key or keys—i.e., information known only to them. The resulting cipher, although generally inscrutable and not forgeable without the secret key, can be decrypted by anyone knowing the key either to recover the hidden information or to authenticate the source. Secrecy, though still an important function in cryptology, is often no longer the main purpose of using a transformation, and the resulting transformation may be only loosely considered a cipher. Cryptography (from the Greek kryptós and gráphein, “to write”) was originally the study of the principles and techniques by which information could be concealed in ciphers and later revealed by legitimate users employing the secret key. It now encompasses the whole area of key-controlled transformations of information into forms that are either impossible or computationally infeasible for unauthorized persons to duplicate or undo.

Cryptanalysis (from the Greek kryptós and analýein, “to loosen” or “to untie”) is the science (and art) of recovering or forging cryptographically secured information without knowledge of the key. Cryptology is often—and mistakenly—considered a synonym for cryptography and occasionally for cryptanalysis, but specialists in the field have for years adopted the convention that cryptology is the more inclusive term, encompassing both cryptography and cryptanalysis. Cryptography was initially only concerned with providing secrecy for written messages, especially in times of war. Its principles apply equally well, however, to securing data flowing between computers or data stored in them, to encrypting facsimile and television signals, to verifying the identity of participants in electronic commerce ( e-commerce ) and providing legally acceptable records of those transactions. Because of this broadened interpretation of cryptography, the field of cryptanalysis has also been enlarged. Similar Topics Moon type This article discusses the basic elements of cryptology, delineating the principal systems and techniques of cryptography as well as the general types and procedures of cryptanalysis. It also provides a concise historical survey of the development of cryptosystems and cryptodevices.

A brief introduction is also given to the revolution in cryptology brought on by the information age, e-commerce, and the Internet . For additional information on the encoding and encryption of facsimile and television signals and of computer data, see telecommunications system and information processing . General considerations Because much of the terminology of cryptology dates to a time when written messages were the only things being secured, the source information, even if it is an apparently incomprehensible binary stream of 1s and 0s, as in computer output, is referred to as the plaintext. As noted above, the secret information known only to the legitimate users is the key , and the transformation of the plaintext under the control of the key into a cipher (also called ciphertext) is referred to as encryption . The inverse operation, by which a legitimate receiver recovers the concealed information from the cipher using the key, is known as decryption . The fundamentals of codes, ciphers, and authentication The most frequently confused, and misused, terms in the lexicon of cryptology are code and cipher. Even experts occasionally employ these terms as though they were synonymous.

A code is simply an unvarying rule for replacing a piece of information (e.g., letter, word, or phrase) with another object, but not necessarily of the same sort; Morse code , which replaces alphanumeric characters with patterns of dots and dashes, is a familiar example. Probably the most widely known code in use today is the American Standard Code for Information Interchange ( ASCII ). Employed in all personal computers and terminals, it represents 128 characters (and operations such as backspace and carriage return) in the form of seven-bit binary numbers—i.e., as a string of seven 1s and 0s. In ASCII a lowercase a is always 1100001, an uppercase A always 1000001, and so on. Acronyms are also widely known and used codes, as, for example, Y2K (for “Year 2000”) and COD (meaning “cash on delivery”). Occasionally such a code word achieves an independent existence (and meaning) while the original equivalent phrase is forgotten or at least no longer has the precise meaning attributed to the code word—e.g., modem (originally standing for “modulator-demodulator”).

Britannica Stories Eyjafjallajökull volcano At the very end of the 20th century, a revolution occurred in the way private citizens and businesses made use of and were dependent on pure information, i.e., information with no meaningful physical embodiment. This was sparked by two technical developments: an almost universal access to affordable real-time global communications, and the practical capability to acquire, process, store, and disseminate virtually unlimited amounts of information. Electronic banking, personal computers, the Internet and associated e-commerce, and “smart” cards were some of the more obvious instances where this revolution affected every aspect of private and commercial life. To appreciate how this involved cryptology, contrast what is involved when a customer makes a noncash purchase in person with what is involved in a similar transaction in e-commerce. For a direct purchase, the merchant routinely asks for some photo identification, usually a driver’s license, to verify the customer’s identity. Neither party is ordinarily concerned with secrecy; both are vitally concerned with other aspects of information integrity . Next, consider an analogous transaction over the Internet.

The merchant must still verify the customer’s identity, even though they may be separated by thousands of miles, and the customer must still be assured that he will only be charged the agreed amount. However, there is a whole gamut of new concerns. The customer must be assured that information he communicates to the merchant is confidential and protected from interception by others. And while the merchant retains the customer’s signature as material proof of a direct transaction, he has only a string of 0s and 1s on a hard disk following an e-commerce transaction. The merchant must be confident that this “information” will suffice for him to collect payment, as well as protect him should the customer later disavow the transaction or claim that it was for a different amount. All of these concerns, and more, have to be met before the simplest e-commerce transactions can be made securely. As a result, cryptology has been extended far beyond its original function of providing secrecy. The conduct of commerce, affairs of state, military actions, and personal affairs all depend on the existence of generally accepted means of authenticating identity, authority, ownership, license, signature, notarization, date of action, receipt, and so on.

In the past these have depended almost entirely on documents, and on protocols for the creation of those documents, for authentication. Society has evolved and adopted a complex set of legal and forensic procedures, depending almost entirely on the physical evidence intrinsic to the documents themselves, to resolve disputes over authenticity. In the information age, however, possession, control, transfer, or access to real assets is frequently based on electronic information, and a license to use, modify, or disseminate valuable information itself is similarly determined. Thus, it is essential that internal evidence be present in the information itself—since that is the only thing available. Modern cryptology, therefore, must provide every function presently served by documents—public and private. In fact, it frequently must do more. When someone mails a document by certified mail with a request for a delivery receipt, the receipt only proves that an envelope was delivered; it says nothing about the contents. Digital certificates of origination and digital receipts, though, are inextricably linked to each electronic document. Many other functions, such as signatures, are also much more demanding in a digital setting. In June 2000 the U.S. Congress gave digital signatures the same legal status as written signatures—the first such legislation in the world.

In classical cryptology the participants trust each other but not outsiders; typical examples include diplomatic communications and military commands. In business and personal transactions, though, the situation is almost the opposite, as the participants may have various motives for cheating. For example, the cheater may wish to impersonate some other participant, to eavesdrop on communications between other participants, or to intercept and modify information being communicated between other users. The cheater may be an insider who wishes to disavow communications he actually originated or to claim to have received messages from other participants who did not send them. He may wish to enlarge his license to gain access to information to which he is not supposed to have access or to alter the license of others. He may wish simply to subvert the system to deny services to others or to cause other users to reject as fraudulent information that is in fact legitimate. Therefore, modern cryptology must also prevent every form of cheating or, failing that, detect cheating in information-based systems where the means for cheating depends only on tampering with electronic information. At the beginning of the 1990s, most people would likely have been hard-pressed to say where cryptology had an impact on their day-to-day lives.

Today, people who have purchased merchandise over the Internet are familiar with warnings that they are about to exchange information over a secure link. When a warning appears alerting consumers that a merchant’s authentication has either expired or is not working, they are aware that this is a warning to proceed at their own risk in providing personal information, such as credit card numbers. Only a few consumers are aware, however, that behind this exchange of authentications is a 128-bit cryptography key that has been in common use around the world for transactions over the Internet since it was approved for export by the U.S. government in 2000, replacing an earlier 40-bit key that had been made insecure by the growing power of computers to test it. The 128-bit key offers “strong encryption” that protects Internet transactions against almost any threat; nevertheless, some Web browsers will support an even stronger 256-bit encryption key, which offers a much stronger level of protection required by many governments for top-secret documents. Cryptology, indeed, has long been a part of modern daily life. In particular, electronic banking and various financial, medical, and legal databases depend on cryptology for security.

One example is the personal identity number ( PIN ), a coded identification that must be entered into an automated teller machine (ATM) along with a bankcard to corroborate that the card is being used by an authorized bearer. The PIN may be stored in an encrypted form (as a cipher) either in the bank’s computers or on the card itself. The transformation used in this type of cryptography is called one-way; i.e., it is easy to compute a cipher when given the bank’s key and the customer’s PIN, but it is computationally infeasible to compute the plaintext PIN from the cipher even when the key is known. This protects the cardholder from being impersonated by someone who has access to the bank’s computer files. Similarly, communications between the ATM and the bank’s central computer are encrypted to prevent a would-be thief from tapping into the phone lines and recording the signals sent to the ATM to authorize the dispensing of cash in response to a legitimate user request and then later feeding the same signals to the ATM repeatedly to deceive it into dispensing money illegitimately from the customer’s account. A novel application that involves all aspects of cryptography is the “smart” credit card, which has a microprocessor built into the card itself.

The user must corroborate his identity to the card each time a transaction is made, in much the same way that a PIN is used with an ATM. The card and the card reader execute a sequence of encrypted sign/countersign-like exchanges to verify that each is dealing with a legitimate counterpart. Once this has been established, the transaction itself is carried out in encrypted form to prevent anyone, including the cardholder or the merchant whose card reader is involved, from eavesdropping on the exchange and then later impersonating either party to defraud the system. This elaborate protocol is carried out in a way that is invisible to the user, except for the necessity of entering a PIN to initiate the transaction. Smart cards are in widespread use throughout Europe, much more so than the “dumb” plastic cards common in the United States . The Advanced Encryption Standard (AES; see History of cryptology ), approved as a secure communications standard by the U.S. National Institute of Standards and Technology (NIST) in 2000, is compatible with implementation in smart cards, unlike its predecessor, the Data Encryption Standard (DES).

Cryptography Cryptography, as defined in the introduction to this article, is the science of transforming information into a form that is impossible or infeasible to duplicate or undo without knowledge of a secret key. Cryptographic systems are generically classified (1) by the mathematical operations through which the information (called the “plaintext”) is concealed using the encryption key—namely, transposition, substitution, or product ciphers in which two such operations are cascaded; (2) according to whether the transmitter and receiver use the same key (symmetric [single-key] cryptosystem) or different keys (asymmetric [two-key or public-key] cryptosystem); and (3) by whether they produce block or stream ciphers. These three types of system are described in turn below. Cipher systems The easiest way to describe the techniques on which cryptography depends is first to examine some simple cipher systems and then abstract from these examples features that apply to more complex systems. There are two basic kinds of mathematical operations used in cipher systems: transpositions and substitutions. Transpositions rearrange the symbols in the plaintext without changing the symbols themselves.

Substitutions replace plaintext elements (symbols, pairs of symbols, etc.) with other symbols or groups of symbols without changing the sequence in which they occur. Transposition ciphers In manual systems transpositions are generally carried out with the aid of an easily remembered mnemonic . For example, a popular schoolboy cipher is the “rail fence,” in which letters of the plaintext are written alternating between rows and the rows are then read sequentially to give the cipher. In a depth-two rail fence (two rows) the message WE ARE DISCOVERED SAVE YOURSELF would be written Simple frequency counts on the ciphertext would reveal to the cryptanalyst that letters occur with precisely the same frequency in the cipher as in an average plaintext and, hence, that a simple rearrangement of the letters is probable. The rail fence is the simplest example of a class of transposition ciphers, known as route ciphers , that enjoyed considerable popularity in the early history of cryptology. In general, the elements of the plaintext (usually single letters) are written in a prearranged order (route) into a geometric array (matrix)—typically a rectangle—agreed upon in advance by the transmitter and receiver and then read off by following another prescribed route through the matrix to produce the cipher.

The key in a route cipher consists of keeping secret the geometric array, the starting point, and the routes. Clearly, both the matrix and the routes can be much more complex than in this example; but even so, they provide little security. One form of transposition ( permutation ) that was widely used depends on an easily remembered key word for identifying the route in which the columns of a rectangular matrix are to be read. For example, using the key word AUTHOR and ordering the columns by the lexicographic order of the letters in the key word In decrypting a route cipher, the receiver enters the ciphertext symbols into the agreed-upon matrix according to the encryption route and then reads the plaintext according to the original order of entry. A significant improvement in cryptosecurity can be achieved by reencrypting the cipher obtained from one transposition with another transposition. Because the result (product) of two transpositions is also a transposition, the effect of multiple transpositions is to define a complex route in the matrix, which in itself would be difficult to describe by any simple mnemonic.

(See Product ciphers , below.) In the same class also fall systems that make use of perforated cardboard matrices called grilles; descriptions of such systems can be found in most older books on cryptography. In contemporary cryptography, transpositions serve principally as one of several encryption steps in forming a compound or product cipher. Substitution ciphers In substitution ciphers, units of the plaintext (generally single letters or pairs of letters) are replaced with other symbols or groups of symbols, which need not be the same as those used in the plaintext. For instance, in Sir Arthur Conan Doyle’s Adventure of the Dancing Men (1903), Sherlock Holmes solves a monoalphabetic substitution cipher in which the ciphertext symbols are stick figures of a human in various dancelike poses. The simplest of all substitution ciphers are those in which the cipher alphabet is merely a cyclical shift of the plaintext alphabet. Of these, the best-known is the Caesar cipher , used by Julius Caesar , in which A is encrypted as D, B as E, and so forth. As many a schoolboy has discovered to his embarrassment, cyclical-shift substitution ciphers are not secure.

And as is pointed out in the section Cryptanalysis , neither is any other monoalphabetic substitution cipher in which a given plaintext symbol is always encrypted into the same ciphertext symbol. Because of the redundancy of the English language , only about 25 symbols of ciphertext are required to permit the cryptanalysis of monoalphabetic substitution ciphers, which makes them a popular source for recreational cryptograms. The explanation for this weakness is that the frequency distributions of symbols in the plaintext and in the ciphertext are identical, only the symbols having been relabeled. In fact, any structure or pattern in the plaintext is preserved intact in the ciphertext, so that the cryptanalyst’s task is an easy one. There are two main approaches that have been employed with substitution ciphers to lessen the extent to which structure in the plaintext—primarily single-letter frequencies—survives in the ciphertext. One approach is to encrypt elements of plaintext consisting of two or more symbols; e.g., digraphs and trigraphs. The other is to use several cipher alphabets. When this approach of polyalphabetic substitution is carried to its limit, it results in onetime keys, or pads.

Playfair ciphers In cryptosystems for manually encrypting units of plaintext made up of more than a single letter, only digraphs were ever used. By treating digraphs in the plaintext as units rather than as single letters, the extent to which the raw frequency distribution survives the encryption process can be lessened but not eliminated, as letter pairs are themselves highly correlated. The best-known digraph substitution cipher is the Playfair, invented by Sir Charles Wheatstone but championed at the British Foreign Office by Lyon Playfair, the first Baron Playfair of St. Andrews . Below is an example of a Playfair cipher, solved by Lord Peter Wimsey in Dorothy L. Sayers ’s Have His Carcase (1932). Here, the mnemonic aid used to carry out the encryption is a 5 × 5-square matrix containing the letters of the alphabet (I and J are treated as the same letter). A key word, MONARCHY in this example, is filled in first, and the remaining unused letters of the alphabet are entered in their lexicographic order: Plaintext digraphs are encrypted with the matrix by first locating the two plaintext letters in the matrix.

They are (1) in different rows and columns; (2) in the same row; (3) in the same column; or (4) alike. The corresponding encryption (replacement) rules are the following: When the two letters are in different rows and columns, each is replaced by the letter that is in the same row but in the other column; i.e., to encrypt WE, W is replaced by U and E by G. When A and R are in the same row, A is encrypted as R and R (reading the row cyclically) as M. When I and S are in the same column, I is encrypted as S and S as X. When a double letter occurs, a spurious symbol, say Q, is introduced so that the MM in SUMMER is encrypted as NL for MQ and CL for ME. An X is appended to the end of the plaintext if necessary to give the plaintext an even number of letters. Encrypting the familiar plaintext example using Sayers’s Playfair array yields: If the frequency distribution information were totally concealed in the encryption process, the ciphertext plot of letter frequencies in Playfair ciphers would be flat. It is not.

The deviation from this ideal is a measure of the tendency of some letter pairs to occur more frequently than others and of the Playfair’s row-and-column correlation of symbols in the ciphertext—the essential structure exploited by a cryptanalyst in solving Playfair ciphers. The loss of a significant part of the plaintext frequency distribution, however, makes a Playfair cipher harder to cryptanalyze than a monoalphabetic cipher. Vigenère ciphers The other approach to concealing plaintext structure in the ciphertext involves using several different monoalphabetic substitution ciphers rather than just one; the key specifies which particular substitution is to be employed for encrypting each plaintext symbol. The resulting ciphers, known generically as polyalphabetics, have a long history of usage. The systems differ mainly in the way in which the key is used to choose among the collection of monoalphabetic substitution rules. The best-known polyalphabetics are the simple Vigenère ciphers, named for the 16th-century French cryptographer Blaise de Vigenère.

For many years this type of cipher was thought to be impregnable and was known as le chiffre indéchiffrable, literally “the unbreakable cipher.” The procedure for encrypting and decrypting Vigenère ciphers is illustrated in the figure . In the simplest systems of the Vigenère type, the key is a word or phrase that is repeated as many times as required to encipher a message. If the key is DECEPTIVE and the message is WE ARE DISCOVERED SAVE YOURSELF, then the resulting cipher will be The graph shows the extent to which the raw frequency of occurrence pattern is obscured by encrypting the text of this article using the repeating key DECEPTIVE. Nevertheless, in 1861 Friedrich W. Kasiski , formerly a German army officer and cryptanalyst, published a solution of repeated-key Vigenère ciphers based on the fact that identical pairings of message and key symbols generate the same cipher symbols. Cryptanalysts look for precisely such repetitions. In the example given above, the group VTW appears twice, separated by six letters, suggesting that the key (i.e., word) length is either three or nine.

Consequently, the cryptanalyst would partition the cipher symbols into three and nine monoalphabets and attempt to solve each of these as a simple substitution cipher. With sufficient ciphertext, it would be easy to solve for the unknown key word. The periodicity of a repeating key exploited by Kasiski can be eliminated by means of a running-key Vigenère cipher. Such a cipher is produced when a nonrepeating text is used for the key. Vigenère actually proposed concatenating the plaintext itself to follow a secret key word in order to provide a running key in what is known as an autokey. Even though running-key or autokey ciphers eliminate periodicity, two methods exist to cryptanalyze them. In one, the cryptanalyst proceeds under the assumption that both the ciphertext and the key share the same frequency distribution of symbols and applies statistical analysis. For example, E occurs in English plaintext with a frequency of 0.0169, and T occurs only half as often. The cryptanalyst would, of course, need a much larger segment of ciphertext to solve a running-key Vigenère cipher, but the basic principle is essentially the same as before—i.e., the recurrence of like events yields identical effects in the ciphertext.

The second method of solving running-key ciphers is commonly known as the probable-word method. In this approach, words that are thought most likely to occur in the text are subtracted from the cipher. For example, suppose that an encrypted message to President Jefferson Davis of the Confederate States of America was intercepted. Based on a statistical analysis of the letter frequencies in the ciphertext, and the South’s encryption habits, it appears to employ a running-key Vigenère cipher. A reasonable choice for a probable word in the plaintext might be “PRESIDENT.” For simplicity a space will be encoded as a “0.” PRESIDENT would then be encoded—not encrypted—as “16, 18, 5, 19, 9, 4, 5, 14, 20” using the rule A = 1, B = 2, and so forth. Now these nine numbers are added modulo 27 (for the 26 letters plus a space symbol) to each successive block of nine symbols of ciphertext—shifting one letter each time to form a new block. Almost all such additions will produce random-like groups of nine symbols as a result, but some may produce a block that contains meaningful English fragments.

These fragments can then be extended with either of the two techniques described above. If provided with enough ciphertext, the cryptanalyst can ultimately decrypt the cipher. What is important to bear in mind here is that the redundancy of the English language is high enough that the amount of information conveyed by every ciphertext component is greater than the rate at which equivocation (i.e., the uncertainty about the plaintext that the cryptanalyst must resolve to cryptanalyze the cipher) is introduced by the running key. In principle, when the equivocation is reduced to zero, the cipher can be solved. The number of symbols needed to reach this point is called the unicity distance—and is only about 25 symbols, on average, for simple substitution ciphers. Vernam-Vigenère ciphers In 1918 Gilbert S. Vernam , an engineer for the American Telephone & Telegraph Company (AT&T), introduced the most important key variant to the Vigenère system. At that time all messages transmitted over AT&T’s teleprinter system were encoded in the Baudot Code , a binary code in which a combination of marks and spaces represents a letter, number, or other symbol.

Vernam suggested a means of introducing equivocation at the same rate at which it was reduced by redundancy among symbols of the message, thereby safeguarding communications against cryptanalytic attack. He saw that periodicity (as well as frequency information and intersymbol correlation), on which earlier methods of decryption of different Vigenère systems had relied, could be eliminated if a random series of marks and spaces (a running key) were mingled with the message during encryption to produce what is known as a stream or streaming cipher. There was one serious weakness in Vernam’s system, however. It required one key symbol for each message symbol, which meant that communicants would have to exchange an impractically large key in advance—i.e., they had to securely exchange a key as large as the message they would eventually send. The key itself consisted of a punched paper tape that could be read automatically while symbols were typed at the teletypewriter keyboard and encrypted for transmission. This operation was performed in reverse using a copy of the paper tape at the receiving teletypewriter to decrypt the cipher.

Vernam initially believed that a short random key could safely be reused many times, thus justifying the effort to deliver such a large key, but reuse of the key turned out to be vulnerable to attack by methods of the type devised by Kasiski. Vernam offered an alternative solution: a key generated by combining two shorter key tapes of m and n binary digits, or bits, where m and n share no common factor other than 1 (they are relatively prime). A bit stream so computed does not repeat until mn bits of key have been produced. This version of the Vernam cipher system was adopted and employed by the U.S. Army until Major Joseph O. Mauborgne of the Army Signal Corps demonstrated during World War I that a cipher constructed from a key produced by linearly combining two or more short tapes could be decrypted by methods of the sort employed to cryptanalyze running-key ciphers. Mauborgne’s work led to the realization that neither the repeating single-key nor the two-tape Vernam-Vigenère cipher system was cryptosecure. Of far greater consequence to modern cryptology—in fact, an idea that remains its cornerstone—was the conclusion drawn by Mauborgne and William F.

Friedman that the only type of cryptosystem that is unconditionally secure uses a random onetime key. The proof of this, however, was provided almost 30 years later by another AT&T researcher, Claude Shannon , the father of modern information theory . In a streaming cipher the key is incoherent—i.e., the uncertainty that the cryptanalyst has about each successive key symbol must be no less than the average information content of a message symbol. The dotted curve in the figure indicates that the raw frequency of occurrence pattern is lost when the draft text of this article is encrypted with a random onetime key. The same would be true if digraph or trigraph frequencies were plotted for a sufficiently long ciphertext. In other words, the system is unconditionally secure, not because of any failure on the part of the cryptanalyst to find the right cryptanalytic technique but rather because he is faced with an irresolvable number of choices for the key or plaintext message. Product ciphers In the discussion of transposition ciphers it was pointed out that by combining two or more simple transpositions, a more secure encryption may result.

In the days of manual cryptography this was a useful device for the cryptographer, and in fact double transposition or product ciphers on key word-based rectangular matrices were widely used. There was also some use of a class of product ciphers known as fractionation systems , wherein a substitution was first made from symbols in the plaintext to multiple symbols (usually pairs, in which case the cipher is called a biliteral cipher) in the ciphertext, which was then encrypted by a final transposition, known as superencryption. One of the most famous field ciphers of all time was a fractionation system, the ADFGVX cipher employed by the German army during World War I. This system used a 6 × 6 matrix to substitution-encrypt the 26 letters and 10 digits into pairs of the symbols A, D, F, G, V, and X. The resulting biliteral cipher was then written into a rectangular array and route encrypted by reading the columns in the order indicated by a key word, as illustrated in the figure . The great French cryptanalyst Georges J. Painvin succeeded in cryptanalyzing critical ADFGVX ciphers in 1918, with devastating effect for the German army in the battle for Paris.

Key cryptosystems Single-key cryptography Single-key cryptography is limited in practice by what is known as the key distribution problem. Since all participants must possess the same secret key, if they are physically separated—as is usually the case—there is the problem of how they get the key in the first place. Diplomatic and military organizations traditionally use couriers to distribute keys for the highest-level communications systems, which are then used to superencrypt and distribute keys for lower-level systems. This is impractical, though, for most business and private needs. In addition, key holders are compelled to trust each other unconditionally to protect the keys in their possession and not to misuse them. Again, while this may be a tolerable condition in diplomatic and military organizations, it is almost never acceptable in the commercial realm. Another key distribution problem is the sheer number of keys required for flexible, secure communications among even a modest number of users. While only a single key is needed for secure communication between two parties, every potential pair of participants in a larger group needs a unique key. To illustrate this point, consider an organization with only 1,000 users: each individual would need a different private key for each of the other 999 users.

Such a system would require 499,500 different keys in all, with each user having to protect 999 keys. The number of different keys increases in proportion to the square of the number of users. Secure distribution for so many keys is simply insolvable, as are the demands on the users for the secure storage of their keys. In other words, symmetric key cryptography is impractical in a network in which all participants are equals in all respects. One “solution” is to create a trusted authority—unconditionally trusted by all users—with whom each user can communicate securely to generate and distribute temporary session keys as needed. Each user then has only to protect one key, while the burden for the protection of all of the keys in the network is shifted to the central authority. Two-key cryptography Public-key cryptography In 1976, in one of the most inspired insights in the history of cryptology, Sun Microsystems, Inc.

, computer engineer Whitfield Diffie and Stanford University electrical engineer Martin Hellman realized that the key distribution problem could be almost completely solved if a cryptosystem, T (and perhaps an inverse system, T′), could be devised that used two keys and satisfied the following conditions: It must be easy for the cryptographer to calculate a matched pair of keys, e (encryption) and d (decryption), for which TeT′d = I. Although not essential, it is desirable that T′dTe = I and that T = T′. Since most of the systems devised to meet points 1–4 satisfy these conditions as well, we will assume they hold hereafter—but that is not necessary. The encryption and decryption operation, T, should be (computationally) easy to carry out. At least one of the keys must be computationally infeasible for the cryptanalyst to recover even when he knows T, the other key, and arbitrarily many matching plaintext and ciphertext pairs. It should not be computationally feasible to recover x given y, where y = Tk(x) for almost all keys k and messages x.

Given such a system, Diffie and Hellman proposed that each user keep his decryption key secret and publish his encryption key in a public directory. Secrecy was not required, either in distributing or in storing this directory of “public” keys. Anyone wishing to communicate privately with a user whose key is in the directory only has to look up the recipient’s public key to encrypt a message that only the intended receiver can decrypt. The total number of keys involved is just twice the number of users, with each user having a key in the public directory and his own secret key, which he must protect in his own self-interest. Obviously, the public directory must be authenticated, otherwise A could be tricked into communicating with C when he thinks he is communicating with B simply by substituting C’s key for B’s in A’s copy of the directory. Since they were focused on the key distribution problem, Diffie and Hellman called their discovery public-key cryptography. This was the first discussion of two-key cryptography in the open literature. However, Admiral Bobby Inman, while director of the U.S.

National Security Agency (NSA) from 1977 to 1981, revealed that two-key cryptography had been known to the agency almost a decade earlier, having been discovered by James Ellis, Clifford Cocks, and Malcolm Williamson at the British Government Code Headquarters (GCHQ). In this system, ciphers created with a secret key can be decrypted by anyone using the corresponding public key—thereby providing a means to identify the originator at the expense of completely giving up secrecy. Ciphers generated using the public key can only be decrypted by users holding the secret key, not by others holding the public key—however, the secret-key holder receives no information concerning the sender. In other words, the system provides secrecy at the expense of completely giving up any capability of authentication. What Diffie and Hellman had done was to separate the secrecy channel from the authentication channel—a striking example of the sum of the parts being greater than the whole. Single-key cryptography is called symmetric for obvious reasons. A cryptosystem satisfying conditions 1–4 above is called asymmetric for equally obvious reasons.

There are symmetric cryptosystems in which the encryption and decryption keys are not the same—for example, matrix transforms of the text in which one key is a nonsingular (invertible) matrix and the other its inverse. Even though this is a two-key cryptosystem, since it is easy to calculate the inverse to a non-singular matrix, it does not satisfy condition 3 and is not considered to be asymmetric. Since in an asymmetric cryptosystem each user has a secrecy channel from every other user to him (using his public key) and an authentication channel from him to all other users (using his secret key), it is possible to achieve both secrecy and authentication using superencryption. Say A wishes to communicate a message in secret to B, but B wants to be sure the message was sent by A. A first encrypts the message with his secret key and then superencrypts the resulting cipher with B’s public key. The resulting outer cipher can only be decrypted by B, thus guaranteeing to A that only B can recover the inner cipher. When B opens the inner cipher using A’s public key he is certain the message came from someone knowing A’s key, presumably A. Simple as it is, this protocol is a paradigm for many contemporary applications.

Cryptographers have constructed several cryptographic schemes of this sort by starting with a “hard” mathematical problem—such as factoring a number that is the product of two very large primes—and attempting to make the cryptanalysis of the scheme be equivalent to solving the hard problem. If this can be done, the cryptosecurity of the scheme will be at least as good as the underlying mathematical problem is hard to solve. This has not been proven for any of the candidate schemes thus far, although it is believed to hold in each instance. However, a simple and secure proof of identity is possible based on such computational asymmetry. A user first secretly selects two large primes and then openly publishes their product. Although it is easy to compute a modular square root (a number whose square leaves a designated remainder when divided by the product) if the prime factors are known, it is just as hard as factoring (in fact equivalent to factoring) the product if the primes are unknown. A user can therefore prove his identity, i.e., that he knows the original primes, by demonstrating that he can extract modular square roots. The user can be confident that no one can impersonate him since to do so they would have to be able to factor his product.

There are some subtleties to the protocol that must be observed, but this illustrates how modern computational cryptography depends on hard problems. Secret-sharing To understand public-key cryptography fully, one must first understand the essentials of one of the basic tools in contemporary cryptology: secret-sharing. There is only one way to design systems whose overall reliability must be greater than that of some critical components—as is the case for aircraft, nuclear weapons, and communications systems—and that is by the appropriate use of redundancy so the system can continue to function even though some components fail. The same is true for information-based systems in which the probability of the security functions being realized must be greater than the probability that some of the participants will not cheat. Secret-sharing, which requires a combination of information held by each participant in order to decipher the key, is a means to enforce concurrence of several participants in the expectation that it is less likely that many will cheat than that one will. The RSA cryptoalgorithm described in the next section is a two-out-of-two secret-sharing scheme in which each key individually provides no information. Other security functions, such as digital notarization or certification of origination or receipt, depend on more complex sharing of information related to a concealed secret.

RSA encryption The best-known public-key scheme is the Rivest–Shamir–Adleman (RSA) cryptoalgorithm. In this system a user secretly chooses a pair of prime numbers p and q so large that factoring the product n = pq is well beyond projected computing capabilities for the lifetime of the ciphers. At the beginning of the 21st century, U.S. government security standards called for the modulus to be 1,024 bits in size—i.e., p and q each were to be about 155 decimal digits in size, with n roughly a 310-digit number. However, over the following decade, as processor speeds grew and computing techniques became more sophisticated, numbers approaching this size were factored, making it likely that, sooner rather than later, 1,024-bit moduli would no longer be safe, so the U.S. government recommended shifting in 2011 to 2,048-bit moduli.

Having chosen p and q, the user selects an arbitrary integer e less than n and relatively prime to p − 1 and q − 1, that is, so that 1 is the only factor in common between e and the product (p − 1)(q − 1). This assures that there is another number d for which the product ed will leave a remainder of 1 when divided by the least common multiple of p − 1 and q − 1. With knowledge of p and q, the number d can easily be calculated using the Euclidean algorithm . If one does not know p and q, it is equally difficult to find either e or d given the other as to factor n, which is the basis for the cryptosecurity of the RSA algorithm. We will use the labels d and e to denote the function to which a key is put, but as keys are completely interchangeable, this is only a convenience for exposition. To implement a secrecy channel using the standard two-key version of the RSA cryptosystem, user A would publish e and n in an authenticated public directory but keep d secret.

Anyone wishing to send a private message to A would encode it into numbers less than n and then encrypt it using a special formula based on e and n. A can decrypt such a message based on knowing d, but the presumption—and evidence thus far—is that for almost all ciphers no one else can decrypt the message unless he can also factor n. Similarly, to implement an authentication channel, A would publish d and n and keep e secret. In the simplest use of this channel for identity verification, B can verify that he is in communication with A by looking in the directory to find A’s decryption key d and sending him a message to be encrypted. If he gets back a cipher that decrypts to his challenge message using d to decrypt it, he will know that it was in all probability created by someone knowing e and hence that the other communicant is probably A. Digitally signing a message is a more complex operation and requires a cryptosecure “hashing” function.

This is a publicly known function that maps any message into a smaller message—called a digest—in which each bit of the digest is dependent on every bit of the message in such a way that changing even one bit in the message is apt to change, in a cryptosecure way, half of the bits in the digest. By cryptosecure is meant that it is computationally infeasible for anyone to find a message that will produce a preassigned digest and equally hard to find another message with the same digest as a known one. To sign a message—which may not even need to be kept secret—A encrypts the digest with the secret e, which he appends to the message. Anyone can then decrypt the message using the public key d to recover the digest, which he can also compute independently from the message. If the two agree, he must conclude that A originated the cipher, since only A knew e and hence could have encrypted the message. Thus far, all proposed two-key cryptosystems exact a very high price for the separation of the privacy or secrecy channel from the authentication or signature channel. The greatly increased amount of computation involved in the asymmetric encryption/decryption process significantly cuts the channel capacity (bits per second of message information communicated).

As a result, the main application of two-key cryptography is in hybrid systems. In such a system a two-key algorithm is used for authentication and digital signatures or to exchange a randomly generated session key to be used with a single-key algorithm at high speed for the main communication. At the end of the session this key is discarded. Block and stream ciphers In general, cipher systems transform fixed-size pieces of plaintext into ciphertext. In older manual systems these pieces were usually single letters or characters—or occasionally, as in the Playfair cipher, digraphs, since this was as large a unit as could feasibly be encrypted and decrypted by hand. Systems that operated on trigrams or larger groups of letters were proposed and understood to be potentially more secure, but they were never implemented because of the difficulty in manual encryption and decryption. In modern single-key cryptography the units of information are often as large as 64 bits, or about 131/2 alphabetic characters, whereas two-key cryptography based on the RSA algorithm appears to have settled on 1,024 to 2,048 bits, or between 310 and 620 alphabetic characters, as the unit of encryption.

A block cipher breaks the plaintext into blocks of the same size for encryption using a common key: the block size for a Playfair cipher is two letters, and for the DES (described in the section History of cryptology: The Data Encryption Standard and the Advanced Encryption Standard ) used in electronic codebook mode it is 64 bits of binary-encoded plaintext. Although a block could consist of a single symbol, normally it is larger. A stream cipher also breaks the plaintext into units, normally of a single character, and then encrypts the ith unit of the plaintext with the ith unit of a key stream. Vernam encryption with a onetime key is an example of such a system, as are rotor cipher machines and the DES used in the output feedback mode (in which the ciphertext from one encryption is fed back in as the plaintext for the next encryption) to generate a key stream. Stream ciphers depend on the receiver’s using precisely the same part of the key stream to decrypt the cipher that was employed to encrypt the plaintext. They thus require that the transmitter’s and receiver’s key-stream generators be synchronized.

This means that they must be synchronized initially and stay in sync thereafter, or else the cipher will be decrypted into a garbled form until synchrony can be reestablished. This latter property of self-synchronizing cipher systems results in what is known as error propagation , an important parameter in any stream-cipher system. Page 1 of 2 What is Cryptology? (with pictures) Hobbies What is Cryptology? Last Modified Date: 09 December 2016 Copyright Protected: 10 most extreme places on Earth Cryptology or cryptography is the study and process of encoding and decoding plain text messages so that they cannot be read by anyone without a guide or key. Historians date the use of cryptology back to Ancient Egyptian times and suggests that secret codes developed quite soon after written language was developed. As well, conversation might be encoded, as is frequent radio transmissions or cell phone conversations. Cryptology seems to many a rather romantic field, and the deciphering of secret messages is the subject of many thriller novels. Most recently, The Da Vinci Code involved a mystery of a series of clues and codes that pointed to a Catholic Church conspiracy to keep people from finding out that Mary Magdalene was one of the early disciples of Jesus Christ .

The idea of secret codes and hidden messages enchants many, accounting for the great popularity of Dan Brown ’s novel. Today, cryptology is often very technical in encoding or decoding processes, due to the use of computers. Computers can frequently evolve codes that are virtually unbreakable. A certain amount of cryptology is necessary too, to protect the security of computers. Codes and passwords help protect software and hardware from “hacking” which can reveal information about private plans, social security numbers or credit card numbers. In fact the majority of illegal decryption of secure information in computers is to steal identities. Some decryptors are excellent at breaking into what are thought to be “secure” systems. Ad Another primary reason for encrypting information is to protect secret operations of a country, particularly in times of war. While some codes are simplistic, usually computer produced codes are based on algorithmic patterns that prevent illegal decryptors from finding out information about military plans or weaponry. Low-level security is often protected by the use of things like digital signatures, which can be verified to protect systems from unwanted intrusion. Since virtually all codes can be broken, given enough time and effort, those in the field of cryptology must constantly work to develop new codes to keep customers or information secure.

Decisions about the best codes to use are made by cryptographic engineers, who rely heavily on cryptology to determine the history of how easily certain types of encryptions are deciphered. Research about military codes done by a cryptologist may never be published. In fact there is great concern within certain countries about allowing access to previously secret codes since this may allow access to information that is still considered secret. As well, analysis of codes used before can help illegal decryptors guess what codes might be used in the future. Thus encryption methods are often guarded as carefully as any material that is encrypted and sale of such information to foreign interests can carry heavy criminal penalties. Some methods, like the use of algorithms are a predictable type of cryptology, and occasionally, to protect certain secrets, the military or other secure organization may resort to earlier written or spoken codes, or variations on such. Someone with a working knowledge of the history of cryptology may be able to break such codes, but often if the codes are in use for only a short period of time, there is not enough time for information to escape before another method is employed.

Ad Cryptologic Technicians - CTI & CTM Careers : Navy.com Next: next section » Within Navy Cryptology, there are distinct focus areas that have their own training paths and job descriptions. Each CT role works under the oversight of Cryptologic Warfare Officers (four-year degree required) or Cyber Warfare Engineers (four-year degree required) – and potentially both. Cryptologic Technician Interpretive (CTI) – CTIs serve as experts in linguistics (including Arabic, Chinese, Korean, Persian-Farsi, Russian and Spanish) and deciphering information in other languages. Their responsibilities include: Collecting, analyzing and exploiting foreign language communications of interest Transcribing, translating and interpreting foreign language materials Providing cultural and regional guidance in support of Navy, Joint Force, national and multinational needs Cryptologic Technician Technical (CTT) – CTTs serve as experts in airborne, shipborne and land-based radar signals.

Their responsibilities include: Operating electronic intelligence-receiving and direction-finding systems, digital recording devices, analysis terminals, and associated computer equipment Operating systems that produce high-power jamming signals used to deceive electronic sensors and defeat radar-guided weapons systems Providing technical and tactical guidance in support of surface, subsurface, air and special warfare operations Cryptologic Technician Networks (CTN) – CTNs serve as experts in communication network defense and forensics. Their responsibilities include: Monitoring, identifying, collecting and analyzing information Providing computer network risk mitigation and network vulnerability assessments and incident response/reconstruction Providing network target access tool development Conducting computer network operations worldwide in support of Navy and Department of Defense missions Cryptologic Technician Maintenance (CTM) – CTMs serve as experts in the preventive and corrective maintenance of sophisticated cryptologic equipment, networks and systems. Their responsibilities include: Installing, testing, troubleshooting, repairing or replacing cryptologic networks, physical security systems, electronic equipment, antennas, personal computers, auxiliary equipment, digital and optical interfaces, and data systems Configuring, monitoring and evaluating Information Operations (IO), Information Warfare (IW) systems and Information Assurance (IA) operations Cryptologic Technician Collection (CTR) – CTRs serve as experts in intercepting signals.

Their responsibilities include: Analyzing and reporting on communication signals using computers, specialized computer-assisted communications equipment, video display terminals and electronic/magnetic tape recorders Exploiting signals of interest to identify, locate and report worldwide threats Providing tactical and strategic signals intelligence, technical guidance, and information warfare support to surface, subsurface, air and special warfare units. Full Time Next: next section » Within Navy Cryptology, there are distinct focus areas that have their own training paths and job descriptions. Each CT role works under the oversight of Cryptologic Warfare Officers (four-year degree required) or Cyber Warfare Engineers (four-year degree required) – and potentially both. Cryptologic Technician Interpretive (CTI) – CTIs serve as experts in linguistics (including Arabic, Chinese, Korean, Persian-Farsi, Russian and Spanish) and deciphering information in other languages. Their responsibilities include: Collecting, analyzing and exploiting foreign language communications of interest Transcribing, translating and interpreting foreign language materials Providing cultural and regional guidance in support of Navy, Joint Force, national and multinational needs Cryptologic Technician Technical (CTT) – CTTs serve as experts in airborne, shipborne and land-based radar signals.

Their responsibilities include: Operating electronic intelligence-receiving and direction-finding systems, digital recording devices, analysis terminals, and associated computer equipment Operating systems that produce high-power jamming signals used to deceive electronic sensors and defeat radar-guided weapons systems Providing technical and tactical guidance in support of surface, subsurface, air and special warfare operations Cryptologic Technician Networks (CTN) – CTNs serve as experts in communication network defense and forensics. Their responsibilities include: Monitoring, identifying, collecting and analyzing information Providing computer network risk mitigation and network vulnerability assessments and incident response/reconstruction Providing network target access tool development Conducting computer network operations worldwide in support of Navy and Department of Defense missions Cryptologic Technician Maintenance (CTM) – CTMs serve as experts in the preventive and corrective maintenance of sophisticated cryptologic equipment, networks and systems. Their responsibilities include: Installing, testing, troubleshooting, repairing or replacing cryptologic networks, physical security systems, electronic equipment, antennas, personal computers, auxiliary equipment, digital and optical interfaces, and data systems Configuring, monitoring and evaluating Information Operations (IO), Information Warfare (IW) systems and Information Assurance (IA) operations Cryptologic Technician Collection (CTR) – CTRs serve as experts in intercepting signals.

Their responsibilities include: Analyzing and reporting on communication signals using computers, specialized computer-assisted communications equipment, video display terminals and electronic/magnetic tape recorders Exploiting signals of interest to identify, locate and report worldwide threats Providing tactical and strategic signals intelligence, technical guidance, and information warfare support to surface, subsurface, air and special warfare units. Full Time Next: next section » Cryptologic Technicians perform a variety of duties worldwide, at numerous overseas and stateside shore commands; aboard surface ships, aircraft and submarines; and with Naval Special Warfare – generally dividing time between assignments ashore and afloat. Duties could be performed in an office setting, lab-type setting, specialized maintenance shop, secure space or watch environment. As a CT, you may work independently or as part of small, coordinated teams – ultimately under the supervision of Information Warfare Officers (four-year degree required) or Cyber Warfare Engineers (four-year degree required). Learn more about the different disciplines that make up the Information Dominance Corps and how their expertise affects every part of the Navy, including the Department of Defense, and more.

Full Time Next: next section » Cryptologic Technicians perform a variety of duties worldwide, at numerous overseas and stateside shore commands; aboard surface ships, aircraft and submarines; and with Naval Special Warfare – generally dividing time between assignments ashore and afloat. Duties could be performed in an office setting, lab-type setting, specialized maintenance shop, secure space or watch environment. As a CT, you may work independently or as part of small, coordinated teams – ultimately under the supervision of Cryptologic Warfare Officers (four-year degree required) or Cyber Warfare Engineers (four-year degree required). Learn more about the different disciplines that make up the Information Dominance Corps and how their expertise affects every part of the Navy, including the Department of Defense, and more. Full Time Next: next section » Upon completion of initial 7–9 week Recruit Training (known as Boot Camp), those pursuing a Cryptologic Technician role report to either Pensacola, Fla., or Monterey, Calif., to receive formal Navy schooling in their specialty area within the field of cryptology. This consists of technical “A” School and possibly advanced “C” School or “F” School. CTI training – Class “A" School is broken into two phases.

Phase One takes place at the Defense Language Institute, Monterey, Calif., and is anywhere from 27 to 64 weeks long. Phase Two is 12 weeks long. Class “F” School is conducted at the Regional Center for Excellence in Monterey, Calif. CTT training – Class “A” School is approximately 17 weeks long. After “A” school, some CTTs will attend a Class “C” School that is approximately 26 weeks in duration. The schools are located in Pensacola, Fla. CTN training – Class “A” School is 26 weeks long and located in Pensacola, Fla. CTM training – Class “A” School is approximately 10 weeks in duration and located in Pensacola, Fla. CTR training – Class “A” School is approximately 22 weeks long. The school is located in Pensacola, Fla. Promotion opportunities are regularly available but competitive and based on performance. It’s also important to note that specialized training received and work experience gained in the course of service can lead to valuable credentialing and occupational opportunities in related fields.

To learn more about the specific training path for any of the focus areas within the field of cryptology, locate a recruiter . Full Time Next: next section » Most of what you do in the Navy Reserve is considered training. The basic Navy Reserve commitment involves training a minimum of one weekend a month (referred to as drilling) and two weeks a year (referred to as Annual Training) – or the equivalent. CTs in the Navy Reserve serve in an Enlisted role. Before receiving the ongoing professional training that comes with the job, initial training requirements must be met. For current or former military Enlisted servicemembers: Prior experience satisfies the initial Recruit Training requirement – so you will not need to go through Boot Camp again. For those without prior military experience: You will need to meet the initial Recruit Training requirement by attending Boot Camp for 7-9 weeks in Great Lakes, Ill. This training course will prepare you for service in the Navy Reserve and count as your first Annual Training. Full Time Next: next section » Beyond offering access to professional credentials and certifications, Navy technical and operational training in the field of intelligence can translate to credit hours toward a bachelor's or associate degree through the American Council on Education .

You may also continue your education through opportunities like the following: Next: next section » A four-year degree is not required to become a member of the Navy electronics community. There are some specific requirements that apply to electronics jobs in advanced programs such as SECF and NF. Contact a recruiter for details. A high school diploma or equivalent is required to become an Enlisted Sailor in the cryptology field in the Navy. Those seeking a Cryptologic Technician position must be U.S. citizens who can meet eligibility requirements for a Top Secret/Sensitive Compartmented Information security clearance. They should have an interest in advanced electronics and technology; exceptionally good character; good speaking, writing and record-keeping skills; a good working aptitude of math; and the capability to do highly detail-oriented, highly classified work. Specific qualifications vary depending upon specialization area within the field of cryptology. Contact a recruiter for details . General qualifications may vary depending upon whether you’re currently serving , whether you’ve served before or whether you’ve never served before . Get Social Learn Cryptography - Home Computer Security Cryptography is both the practice and study of the techniques used to communicate and/or store information or data privately and securely, without being intercepted by third parties.

This can include processes such as encryption, hashing, and steganography. Cryptography is a broad field with applications in many critical areas of our lives. Learn Cryptography is dedicated to helping people understand how and why the cryptographic systems they use everyday without realizing (such as banking transactions, website logins, etc) work to secure and protect their privacy. Cryptography & Encryption Cryptography & Encryption By Yaman Akdeniz MA Research student at the Criminal Justice Studies of the Law Faculty of University of Leeds, Leeds LS2 9JT. E-mail: lawya@leeds.ac.uk. Copyright © 1996 Yaman Akdeniz. Please cite as Yaman Akdeniz, "Cryptography & Encryption" August 1996, Cyber-Rights & Cyber-Liberties (UK) at This paper is a short introduction to cryptography and encryption. It explains the different kind of cryptographic systems and why it is essential for the privacy of the online users. Introduction Over the Internet various communications such as electronic mail, or the use of world wide web browsers are not secure for sending and receiving information. Information sent by those means may include sensitive personal data which may be intercepted.

There is commercial activity going on the Internet and many web sites require the users to fill forms and include sensitive personal information such as telephone numbers, addresses, and credit card information. To be able to do that users would like to have a secure, private communication with the other party. Online users may need private and secure communications for other reasons as well. They may simply not want third parties to browse and read their e-mails or alter their content. What is Cryptography ? (1) Cryptography defined as "the science and study of secret writing," concerns the ways in which communications and data can be encoded to prevent disclosure of their contents through eavesdropping or message interception, using codes (2), ciphers (3), and other methods, so that only certain people can see the real message. Although the science of cryptography is very old, the desktop-computer revolution has made it possible for cryptographic techniques to become widely used and accessible to nonexperts. David Kahn traces the history of cryptography from Ancient Egypt into the computer age (4). According to Kahn's research from Julius Caesar to Mary, Queen of Scots (5) to Abraham Lincoln's Civil War ciphers, cryptography has been a part of the history.

Over the centuries complex computer-based codes, algorithms and machines were created. During World War I, the Germans developed the Enigma machine to have secure communications (6). Enigma codes were decrypted under the secret Ultra project during World War II by the British. What is Encryption ? "Encryption is basically an indication of users' distrust of the security of the system, the owner or operator of the system, or law enforcement authorities." (7) Encryption transforms original information, called plaintext or cleartext, into transformed information, called ciphertext, codetext or simply cipher, which usually has the appearance of random, unintelligible data. The transformed information, in its encrypted form, is called the cryptogram. (8) Encryption algorithm determines how simple or how complex the process of transformation will be (9). Encryption provides confidentiality, integrity and authenticity of the information transferred from A to B. It will be a secret transmission ensuring that its integrity has not been tampered and also it is authentic, that the information was sent by A. All these three points may be important for different reasons for the transmission of data over the Internet (10). Who needs Cryptography ?

The ability to protect and secure information is vital to the growth of electronic commerce and to the growth of the Internet itself. Many people need or want to use communications and data security in different areas. Banks use encryption methods all around the world (11) to process financial transactions. These involve transfer of huge amount of money from one bank to another. Banks also use encryption methods to protect their customers ID numbers at bank automated teller machines. "As the economy continues to move away from cash transactions towards "digital cash", both customers and merchants will need the authentication provided by unforgeable digital signatures in order to prevent forgery and transact with confidence." (12) This is an important issue related to the Internet users. There are many companies and even shopping malls selling anything from flowers to bottles of wines over the Internet and these transactions are made by the use of credit cards and secure Internet browsers including encryption techniques. The customers over the Internet would like to be secure about sending their credit card information and other financial details related to them over a multi-national environment. It will only work by the use of strong and unforgeable encryption methods. Also business and commercial companies with trade secrets use or would like to use encryption against high-tech eavesdropping and industrial espionage.

Professionals such as lawyers, doctors, dentists or accountants who have confidential information throughout their activities will need encryption if they will rely on the use of Internet in the future. Criminals do use encryption and will use it to cover their illegal activities and to make untraceable perfect crimes possible. More important, people need or desire electronic security from government intrusions or surveillance (13) into their activites on the Internet. Cryptographic Keys: Private and Public More complex ciphers use a secret key to control a long sequence of complicated substitutions (14) and transpositions (15). There are two general categories of cryptographic keys: Private key and public key systems. Private Key Cryptography Private key systems use a single key. The single key is used both to encrypt and decrypt the information. Both sides of the transmission need a separate key and the key must be kept secret from. The security of the transmission will depend on how well the key is protected. The US Government developed the Data Encryption Standard ("DES") which operates on this basis and it is the actual US standard. DES keys are 56 bits (16) long.

The length of the key was criticised and it was suggested that the short key was designed to be long enough to frustrate corporate eavesdroppers, but short enough to be broken by the National Security Agency ("NSA") (17). Export of DES is controlled by the State Department. DES system is getting old and becoming insecure. US government offered to replace the DES with a new algorithm called Skipjack which involves escrowed encryption. Public Key Cryptography In the public key system there are two keys: a public and a private key. Each user has both keys and while the private key must be kept secret the public key is publicly known. Both keys are mathematically related. If A encrypts a message with his private key then B, the recipient of the message can decrypt it with A's public key. Similarly anyone who knows A's public key can send him a message by encrypting it with his public key. A will than decrypt it with his private key. Public key cryptography was developed in 1977 by Rivest, Shamir and Adleman ("RSA") in the US.

This kind of cryptography is more eficient than the private key cryptography because each user has only one key to encrypt and decrypt all the messages that he or she sends or receives. Endnotes: The word cryptography comes from Greek and kryptos means "hidden" while graphia stands for "writing". A code is a system of communication that relies on a pre-arranged mapping of meanings such as those found in a codebook. A cipher is different from a code and it is a method of encrypting any text regardless of its content. David Kahn, The Codebreakers, Macmillan Company, New York: 1972. Mary, Queen of Scots, lost her life in the 16th century because an encrypted message she sent from prison was intercepted and deciphered. See David Kahn, Seizing the Enigma, Houghton Mifflin, Boston: 1991. Lance Rose, Netlaw: Your Rights in the Online World, Osborne Mc Graw-Hill, 1995, page 182. Deborah Russell and G.T.

Gangemi, Sr., "Encryption" from Computer Security Basics, O'Reilly & Associates, Inc., California: 1991, pp 165-179 taken from Lance J. Hoffman, Building in Big Brother: TheCryptography Policy Debate, Spriner-Verlag, New York: 1995, at page 14. ibid. While military and secret services will require a confidential transmission, it will be important for banks to have accurate information of their transactions by electronic means. Authentication technique provides digital signatures which are unique for every transcation and cannot be forged. The U.S. Department of the Treasury requires encryption of all U.S. electronic funds transfer messages. See Gerald Murphy, U.S. Dep't of Treasury, Directive: Electronic Funds and Securities Transfer Policy - Message Authentication and Enhanced Security, No. 16-02, section 3 (Dec. 21, 1992). A. Michael Froomkin, "The Metaphor is the Key: Cryptography, the Clipper Chip and the Constitution" [1995] U. Penn. L. Rev.

143, 709-897, at 720. E.g. the FBI during 1970s wiretapped and bugged the communications of Black Panthers and other dissident groups. See Sanford J. Ungar, FBI 137, (1975). Also between 1953 and 1973, the CIA opened and photographed almost 250000 first class letters within the US from which it compiled a database of almost 1.5 million names. See Church Committee Report, S. Rep. No. 755, 94th Cong., 2d Sess., pt. 2, 1976, at 6. Substitution ciphers replace the actual bits, characters, or blocks of characters with substitutes, eg. one letter replaces another letter. Julius Caesar's military use of such a cipher was the first clearly documented case. In Caesar's cipher each letter of an original message is replaced with the letter three palces beyond it in the alphabet. Transposition ciphers rearrange the order of the bits, characters, or blocks of characters that are being encrypted and decrypted.

This means that there are 72 quadrillion different possible keys. See James Bamford, The Puzzle Palace: A Report on America's Most Secret Agency, 1982. A Cryptography Tutorial and Introduction. Encryption, Decryption and Key Management EASIER THE CRYPTOGRAPHY INTRODUCTION AND GUIDE Cryptography is often seen as a 'black art': something OTHERS understand but YOU need. This of course need not the the case at all. Yes, there are some complex concepts to embrace, but basic understanding need not be a trial. This web site is designed to help you understand the basics of cryptography, presenting the main ideas in simple language. It also provides access to a series of resources to help you apply, and implement, cryptographic solutions. It will hopefully prove to be invaluable to all who use it - both beginners and seasoned professionals. Crypto 101 DRM-free and available in all common formats: PDF (for Mac and PC) EPUB (for most ebook readers, iPad and iPhone) Mobi (for Kindle) Sponsors Rackspace is a world-leading cloud services provider. They have incredibly generously offered to take care of all of Crypto 101's hosting requirements free of charge.

This project simply wouldn't be possible without their help. Thanks, Rackspace! Crypto 101: the presentation Crypto 101 started as a presentation at PyCon 2013. It tries to go through all of the major dramatis personae of cryptography to make TLS work in 45 minutes. This book is the natural extension of that, with an extensive focus on breaking cryptography. Made with love by lvh . Crypto 101 is made possible by the incredibly generous contributions of Rackspace , who provide our hosting requirements!

Question: What is cryptology the study of
Answer: Codes and ciphers