cryptography secret code redirects here for the aya kamiki album see secret code cryptology redirects here for the david s ware album see cryptology album german lorenz cipher machine used in world warii to encrypt veryhighlevel general staff messages cryptography or cryptology from ancient greek translitkrypts hidden secret and graphein to write or logia study respectively are central to modern cryptography modern cryptography exists at the intersection of the disciplines of mathematics computer science electrical engineering communication science and physics applications of cryptography include electronic commerce chipbased payment cards digital currencies computer passwords and military communications cryptography prior to the modern age was effectively synonymous with encryption the conversion of information from a readable state to apparent nonsense the originator of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries the cryptography literature often uses the name alice a for the sender bob b for the intended recipient and eve eavesdropper for the adversary since the development of rotor cipher machines in world wari and the advent of computers in world warii the methods used to carry out cryptology have become increasingly complex and its application more widespread modern cryptography is heavily based on mathematical theory and computer science practice cryptographic algorithms are designed around computational hardness assumptions making such algorithms hard to break in practice by any adversary it is theoretically possible to break such a system but it is infeasible to do so by any known practical means these schemes are therefore termed computationally secure theoretical advances eg improvements in integer factorization algorithms and faster computing technology require these solutions to be continually adapted there exist informationtheoretically secure schemes that probably cannot be broken even with unlimited computing poweran example is the onetime padbut these schemes are more difficult to implement than the best theoretically breakable but computationally secure mechanisms the growth of cryptographic technology has raised a number of legal issues in the information age cryptographys potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export terminology alphabet shift ciphers are believed to have been used by julius caesar over 2000 years ago this is an example with k3 in other words the letters in the alphabet are shifted three in one direction to encrypt and three in the other direction to decrypt the first use of the term cryptograph as opposed to cryptogram dates back to the 19th century it originated in the goldbug a novel by edgar allan poe until modern times cryptography referred almost exclusively to encryption which is the process of converting ordinary information called plaintext into unintelligible form called ciphertext decryption is the reverse in other words moving from the unintelligible ciphertext back to plaintext a cipher or cypher is a pair of algorithms that create the encryption and the reversing decryption the detailed operation of a cipher is controlled both by the algorithm and in each instance by a key the key is a secret ideally known only to the communicants usually a short string of characters which is needed to decrypt the ciphertext formally a cryptosystem is the ordered list of elements of finite possible plaintexts finite possible cyphertexts finite possible keys and the encryption and decryption algorithms which correspond to each key keys are important both formally and in actual practice as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless or even counterproductive for most purposes historically ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks there are two kinds of cryptosystems symmetric and asymmetric in symmetric systems the same key the secret key is used to encrypt and decrypt a message data manipulation in symmetric systems is faster than asymmetric systems as they generally use shorter key lengths asymmetric systems use a public key to encrypt a message and a private key to decrypt it use of asymmetric systems enhances the security of communication in colloquial use the term code is often used to mean any method of encryption or concealment of meaning however in cryptography code has a more specific meaning it means the replacement of a unit of plaintext ie a meaningful word or phrase with a code word for example wallaby replaces attack at dawn cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so ie it is the study of how to crack encryption algorithms or their implementations some use the terms cryptography and cryptology interchangeably in english while others including us military practice generally use cryptography to refer specifically to the use and practice of cryptographic techniques and cryptology to refer to the combined study of cryptography and cryptanalysis the study of characteristics of languages that have some application in cryptography or cryptology eg frequency data letter combinations universal patterns etc is called cryptolinguistics history of cryptography and cryptanalysis history of cryptography before the modern era cryptography focused on message confidentiality ie encryptionconversion of messages from a comprehensible form into an incomprehensible one and back again at the other end rendering it unreadable by interceptors or eavesdroppers without secret knowledge namely the key needed for decryption of that message encryption attempted to ensure secrecy in communications such as those of spies military leaders and diplomats in recent decades the field has expanded beyond confidentiality concerns to include techniques for message integrity checking senderreceiver identity authentication digital signatures interactive proofs and secure computation among others classic cryptography reconstructed ancient greek scytale an early cipher device the main classical cipher types are transposition ciphers which rearrange the order of letters in a message eg hello world becomes ehlol owrdl in a trivially simple rearrangement scheme and substitution ciphers which systematically replace letters or groups of letters with other letters or groups of letters eg fly at once becomes gmz bu podf by replacing each letter with the one following it in the latin alphabet simple versions of either have never offered much confidentiality from enterprising opponents an early substitution cipher was the caesar cipher in which each letter in the plaintext was replaced by a letter some fixed number of positions further down the alphabet suetonius reports that julius caesar used it with a shift of three to communicate with his generals atbash is an example of an early hebrew cipher the earliest known use of cryptography is some carved ciphertext on stone in egypt ca 1900 bce but this may have been done for the amusement of literate observers rather than as a way of concealing information the greeks of classical times are said to have known of ciphers eg the scytale transposition cipher claimed to have been used by the spartan military more modern examples of steganography include the use of invisible ink microdots and digital watermarks to conceal information in india the 2000yearold kamasutra of vtsyyana speaks of two different kinds of ciphers called kautiliyam and mulavediya in the kautiliyam the cipher letter substitutions are based on phonetic relations such as vowels becoming consonants in the mulavediya the cipher alphabet consists of pairing letters and using the reciprocal ones in sassanid persia there were two secret scripts according to the muslim author ibn alnadim the hdabrya literally kings script which was used for official correspondence and the rzsaharya which was used to communicate secret messages with other countries first page of a book by alkindi which discusses encryption of messages ciphertexts produced by a classical cipher and some modern ciphers will reveal statistical information about the plaintext and that information can often be used to break the cipher after the discovery of frequency analysis perhaps by the arab mathematician and polymath alkindi also known as alkindus in the 9th century 16thcentury bookshaped french cipher machine with arms of henri ii of france enciphered letter from gabriel de luetz daramon french ambassador to the ottoman empire after 1546 with partial decipherment language letter frequencies may offer little help for some extended historical encryption techniques such as homophonic cipher that tend to flatten the frequency distribution for those ciphers language letter group or ngram frequencies may provide an attack essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of the polyalphabetic cipher most clearly by leon battista alberti around the year 1467 though there is some indication that it was already known to alkindi although frequency analysis can be a powerful and general technique against many ciphers encryption has still often been effective in practice as many a wouldbe cryptanalyst was unaware of the technique breaking a message without using frequency analysis essentially required knowledge of the cipher used and perhaps of the key involved thus making espionage bribery burglary defection etc more attractive approaches to the cryptanalytically uninformed it was finally explicitly recognized in the 19th century that secrecy of a ciphers algorithm is not a sensible nor practical safeguard of message security in fact it was further realized that any adequate cryptographic scheme including ciphers should remain secure even if the adversary fully understands the cipher algorithm itself security of the key used should alone be sufficient for a good cipher to maintain confidentiality under an attack this fundamental principle was first explicitly stated in 1883 by auguste kerckhoffs and is generally called kerckhoffss principle alternatively and more bluntly it was restated by claude shannon the inventor of information theory and the fundamentals of theoretical cryptography as shannons maximthe enemy knows the system different physical devices and aids have been used to assist with ciphers one of the earliest may have been the scytale of ancient greece a rod supposedly used by the spartans as an aid for a transposition cipher see image above in medieval times other aids were invented such as the cipher grille which was also used for a kind of steganography with the invention of polyalphabetic ciphers came more sophisticated aids such as albertis own cipher disk johannes trithemius tabula recta scheme and thomas jeffersons wheel cypher not publicly known and reinvented independently by bazeries around 1900 many mechanical encryptiondecryption devices were invented early in the 20th century and several patented among them rotor machinesfamously including the enigma machine used by the german government and military from the late 1920s and during world war ii computer era cryptanalysis of the new mechanical devices proved to be both difficult and laborious in the united kingdom cryptanalytic efforts at bletchley park during wwii spurred the development of more efficient means for carrying out repetitious tasks this culminated in the development of the colossus the worlds first fully electronic digital programmable computer which assisted in the decryption of ciphers generated by the german armys lorenz sz4042 machine just as the development of digital computers and electronics helped in cryptanalysis it made possible much more complex ciphers furthermore computers allowed for the encryption of any kind of data representable in any binary format unlike classical ciphers which only encrypted written language texts this was new and significant computer use has thus supplanted linguistic cryptography both for cipher design and cryptanalysis many computer ciphers can be characterized by their operation on binary bit sequences sometimes in groups or blocks unlike classical and mechanical schemes which generally manipulate traditional characters ie letters and digits directly however computers have also assisted cryptanalysis which has compensated to some extent for increased cipher complexity nonetheless good modern ciphers have stayed ahead of cryptanalysis it is typically the case that use of a quality cipher is very efficient ie fast and requiring few resources such as memory or cpu capability while breaking it requires an effort many orders of magnitude larger and vastly larger than that required for any classical cipher making cryptanalysis so inefficient and impractical as to be effectively impossible extensive open academic research into cryptography is relatively recent it began only in the mid1970s in recent times ibm personnel designed the algorithm that became the federal ie us data encryption standard whitfield diffie and martin hellman published their key agreement algorithm as well as being aware of cryptographic history cryptographic algorithm and system designers must also sensibly consider probable future developments while working on their designs for instance continuous improvements in computer processing power have increased the scope of bruteforce attacks so when specifying key lengths the required key lengths are similarly advancing essentially prior to the early 20th century cryptography was chiefly concerned with linguistic and lexicographic patterns since then the emphasis has shifted and cryptography now makes extensive use of mathematics including aspects of information theory computational complexity statistics combinatorics abstract algebra number theory and finite mathematics generally cryptography is also a branch of engineering but an unusual one since it deals with active intelligent and malevolent opposition see cryptographic engineering and security engineering other kinds of engineering eg civil or chemical engineering need deal only with neutral natural forces there is also active research examining the relationship between cryptographic problems and quantum physics see quantum cryptography and quantum computer modern cryptography the modern field of cryptography can be divided into several areas of study the chief ones are discussed here see topics in cryptography for more symmetrickey cryptography symmetrickey algorithm symmetrickey cryptography where a single key is used for encryption and decryption symmetrickey cryptography refers to encryption methods in which both the sender and receiver share the same key or less commonly in which their keys are different but related in an easily computable way this was the only kind of encryption publicly known until june 1976 one round out of 85 of the idea cipher used in some versions of pgp for highspeed encryption of for instance email symmetric key ciphers are implemented as either block ciphers or stream ciphers a block cipher enciphers input in blocks of plaintext as opposed to individual characters the input form used by a stream cipher the data encryption standard des and the advanced encryption standard aes are block cipher designs that have been designated cryptography standards by the us government though dess designation was finally withdrawn after the aes was adopted stream ciphers in contrast to the block type create an arbitrarily long stream of key material which is combined with the plaintext bitbybit or characterbycharacter somewhat like the onetime pad in a stream cipher the output stream is created based on a hidden internal state that changes as the cipher operates that internal state is initially set up using the secret key material rc4 is a widely used stream cipher see categorystream ciphers block ciphers can be used as stream ciphers see block cipher modes of operation cryptographic hash functions are a third type of cryptographic algorithm they take a message of any length as input and output a short fixed length hash which can be used in for example a digital signature for good hash functions an attacker cannot find two messages that produce the same hash md4 is a longused hash function that is now broken md5 a strengthened variant of md4 is also widely used but broken in practice the us national security agency developed the secure hash algorithm series of md5like hash functions sha0 was a flawed algorithm that the agency withdrew sha1 is widely deployed and more secure than md5 but cryptanalysts have identified attacks against it the sha2 family improves on sha1 but it isnt yet widely deployed and the us standards authority thought it prudent from a security perspective to develop a new standard to significantly improve the robustness of nists overall hash algorithm toolkit unlike block and stream ciphers that are invertible cryptographic hash functions produce a hashed output that cannot be used to retrieve the original input data cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security message authentication codes macs are much like cryptographic hash functions except that a secret key can be used to authenticate the hash value upon receipt this additional complication blocks an attack scheme against bare digest algorithms and so has been thought worth the effort publickey cryptography publickey cryptography publickey cryptography where different keys are used for encryption and decryption padlock icon from the firefox web browser which indicates that tls a publickey cryptography system is in use symmetrickey cryptosystems use the same key for encryption and decryption of a message although a message or group of messages can have a different key than others a significant disadvantage of symmetric ciphers is the key management necessary to use them securely each distinct pair of communicating parties must ideally share a different key and perhaps for each ciphertext exchanged as well the number of keys required increases as the square of the number of network members which very quickly requires complex key management schemes to keep them all consistent and secret the difficulty of securely establishing a secret key between two communicating parties when a secure channel does not already exist between them also presents a chickenandegg problem which is a considerable practical obstacle for cryptography users in the real world whitfield diffie and martin hellman authors of the first published paper on publickey cryptography in a groundbreaking 1976 paper whitfield diffie and martin hellman proposed the notion of publickey also more generally called asymmetric key cryptography in which two different but mathematically related keys are useda public key and a private key in publickey cryptosystems the public key may be freely distributed while its paired private key must remain secret in a publickey encryption system the public key is used for encryption while the private or secret key is used for decryption while diffie and hellman could not find such a system they showed that publickey cryptography was indeed possible by presenting the diffiehellman key exchange protocol a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key diffie and hellmans publication sparked widespread academic efforts in finding a practical publickey encryption system this race was finally won in 1978 by ronald rivest adi shamir and len adleman whose solution has since become known as the rsa algorithm the diffiehellman and rsa algorithms in addition to being the first publicly known examples of high quality publickey algorithms have been among the most widely used other asymmetrickey algorithms include the cramershoup cryptosystem elgamal encryption and various elliptic curve techniques to much surprise a document published in 1997 by the government communications headquarters gchq a british intelligence organization revealed that cryptographers at gchq had anticipated several academic developments in this example the message is only signed and not encrypted 1 alice signs a message with her private key 2 bob can verify that alice sent the message and that the message has not been modified publickey cryptography can also be used for implementing digital signature schemes a digital signature is reminiscent of an ordinary signature they both have the characteristic of being easy for a user to produce but difficult for anyone else to forge digital signatures can also be permanently tied to the content of the message being signed they cannot then be moved from one document to another for any attempt will be detectable in digital signature schemes there are two algorithms one for signing in which a secret key is used to process the message or a hash of the message or both and one for verification in which the matching public key is used with the message to check the validity of the signature rsa and dsa are two of the most popular digital signature schemes digital signatures are central to the operation of public key infrastructures and many network security schemes eg ssltls many vpns etc publickey algorithms are most often based on the computational complexity of hard problems often from number theory for example the hardness of rsa is related to the integer factorization problem while diffiehellman and dsa are related to the discrete logarithm problem more recently elliptic curve cryptography has developed a system in which security is based on number theoretic problems involving elliptic curves because of the difficulty of the underlying problems most publickey algorithms involve operations such as modular multiplication and exponentiation which are much more computationally expensive than the techniques used in most block ciphers especially with typical key sizes as a result publickey cryptosystems are commonly hybrid cryptosystems in which a fast highquality symmetrickey encryption algorithm is used for the message itself while the relevant symmetric key is sent with the message but encrypted using a publickey algorithm similarly hybrid signature schemes are often used in which a cryptographic hash function is computed and only the resulting hash is digitally signed cryptanalysis cryptanalysis variants of the enigma machine used by germanys military and civil authorities from the late 1920s through world war ii implemented a complex electromechanical polyalphabetic cipher breaking and reading of the enigma cipher at polands cipher bureau for 7 years before the war and subsequent decryption at bletchley park was important to allied victory the goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme thus permitting its subversion or evasion it is a common misconception that every encryption method can be broken in connection with his wwii work at bell labs claude shannon proved that the onetime pad cipher is unbreakable provided the key material is truly random never reused kept secret from all possible attackers and of equal or greater length than the message most ciphers apart from the onetime pad can be broken with enough computational effort by brute force attack but the amount of effort needed may be exponentially dependent on the key size as compared to the effort needed to make use of the cipher in such cases effective security could be achieved if it is proven that the effort required ie work factor in shannons terms is beyond the ability of any adversary this means it must be shown that no efficient method as opposed to the timeconsuming brute force method can be found to break the cipher since no such proof has been found to date the onetimepad remains the only theoretically unbreakable cipher there are a wide variety of cryptanalytic attacks and they can be classified in any of several ways a common distinction turns on what eve an attacker knows and what capabilities are available in a ciphertextonly attack eve has access only to the ciphertext good modern cryptosystems are usually effectively immune to ciphertextonly attacks in a knownplaintext attack eve has access to a ciphertext and its corresponding plaintext or to many such pairs in a chosenplaintext attack eve may choose a plaintext and learn its corresponding ciphertext perhaps many times an example is gardening used by the british during wwii in a chosenciphertext attack eve may be able to choose ciphertexts and learn their corresponding plaintexts also important often overwhelmingly so are mistakes generally in the design or use of one of the protocols involved see cryptanalysis of the enigma for some historical examples of this pozna monument center to polish cryptologists whose breaking of germanys enigma machine ciphers beginning in 1932 altered the course of world war ii cryptanalysis of symmetrickey ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher for example a simple brute force attack against des requires one known plaintext and 255 decryptions trying approximately half of the possible keys to reach a point at which chances are better than even that the key sought will have been found but this may not be enough assurance a linear cryptanalysis attack against des requires 243 known plaintexts and approximately 243 des operations this is a considerable improvement on brute force attacks publickey algorithms are based on the computational difficulty of various problems the most famous of these is integer factorization eg the rsa algorithm is based on a problem related to integer factoring but the discrete logarithm problem is also important much publickey cryptanalysis concerns numerical algorithms for solving these computational problems or some of them efficiently ie in a practical time for instance the best known algorithms for solving the elliptic curvebased version of discrete logarithm are much more timeconsuming than the best known algorithms for factoring at least for problems of more or less equivalent size thus other things being equal to achieve an equivalent strength of attack resistance factoringbased encryption techniques must use larger keys than elliptic curve techniques for this reason publickey cryptosystems based on elliptic curves have become popular since their invention in the mid1990s while pure cryptanalysis uses weaknesses in the algorithms themselves other attacks on cryptosystems are based on actual use of the algorithms in real devices and are called sidechannel attacks if a cryptanalyst has access to for example the amount of time the device took to encrypt a number of plaintexts or report an error in a password or pin character he may be able to use a timing attack to break a cipher that is otherwise resistant to analysis an attacker might also study the pattern and length of messages to derive valuable information this is known as traffic analysis and can be quite useful to an alert adversary poor administration of a cryptosystem such as permitting too short keys will make any system vulnerable regardless of other virtues social engineering and other attacks against the personnel who work with cryptosystems or the messages they handle eg bribery extortion blackmail espionage torture may be the most productive attacks of all cryptographic primitives much of the theoretical work in cryptography concerns cryptographic primitivesalgorithms with basic cryptographic propertiesand their relationship to other cryptographic problems more complicated cryptographic tools are then built from these basic primitives these primitives provide fundamental properties which are used to develop more complex tools called cryptosystems or cryptographic protocols which guarantee one or more highlevel security properties note however that the distinction between cryptographic primitives and cryptosystems is quite arbitrary for example the rsa algorithm is sometimes considered a cryptosystem and sometimes a primitive typical examples of cryptographic primitives include pseudorandom functions oneway functions etc cryptosystems one or more cryptographic primitives are often used to develop a more complex algorithm called a cryptographic system or cryptosystem cryptosystems eg elgamal encryption are designed to provide particular functionality eg public key encryption while guaranteeing certain security properties eg chosenplaintext attack cpa security in the random oracle model cryptosystems use the properties of the underlying cryptographic primitives to support the systems security properties as the distinction between primitives and cryptosystems is somewhat arbitrary a sophisticated cryptosystem can be derived from a combination of several more primitive cryptosystems in many cases the cryptosystems structure involves back and forth communication among two or more parties in space eg between the sender of a secure message and its receiver or across time eg cryptographically protected backup data such cryptosystems are sometimes called cryptographic protocols some widely known cryptosystems include rsa encryption schnorr signature elgamal encryption pgp etc more complex cryptosystems include electronic cash etc until recently there has been considerable effort to develop formal techniques for establishing the security of cryptosystems this has been generally called provable security the general idea of provable security is to give arguments about the computational difficulty needed to compromise some security aspect of the cryptosystem ie to any adversary the study of how best to implement and integrate cryptography in software applications is itself a distinct field see cryptographic engineering and security engineering legal issues see also cryptography laws in different nations prohibitions cryptography has long been of interest to intelligence gathering and law enforcement agencies because of its facilitation of privacy and the diminution of privacy attendant on its prohibition cryptography is also of considerable interest to civil rights supporters accordingly there has been a history of controversial legal issues surrounding cryptography especially since the advent of inexpensive computers has made widespread access to high quality cryptography possible in some countries even the domestic use of cryptography is or has been restricted until 1999 france significantly restricted the use of cryptography domestically though it has since relaxed many of these rules in china and iran a license is still required to use cryptography in the united states cryptography is legal for domestic use but there has been much conflict over legal issues related to cryptography until the development of the personal computer asymmetric key algorithms ie public key techniques and the internet this was not especially problematic however as the internet grew and computers became more widely available highquality encryption techniques became well known around the globe export controls export of cryptography in the 1990s there were several challenges to us export regulation of cryptography after the source code for philip zimmermanns pretty good privacy pgp encryption program found its way onto the internet in june 1991 a complaint by rsa security then called rsa data security inc resulted in a lengthy criminal investigation of zimmermann by the us customs service and the fbi though no charges were ever filed in 1996 thirtynine countries signed the wassenaar arrangement an arms control treaty that deals with the export of arms and dualuse technologies such as cryptography the treaty stipulated that the use of cryptography with short keylengths 56bit for symmetric encryption 512bit for rsa would no longer be exportcontrolled nsa involvement nsa headquarters in fort meade maryland see also clipper chip another contentious issue connected to cryptography in the united states is the influence of the national security agency on cipher development and policy but kept the technique secret at the nsas request the technique became publicly known only when biham and shamir rediscovered and announced it some years later the entire affair illustrates the difficulty of determining what resources and knowledge an attacker might actually have another instance of the nsas involvement was the 1993 clipper chip affair an encryption microchip intended to be part of the capstone cryptographycontrol initiative clipper was widely criticized by cryptographers for two reasons the cipher algorithm called skipjack was then classified declassified in 1998 long after the clipper initiative lapsed the classified cipher caused concerns that the nsa had deliberately made the cipher weak in order to assist its intelligence efforts the whole initiative was also criticized based on its violation of kerckhoffss principle as the scheme included a special escrow key held by the government for use by law enforcement for example in wiretaps digital rights management digital rights management cryptography is central to digital rights management drm a group of techniques for technologically controlling use of copyrighted material being widely implemented and deployed at the behest of some copyright holders in 1998 us president bill clinton signed the digital millennium copyright act dmca which criminalized all production dissemination and use of certain cryptanalytic techniques and technology now known or later discovered specifically those that could be used to circumvent drm technological schemes this had a noticeable impact on the cryptography research community since an argument can be made that any cryptanalytic research violated or might violate the dmca similar statutes have since been enacted in several countries and regions including the implementation in the eu copyright directive similar restrictions are called for by treaties signed by world intellectual property organization memberstates the united states department of justice and fbi have not enforced the dmca as rigorously as had been feared by some but the law nonetheless remains a controversial one niels ferguson a wellrespected cryptography researcher has publicly stated that he will not release some of his research into an intel security design for fear of prosecution under the dmca triggered by the perceived impact of such notices on fair use and free speech forced disclosure of encryption keys key disclosure law in the united kingdom the regulation of investigatory powers act gives uk police the powers to force suspects to decrypt files or hand over passwords that protect encryption keys failure to comply is an offense in its own right punishable on conviction by a twoyear jail sentence or up to five years in cases involving national security similar forced disclosure laws in australia finland france and india compel individual suspects under investigation to hand over encryption keys or passwords during a criminal investigation in the united states the federal criminal case of united states v fricosu addressed whether a search warrant can compel a person to reveal an encryption passphrase or password in many jurisdictions the legal status of forced disclosure remains unclear the 2016 fbiapple encryption dispute concerns the ability of courts in the united states to compel manufacturers assistance in unlocking cell phones whose contents are cryptographically protected as a potential countermeasure to forced disclosure some cryptographic software supports plausible deniability where the encrypted data is indistinguishable from unused random data for example such as that of a drive which has been securely wiped outline of cryptography list of cryptographers encyclopedia of cryptography and security list of important publications in cryptography list of multiple discoveries see rsa list of unsolved problems in computer science crypto wars global surveillance strong cryptography comparison of cryptography libraries a syllabical and steganographical table first cryptography chart w3cs web cryptography api further information books on cryptography becket b 1988 introduction to cryptology blackwell scientific publications isbn0632018364 oclc16832704 excellent coverage of many classical ciphers and cryptography concepts and of the modern des and rsa systems cryptography and mathematics by bernhard esslinger 200 pages part of the free opensource package cryptool pdf download at the wayback machine archived 22 july 2011 cryptool is the most widespread elearning program about cryptography and cryptanalysis open source in code a mathematical journey by sarah flannery with david flannery popular account of sarahs awardwinning project on publickey cryptography cowritten with her father james gannon stealing secrets telling lies how spies and codebreakers helped shape the twentieth century washington dc brasseys 2001 isbn1574883674 oded goldreich foundations of cryptography in two volumes cambridge university press 2001 and 2004 introduction to modern cryptography by jonathan katz and yehuda lindell alvins secret code by clifford b hicks childrens novel that introduces some basic cryptography and cryptanalysis ibrahim a alkadi the origins of cryptology the arab contributions cryptologia vol 16 no 2 april 1992 pp97126 christof paar jan pelzl understanding cryptography a textbook for students and practitioners springer 2009 slides online cryptography lectures and other information are available on the companion web site very accessible introduction to practical cryptography for nonmathematicians introduction to modern cryptography by phillip rogaway and mihir bellare a mathematical introduction to theoretical cryptography including reductionbased security proofs pdf download johannchristoph woltag coded communications encryption in rdiger wolfrum ed max planck encyclopedia of public international law oxford university press 2009 max planck encyclopedia of public international law giving an overview of international law issues regarding cryptography jonathan arbib john dwyer discrete mathematics for cryptography 1st edition isbn9781907934018 stallings william march 2013 cryptography and network security principles and practice 6th ed prentice hall isbn9780133354690 wikiquote has quotations related to cryptography wikibooks has more on the topic of cryptography at wikiversity you can learn more and teach others about cryptography at the department of cryptography wikisource has the text of the 1911 encyclopdia britannica article cryptography library resources about cryptography online books resources in your library resources in other libraries the dictionary definition of cryptography at wiktionary media related to cryptography at wikimedia commons cryptography on in our time at the bbc crypto glossary and dictionary of technical cryptography nsas cryptokids overview and applications of cryptology by the cryptool team pdf 38mb july 2008 a course in cryptography by raphael pass abhi shelat offered at cornell in the form of lecture notes for more on the use of cryptographic elements in fiction see dooley john f william and marilyn ingersoll professor of computer science knox college 23 august 2012 cryptology in fiction the george fabyan collection at the library of congress has early editions of works of seventeenthcentury english literature publications 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