INTRODUCTION

Cryptography comes from Greek word kryptos, meaning "hidden or secret"; and gráphin means "writing". Cryptography is the practice and study of hiding information. Modern cryptography intersects the disciplines of mathematics, computer science, and electrical engineering. Applications of cryptography include ATM cards, computer passwords, and electronic commerce.

Cryptology prior to the modern age was almost synonymous with encryption, the conversion of information from a readable state to apparent gibberish. The sender retained the ability to decrypt the information and therefore avoid unwanted persons being able to read it. Since First World War and the advent of the computer, the methods used to carry out cryptology have become increasingly complex and its application more widespread.

Modern cryptography follows a strongly scientific approach, and designs cryptographic algorithms around computational hardness assumptions that are assumed hard to break by an adversary. Such systems are not unbreakable in theory but it is infeasible to do so for any practical adversary. Information-theoretically secure schemes that provably cannot be broken exist but they are less practical than computationally-secure mechanisms. An example of such systems is the one-time pad. Alongside the advancement in cryptology-related

technology, the practice has raised a number of legal issues, some of which remain unresolved.

Until modern times cryptography referred almost exclusively to encryption, which is the process of converting ordinary information (called plaintext) into unintelligible gibberish (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. This is a secret parameter (ideally known only to the communicants) for a specific message exchange context.

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, as ciphers without variable keys can be trivially broken with only the knowledge of the cipher used and are therefore useless (or even counter-productive) for most purposes. Historically, ciphers were often

used directly for encryption or decryption without additional procedures such as authentication or integrity checks.

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 (i.e., a meaningful word or phrase) with a code word (for example, wallaby replaces attack at dawn). Codes are no longer used in serious cryptography—except incidentally for such things as unit designations (e.g., Bronco Flight or Operation Overlord)—since properly chosen ciphers are both more practical and more secure than even the best codes and also are better adapted to computers.

Cryptanalysis is the term used for the study of methods for obtaining the meaning of encrypted information without access to the key normally required to do so; i.e., it is the study of how to crack encryption algorithms or their implementations.

Some use the terms cryptography and cryptology interchangeably in English, 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. English is more flexible than several other languages in which cryptology (done by cryptologists) is always used in the second sense above.

The study of characteristics of languages which have some application in cryptography (or cryptology), i.e. frequency data, letter combinations, universal patterns, etc., is called cryptolinguistics.

HISTORYBefore the modern era, cryptography was concerned solely

with message confidentiality (i.e., encryption)—conversion 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 was used to (attempt 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, sender/receiver identity authentication, digital signatures, interactive proofs and secure computation, among others.

CLASSIC CRYPTOGRAPHY:

The earliest forms of secret writing required little more than local pen and paper analogs, as most people could not read. More literacy, or literate opponents, required actual cryptography. The main classical cipher types are transposition ciphers, which rearrange the order of letters in a message (e.g., 'hello world' becomes 'ehlol owrdl' in a trivially simple rearrangement scheme), and substitution ciphers, which systematically replace letters or groups of letters with other letters or groups of letters (e.g., 'fly at once' becomes 'gmz bu podf' by replacing each letter with the one following it in the Latin alphabet). 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. It was named after Julius Caesar who is reported to have used it, with a shift of 3, to communicate with his generals during his military campaigns, just like EXCESS-3 code in boolean algebra. There is record of several early Hebrew ciphers as well. The earliest known use of cryptography is some carved ciphertext on stone in Egypt (ca 1900 BC), but this may have been done for the amusement of literate observers. The next oldest is bakery recipes from Mesopotamia. Cryptography is recommended in the books as a way for lovers to communicate without inconvenient discovery.

The Greeks of Classical times are said to have known of ciphers (e.g., the scytale transposition cipher claimed to have been used by the Spartan military). Steganography (i.e., hiding even the existence of a message so as to keep it confidential) was also first developed in ancient times. An early example, from Herodotus, concealed a message—a tattoo on a slave's shaved head—under the regrown hair. Another Greek method was developed by Polybius (now called the "Polybius Square"). More modern examples of steganography include the use of invisible ink, microdots, and digital watermarks to conceal information.

Ciphertexts produced by a classical cipher (and some modern ciphers) always reveal statistical information about the plaintext, which can often be used to break them. After the discovery of frequency analysis perhaps by the Arab mathematician and polymath, Al-Kindi (also known as

Alkindus), in the 9th century, nearly all such ciphers became more or less readily breakable by any informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles (see cryptogram). Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma (Manuscript for the Deciphering Cryptographic Messages), in which described the first cryptanalysis techniques.

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 Al-Kindi. Alberti's innovation was to use different ciphers (i.e., substitution alphabets) for various parts of a message (perhaps for each successive plaintext letter at the limit). He also invented what was probably the first automatic cipher device, a wheel which implemented a partial realization of his invention. In the polyalphabetic Vigenère cipher, encryption uses a key word, which controls letter substitution depending on which letter of the key word is used. In the mid-19th century Charles Babbage showed that polyalphabetic ciphers of this type remained partially vulnerable to extended frequency analysis techniques.

Although frequency analysis is a powerful and general technique against many ciphers, encryption has still been often effective in practice; many a would-be 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 cipher's algorithm is not a sensible or 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 Kerckhoffs' principle; alternatively and more bluntly, it was restated by Claude Shannon, the inventor of information theory and the fundamentals of theoretical cryptography, as Shannon's Maxim—'the 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. 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 Alberti's own cipher disk, Johannes Trithemius' tabula recta scheme, and Thomas Jefferson's multi-cylinder. Many mechanical

encryption/decryption devices were invented early in the 20th century, and several patented, among them rotor machines—famously including the Enigma machine used by the German government and military from the late '20s and during World War II. The ciphers implemented by better quality examples of these machine designs brought about a substantial increase cryptanalytic difficulty after WWI.

Fig: Enigma Machine

THE COMPUTER ERA:

The development of digital computers and electronics after World War II 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 (i.e., 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 (i.e., 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. Alternate methods of attack (bribery, burglary, threat, torture, ...) have become more attractive in consequence.

Credit card with smart-card capabilities. The 3-by-5-mm chip embedded in the card is shown, enlarged. Smart cards combine low cost and portability with the power to compute cryptographic algorithms.

Extensive open academic research into cryptography is relatively recent; it began only in the mid-1970s. In recent times, IBM personnel designed the algorithm that became the Federal (i.e., US) Data Encryption Standard; Whitfield Diffie and Martin Hellman published their key agreement algorithm known as Diffie-Hellman algorithm; and the RSA algorithm was published in Martin Gardner's Scientific American column.

Since then, cryptography has become a widely used tool in communications, computer networks, and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable, such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics. There are no absolute proofs that a cryptographic technique is secure (but see one-time pad); at best, there are proofs that some techniques are secure if some computational problem is difficult to solve, or this or that assumption about implementation or practical use is met.

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 brute-force attacks, thus when specifying key lengths, the required key lengths are similarly advancing. The potential effects of quantum computing are already being considered by some cryptographic system designers; the announced imminence of small implementations of these machines may be making the need for this preemptive caution rather more than merely speculative.

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 as it deals with active, intelligent, and malevolent opposition (see cryptographic engineering and security engineering); other kinds of engineering (e.g., 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 computing).

A PROJECT REPORT

ON

HIMANSHU BAJORIA

B.E.E -IV

ROLL- 000710801059

Where Complexity Finally Comes In Handy….

CRYPTOGRAPHY

CRYPTOGRAPHY SERVICES

Any new design of Cryptographic technique must accomplish the above requisites. Cryptography not only protects data from theft or alteration, but can also be used for user authentication.Hence, the various security requirements for a Cryptographic technique including:

Authentication: The process of proving one's identity. (The primary forms of host-to-host authentication on the Internet today are name-based or address-based, both of which are notoriously weak.)

Privacy/confidentiality: Ensuring that no one can read the message except the intended receiver.

Integrity: Assuring the receiver that the received message has not been altered in any way from the original.

Non-repudiation: A mechanism to prove that the sender really sent this message.

Access-control: A method in which the access to unauthorized users is prohibited, i.e. only the authorized user can have access to its documents.

Availability: This method guarantees that the system services are always available when needed.

Security-Audit: With the help of this mechanism a record of all the previous transactions are kept which may provide useful information at a later stage.

Key-Management: This method allows negotiating, as well as setup and maintaining keys between the communicating entities.

ATTACKSAccording to the cryptanalyst Kent, there are many ways in

which the personal information shared between two peoples can be interrupted with. Here an intermediate person, known as an attacker, has an access to the information being transferred called as passive attacker, and can even change the information being exchanged with the help of some technology and is called as an active attacker.

PASSIVE ATTACKS:

This kind of attacks is generally carried by a passive intruder who only has an access to the information or message being exchanged. Considering the trivial case of Bob and Alice where Bob wants to send a message to Alice. Here the intruder has

access to the contents only i.e. he can read the message but cannot tamper with it. So due to the inability to create any changes the intruder is called as a passive attacker.

ACTIVE ATTACKS:

This kind of attacks is generally carried by an active intruder who not only has an access to the information or message being exchanged but can also tamper or manipulate the message being exchanged. So due to the ability to create any changes the intruder is called as an active attacker.Some other types of attack can also be considered such as:

CIPHERTEXT ONLY ATTACK:

This is the situation where the attacker does not know anything about the contents of the message, and must work from

ciphertext only. In practice it is quite often possible to make guesses about the plaintext, as many types of messages have fixed format headers. Even ordinary letters and documents begin in a very predictable way. It may also be possible to guess that some ciphertext block contains a common word.

KNOWN PLAINTEXT ATTACK:

The attacker knows or can guess the plaintext for some parts of the ciphertext. The task is to decrypt the rest of the ciphertext blocks using this information. This may be done by determining the key used to encrypt the data, or via some shortcut.

CHOSEN PLAINTEXT ATTACK:

The attacker is able to have any text he likes encrypted with the unknown key. The task is to determine the key used for encryption. Some encryption methods, particularly RSA, are extremely vulnerable to chosen-plaintext attacks. When such algorithms are used, extreme care must be taken to design the entire system so that an attacker can never have chosen plaintext encrypted.

CIPHERA cipher is an algorithm for performing encryption or

decryption using a series of well-defined steps that can be followed as a procedure.

For a cipher to be of practical value:1. It must be difficult to be broken by enemy cryptanalyst.2. It must be easy to encrypt decrypt with knowledge of secret

key.

Data that can be read and understood without any special measures is called plaintext or clear text. The method of disguising plaintext in such a way as to hide its substance is called encryption. Encrypting plaintext results in unreadable gibberish called cipher text. You use encryption to make sure that information is hidden from anyone for whom it is not intended, even those who can see the encrypted data. The process of reverting ciphertext to its original plaintext is called decryption.

CLASSICAL CIPHER

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include simple substitution ciphers or Caesar’s cipher and transposition ciphers. For example “GOOD DOG” can be encrypted as “PLLX XLP” where “L” substitutes for “O”, “P” for “G”, and “X” for “D” in the message. Transposition of the letters “GOOD DOG” can result in “DGOGDOO”. Julius Caesar used to substitute each alphabet key characters down or up accordingly and where the key used by him was 3.

Figure: Caesar Cipher

These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs. Simple ciphers were replaced by polyalphabetic substitution ciphers which changed the substitution alphabet for every letter. For example “GOOD DOG” can be encrypted as “PLSX TWF” where “L”, “S”, and “W” substitute for “O”. With even a small amount of known or estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers designed for pen and paper encryption are easy to crack. Another advancement in the theory

was the transposition cipher where the characters retain their plaintext form but change their positions to create the cipher

text. Here the text is organized into two dimensional tables, and the rows and columns are interchanged according to a key. Consider the plaintext “attackatxdawn” and the ciphertext obtained using the transposition algorithm is “xtawxnattxadakc” as shown in the figure below. In the following example the rows 1-5 and columns 1-3 are permutated to give new set of rows (3,5,1,4,2) and columns (1,3,2).

Figure: Double Transposition

MODERN CIPHER

Permute rowsand columns

In cryptography several new ways of encrypting the message was further devised. These algorithms were a bit more complicated than the previous classical ciphers. Generally modern ciphers are classified according to their input size based or key based.

INPUT BASED CIPHERS:

The most common input size based ciphers are block cipher and stream cipher and are described as follows.

BLOCK CIPHER:

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take (for example) a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext. The exact transformation is controlled using a second input — the secret key. Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of ciphertext together with the secret key, and yields the original 128-bit block of plaintext.

A message longer than the block size (128 bits in the above example) can still be encrypted with a block cipher by breaking

the message into blocks and encrypting each block individually. However, in this method all blocks are encrypted with the same key, which degrades security (because each repetition in the plaintext becomes a repetition in the ciphertext). To overcome this issue, modes of operation are used to make encryption probabilistic.

STREAM CIPHER:

In cryptography, a stream cipher is a symmetric key cipher where plaintext bits are combined with a pseudorandom cipher bit stream (key stream), typically by an exclusive-or (xor) operation. In a stream cipher the plaintext digits are encrypted one at a time, and the transformation of successive digits varies during the encryption. An alternative name is a state cipher, as the encryption of each digit is dependent on the current state. In practice, the digits are typically single bits or bytes.

Stream ciphers represent a different approach to symmetric encryption from block ciphers. Block ciphers operate on large

blocks of digits with a fixed, unvarying transformation. This distinction is not always clear-cut: in some modes of operation, a block cipher primitive is used in such a way that it acts effectively as a stream cipher. Stream ciphers typically execute at a higher speed than block ciphers and have lower hardware complexity. However, stream ciphers can be susceptible to serious security problems if used incorrectly: see stream cipher attacks — in particular, the same starting state must never be used twice.

KEY BASED CIPHER:

Apart from the block and stream ciphers a more enhanced methods were developed involving the usage of a public and private key. The most widely used amongst them are described as follows.

SYMMETRIC KEY CRYPTOGRAPHY:

With secret key cryptography, a single key is used for both encryption and decryption. As shown in figure, the sender uses

the key (or some set of rules) to encrypt the plaintext and sends the cipher text to the receiver. The receiver applies the same key (or rule set) to decrypt the message and recover the plaintext. Because a single key is used for both functions, secret key cryptography is also called symmetric encryption. Secret key cryptography schemes are generally categorized as being either stream ciphers or block ciphers. Stream ciphers operate on a single bit (byte or computer word) at a time and implement some form of feedback mechanism so that the key is constantly changing. A block cipher is so called because the scheme encrypts one block of data at a time using the same key on each block. In general, the same plaintext block will always encrypt to the same cipher text when using the same key in a block cipher whereas the same plaintext will encrypt to different cipher text in a stream cipher.

Figure: Symmetric Key Cryptography

It can be seen that symmetric key cryptography requires less time to encrypt a message so its efficiency is high but on the

other hand it must also be noted that each pair of users must

have a unique key, so N users need N(N-1)/2 keys. As a result the key distribution becomes difficult.

The most commonly used algorithms in symmetric key cryptography to encrypt the message are:

• DES (Data Encryption Standard) and derivatives: double DES and triple DES

• IDEA (International Data Encryption Algorithm)

• Blowfish

• RC5 (Rivest Cipher #5)

• AES (Advance Encryption Standard)

PUBLIC KEY CRYPTOGRAPHY:

Public-key cryptography has been said to be the most significant new development in secure communication over a non-secure communications channel without having to share a secret key. Public Key Cryptography or Asymmetric cryptography provides the same message security guarantees as symmetric cryptography, but additionally provides the non-repudiation guarantee. ‘Asymmetric’ refers to the fact that different keys are used for encryption and decryption. One key is kept secret (‘secret key’) and the other is made public (‘public

key’), and are both unique. The recipient’s public key should be used during the encryption process to ensure message confidentiality as only the recipient has the necessary secret key to decrypt the message. If, however, the message is encrypted using the sender’s private key the sender cannot deny sending the message as his private key is unique and is only known to him. Asymmetric cryptography is extremely powerful, but this comes at a cost. Especially for longer messages and keys, it is much slower than its symmetric cryptography counterparts. This is due in part to the fact that, in order to achieve comparable security, asymmetric keys are generally around an order of magnitude longer than symmetric keys.

Figure: Public Key Encryption

Typically used asymmetric key algorithm includes:

• RSA (Rivest, Shamir, Adleman)

• DH (Diffie-Hellman Key Agreement Algorithm)

• ECDH (Elliptic Curve Diffie-Hellman Key Agreement Algorithm)

• RPK (Raike Public Key)

HASH FUNCTIONS:

The system described above has some problems. It is slow, and it produces an enormous volume of data—at least double the size of the original information. An improvement on the above scheme is the addition of a one-way hash function in the process. A one-way hash function takes variable-length input in this case, a message of any length, even thousands or millions of bits—and produces a fixed-length output; say, 160 bits.

The hash function ensures that, if the information is changed in any way—even by just one bit—an entirely different output value is produced. PGP uses a cryptographically strong hash function on the plaintext the user is signing. This generates a fixed-length data item known as a message digest. Then PGP uses the digest and the private key to create the “signature.” PGP transmits the signature and the plaintext together. Upon receipt of the message, the recipient uses PGP to recompute the digest, thus verifying the signature. PGP can encrypt the plaintext or not; signing plaintext is useful if some of the recipients are not interested in or capable of verifying the signature. As long as a secure hash function is used, there is no way to take someone’s signature from one document and attach it to another, or to alter a signed message in any way. The

slightest change to a signed document will cause the digital signature verification process to fail. Digital signatures play a major role in authenticating and validating the keys of other PGP users.

ENCRYPTION MODES

The ciphers in use are generally following these four encryption modes:

ELECTRONIC CODEBOOK (EBC):

Electronic Codebook (ECB) mode is the simplest, most obvious application: the secret key is used to encrypt the plaintext block to form a cipher text block. Two identical plaintext blocks, then, will always generate the same cipher text block. Although this is the most common mode of block ciphers, it is susceptible to a variety of brute-force attacks

CIPHER BLOCK CHAINING:

Cipher Block Chaining (CBC) mode adds a feedback mechanism to the encryption scheme. In CBC, the plaintext is exclusively-O Red (XORed) with the previous cipher text block prior to encryption. In this mode, two identical blocks of plaintext never encrypt to the same cipher text.

CIPHER FEEDBACK (CFB):

Cipher Feedback (CFB) mode is a block cipher implementation as a self synchronizing stream cipher. CFB mode allows data to be encrypted in units smaller than the block size, which might be useful in some applications such as encrypting interactive terminal input. If we were using 1-byte CFB mode, for example, each incoming character is placed into a shift register the same size as the block, encrypted, and the block transmitted. At the receiving side,

the cipher text is decrypted and the extra bits in the block (i.e., everything above and beyond the one byte) are discarded.

OUTPUT FEEDBACK (OFB):

Output Feedback (OFB) mode is a block cipher implementation conceptually similar to a synchronous stream cipher. OFB prevents the same plaintext block from generating the same cipher text block by using an internal feedback mechanism that is independent of both the plaintext and cipher text bit streams.

APPLICATIONS

Cryptography is best known as a way of keeping the contents of a message secret. Confidentiality of network communications, for example, is of great importance for e-commerce and other network applications. However, the applications of cryptography go far beyond simple confidentiality. In particular, cryptography allows the network business and customer to verify the authenticity and integrity of their transactions. If the trend to a global electronic marketplace continues, better cryptographic techniques will have to be developed to protect business transactions.

Sensitive information sent over an open network may be scrambled into a form that cannot be understood by a hacker or eavesdropper. This is done using a mathematical formula, known as an encryption algorithm, which transforms the bits of the message into an unintelligible form. The intended recipient has a decryption algorithm for extracting the original message. There are many examples of information on open networks, which need to be protected in this way, for instance, bank account details, credit card transactions, or confidential health or tax records.

In order to allow different users to use the same algorithm, the algorithm is used in conjunction with a secret key, a long

sequence of binary numbers, as shown in the illustration, which is known only by the legitimate users. Only users sharing the same key will be able to decrypt each other's encrypted messages. Since the key allows access to the encrypted information, it is of paramount importance that it is kept secret and is frequently changed.

Before two parties can send information securely, they must first exchange a secret key. This however presents a dilemma, sometimes called the ‘Catch 22 of Cryptography’ — how can the two parties exchange a key secretly before they can communicate in secret? Even if the sender and receiver found a channel that they believed to be secure, in the past there has been no way to test the secrecy of each key. Quantum cryptography solves this problem. It allows the sender and receiver to test and guarantee the secrecy of each individual key.

CONCLUSION

Cryptography is a particularly interesting field because of the amount of work that is, by necessity, done in secret. The irony is that today, secrecy is not the key to the goodness of a cryptographic algorithm. Regardless of the mathematical theory behind an algorithm, the best algorithms are those that are well-known and well-documented because they are also well-tested and well-studied! In fact, time is the only true test of good cryptography; any cryptographic scheme that stays in use year after year is most likely a good one. The strength of cryptography lies in the choice (and management) of the keys; longer keys will resist attack better than shorter keys.