Public and private key cryptography pdf

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Chapter 7 Public Key Cryptography and Digital Signatures

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 , chip-based payment cards , digital currencies , computer passwords , and military communications.

Cryptography prior to the modern age was effectively synonymous with encryption , converting information from a readable state to unintelligible nonsense. The sender of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice "A" for the sender, Bob "B" for the intended recipient, and Eve " eavesdropper " for the adversary.

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 actual practice by any adversary. While it is theoretically possible to break into a well-designed such system, it is infeasible in actual practice to do so. Such schemes, if well designed, are therefore termed "computationally secure"; theoretical advances, e.

There exist information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as the one-time pad , but these schemes are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes.

The growth of cryptographic technology has raised a number of legal issues in the information age. Cryptography's 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. The first use of the term cryptograph as opposed to cryptogram dates back to the 19th century—originating from The Gold-Bug , a story 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.

A cipher or cypher is a pair of algorithms that carry out 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 string of characters ideally short so it can be remembered by the user , which is needed to decrypt the ciphertext. In formal mathematical terms, 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 counter-productive for most purposes. Historically, ciphers were often used directly for encryption or decryption without additional procedures such as authentication or integrity checks.

There are, generally, two kinds of cryptosystems: symmetric and asymmetric. In symmetric systems, the only ones known until the s, the same key the secret key is used to encrypt and decrypt a message. Data manipulation in symmetric systems is faster than asymmetric systems in part because they generally use shorter key lengths.

Asymmetric systems use a "public key" to encrypt a message and a related "private key" to decrypt it. Use of asymmetric systems enhances the security of communication, largely because the relation between the two keys is very hard to discover. 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: the replacement of a unit of plaintext i.

A cypher, in contrast, is a scheme for changing or substituting an element below such a level a letter, or a syllable or a pair of letters or 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.

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 e. Before the modern era, cryptography focused on message confidentiality i. Encryption attempted to ensure secrecy in communications , such as those of spies , military leaders, and diplomats. The main classical cipher types are transposition ciphers , which rearrange the order of letters in a message e. 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 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 e.

An early example, from Herodotus , was a message tattooed on a slave's shaved head and concealed under the regrown hair. 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.

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

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 , by the Arab mathematician and polymath Al-Kindi also known as Alkindus in the 9th century, [22] [23] [24] nearly all such ciphers could be broken by an informed attacker. Such classical ciphers still enjoy popularity today, though mostly as puzzles. Al-Kindi wrote a book on cryptography entitled Risalah fi Istikhraj al-Mu'amma Manuscript for the Deciphering Cryptographic Messages , which described the first known use of frequency analysis and cryptanalysis techniques.

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 n-gram frequencies may provide an attack. Essentially all ciphers remained vulnerable to cryptanalysis using the frequency analysis technique until the development of the polyalphabetic cipher.

While it was known to Al-Kindi to some extent, [25] [26] it was first clearly described in the work of Al-Qalqashandi — , based on the earlier work of Ibn al-Durayhim — , describing a polyalphabetic cipher in which each plaintext letter is assigned more than one substitute. He also invented what was probably the first automatic cipher device , a wheel which implemented a partial realization of his invention.

Although frequency analysis can be a powerful and general technique against many ciphers, encryption has still often been effective in practice, as 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.

It was finally explicitly recognized in the 19th century that secrecy of a cipher's 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 by Auguste Kerckhoffs and is generally called Kerckhoffs's 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 wheel cypher not publicly known, and reinvented independently by Bazeries around Prior to the early 20th century, cryptography was mainly 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; other kinds of engineering e. There is also active research examining the relationship between cryptographic problems and quantum physics. 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 i.

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.

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. Extensive open academic research into cryptography is relatively recent; it began only in the mids.

In recent times, IBM personnel designed the algorithm that became the Federal i. 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 very few cryptosystems that are proven to be unconditionally secure.

The one-time pad is one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so proof of unbreakability is unavailable since the underlying mathematical problem remains open.

In practice, these are widely used, and are believed unbreakable in practice by most competent observers. The discrete logarithm problem is the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem. 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 , so when specifying key lengths , the required key lengths are similarly advancing. Symmetric-key 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 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. Many, even some designed by capable practitioners, have been thoroughly broken, such as FEAL. Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the one-time 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. 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 long-used 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 MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 family improves on SHA-1, but is vulnerable to clashes as of ; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST 's overall hash algorithm toolkit.

Chapter 7 Public Key Cryptography and Digital Signatures

Unlike symmetric key cryptography, we do not find historical use of public-key cryptography. It is a relatively new concept. Symmetric cryptography was well suited for organizations such as governments, military, and big financial corporations were involved in the classified communication. With the spread of more unsecure computer networks in last few decades, a genuine need was felt to use cryptography at larger scale. The symmetric key was found to be non-practical due to challenges it faced for key management. This gave rise to the public key cryptosystems.

Public-key cryptography, or asymmetric cryptography, is an encryption scheme that uses two mathematically related, but not identical, keys - a public key and a private key. Unlike symmetric key algorithms that rely on one key to both encrypt and decrypt, each key performs a unique function. The public key is used to encrypt and the private key is used to decrypt. It is computationally infeasible to compute the private key based on the public key. Because of this, public keys can be freely shared, allowing users an easy and convenient method for encrypting content and verifying digital signatures, and private keys can be kept secret, ensuring only the owners of the private keys can decrypt content and create digital signatures. Since public keys need to be shared but are too big to be easily remembered, they are stored on digital certificates for secure transport and sharing.

private key then it serves as a signature that verifies the origin, content and sequencing of the document. Confidentiality and Authentication. If both are​.

Public Key Encryption and PDF

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 , chip-based payment cards , digital currencies , computer passwords , and military communications. Cryptography prior to the modern age was effectively synonymous with encryption , converting information from a readable state to unintelligible nonsense. The sender of an encrypted message shares the decoding technique only with intended recipients to preclude access from adversaries. The cryptography literature often uses the names Alice "A" for the sender, Bob "B" for the intended recipient, and Eve " eavesdropper " for the adversary.


  • We introduce the notion of distributed password-based public-key cryptography, where a virtual high-entropy private key is implicitly defined as a concatenation of low-entropy passwords held in separate locations. Paul P. - 06.06.2021 at 05:30
  • Private key cryptography. Alice. Bob sends a message must have encoding key to encrypt the message must have decoding key to decrypt the message. Sarah H. - 07.06.2021 at 20:50
  • Since that time, this paper has taken on a life of its own Roberta P. - 09.06.2021 at 02:26
  • Form the public key The pair of numbers n,e form the RSA public key and is made public. Clarimunda D. - 10.06.2021 at 23:40