Jonathan Katz and Yehuda Lindell. Introduction to Modern. Cryptography c Jonathan Katz and Yehuda Lindell. All Rights Reserved. CRC PRESS. Jonathan Katz and Yehuda Lindell. Introduction to Modern. Cryptography. CRC PRESS. Boca Raton. London. New York. Washington, D.C. Available online at maroc-evasion.info ▻ Other Relevant Books: ▻ M, Bellare and P. Rogaway, Introduction to Modern. Cryptography. Available.
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Jonathan Katz and Yehuda Lindell, Introduction to Modern International Standard Book Number (eBook - PDF). This book contains. introduce certain plausible assumptions to push our security arguments through. This book Computational ciphers and semantic security. Table of Contents Introduction A systematic method Chapter 1 – Principles and Method of the Work Do not force, do.
In the 2nd half of the hour we discussed the process that we use in modern cryptography to design and analyze algorithms and protocols. We also discussed the relation to P and NP. Section 1 from the notes. We then discussed the exponentiation problem and we discussed how we can get an algorithmic solution that is efficient. This is not in the notes but you can read about it in e. We introduced the inverse problem in the form of computing the logarithm of an element in the group for a given generator.
This problem will be eventually identified as the discrete logarithm problem, see Definition 6. We defined the output probability of a probabilistic algorithm and the events that may be defined with respect to this output.
We explained the importance of using probabilistic algorithms when arguing about the hardness of problems that are relevant to Cryptography. Refer to Section 2.
Section 3. We then recalled the construction of commitment schemes based on multiplicative groups Pedersen commitment. We started the discussion on the security proof focusing on the binding property.
We introduced statistical distance as an important measure of similarity between random variables. We introduced the problem of key exchange and described the Diffie Hellman key exchange protocol.
The lecture corresponds to Sections 2. Bernoulli trials, Binomial distribution, Chernoff bounds. Bitcoin, currencies, double spending attacks, transactions, blocks, proof of work, difficulty. Modeling Bitcoin, Random oracle. 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 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 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.
However, in cryptography, code has a more specific meaning.
It means the replacement of a unit of plaintext i. 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. History of cryptography and cryptanalysis Main article: History of cryptography 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. 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 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. After the discovery of frequency analysis , by the Arab mathematician and polymath Al-Kindi also known as Alkindus in the 9th century,    nearly all such ciphers could be broken by an 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 , which described the first known use of frequency analysis and cryptanalysis techniques.
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,   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. 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 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 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 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 e.
There is also active research examining the relationship between cryptographic problems and quantum physics see quantum cryptography and quantum computer. 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.
Advent of modern cryptography 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 mid's. In recent times, IBM personnel designed the algorithm that became the Federal i.
Following their work in , it became popular to consider cryptography systems based on mathematical problems that are easy to state but have been found difficult to solve. 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.
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. The chief ones are discussed here; see Topics in Cryptography for more.
Symmetric-key cryptography Main article: Symmetric-key algorithm Symmetric-key cryptography, where a single key is used for encryption and decryption 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 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. 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 Category:Stream ciphers. 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.
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.
Public-key cryptography Main article: Public-key cryptography Public-key cryptography, where different keys are used for encryption and decryption. Padlock icon from the Firefox Web browser , which indicates that TLS , a public-key cryptography system, is in use. Symmetric-key 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.