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Merkle's Puzzles
In cryptography, Merkle's Puzzles is an early construction for a public-key cryptosystem, a protocol devised by Ralph Merkle in 1974 and published in 1978. It allows two parties to agree on a shared secret by exchanging messages, even if they have no secrets in common beforehand. Description Suppose Alice and Bob wish to communicate. Bob can send a message to Alice as follows: first he creates a large number of puzzles, each of a moderate amount of difficulty — it must be possible for Alice to solve the puzzle with a moderate amount of computing effort. The puzzles are in the form of an encrypted message with an unknown key; the key must be short enough to allow a brute force attack. Bob sends all of the puzzles (i.e. encrypted messages) to Alice, who chooses one randomly, and solves it. The decrypted solution contains an identifier as well as a session key, so Alice can communicate back to Bob which puzzle she has solved. Both parties now have a common key; Alice, becau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical 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 synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public-key
Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic algorithms based on mathematical problems termed one-way functions. Security of public-key cryptography depends on keeping the private key secret; the public key can be openly distributed without compromising security. In a public-key encryption system, anyone with a public key can encrypt a message, yielding a ciphertext, but only those who know the corresponding private key can decrypt the ciphertext to obtain the original message. For example, a journalist can publish the public key of an encryption key pair on a web site so that sources can send secret messages to the news organization in ciphertext. Only the journalist who knows the corresponding private key can decrypt the ciphertexts to obtain the sources' messages—an eavesdropp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ralph Merkle
Ralph C. Merkle (born February 2, 1952) is a computer scientist and mathematician. He is one of the inventors of public-key cryptography, the inventor of cryptographic hashing, and more recently a researcher and speaker on cryonics. Contributions While an undergraduate, Merkle devised Merkle's Puzzles, a scheme for communication over an insecure channel, as part of a class project. The scheme is now recognized to be an early example of public key cryptography. He co-invented the Merkle–Hellman knapsack cryptosystem, invented cryptographic hashing (now called the Merkle–Damgård construction based on a pair of articles published 10 years later that established the security of the scheme), and invented Merkle trees. The Merkle–Damgård construction is at the heart of many hashing algorithms. While at Xerox PARC, Merkle designed the Khufu and Khafre block ciphers, and the Snefru hash function. Career Merkle was the manager of compiler development at Elxsi from 1980. In 1988, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shared Secret
In cryptography, a shared secret is a piece of data, known only to the parties involved, in a secure communication. This usually refers to the key of a symmetric cryptosystem. The shared secret can be a password, a passphrase, a big number, or an array of randomly chosen bytes. The shared secret is either shared beforehand between the communicating parties, in which case it can also be called a pre-shared key, or it is created at the start of the communication session by using a key-agreement protocol, for instance using public-key cryptography such as Diffie–Hellman or using symmetric-key cryptography such as Kerberos. The shared secret can be used for authentication (for instance when logging into a remote system) using methods such as challenge–response or it can be fed to a key derivation function to produce one or more keys to use for encryption and/or MACing of messages. To make unique session and message keys the shared secret is usually combined with an ini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alice And Bob
Alice and Bob are fictional characters commonly used as placeholders in discussions about cryptographic systems and protocols, and in other science and engineering literature where there are several participants in a thought experiment. The Alice and Bob characters were invented by Ron Rivest, Adi Shamir, and Leonard Adleman in their 1978 paper "A Method for Obtaining Digital Signatures and Public-key Cryptosystems". Subsequently, they have become common archetypes in many scientific and engineering fields, such as quantum cryptography, game theory and physics. As the use of Alice and Bob became more widespread, additional characters were added, sometimes each with a particular meaning. These characters do not have to refer to people; they refer to generic agents which might be different computers or even different programs running on a single computer. Overview Alice and Bob are the names of fictional characters used for convenience and to aid comprehension. For example, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encrypt
In cryptography, encryption is the process of encoding information. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Ideally, only authorized parties can decipher a ciphertext back to plaintext and access the original information. Encryption does not itself prevent interference but denies the intelligible content to a would-be interceptor. For technical reasons, an encryption scheme usually uses a pseudo-random A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Background The generation of random numbers has many uses, such as for rando ... encryption Key (cryptography), key generated by an algorithm. It is possible to decrypt the message without possessing the key but, for a well-designed encryption scheme, considerable computational resources and skills are required. An au ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Key (cryptography)
A key in cryptography is a piece of information, usually a string of numbers or letters that are stored in a file, which, when processed through a cryptographic algorithm, can encode or decode cryptographic data. Based on the used method, the key can be different sizes and varieties, but in all cases, the strength of the encryption relies on the security of the key being maintained. A key’s security strength is dependent on its algorithm, the size of the key, the generation of the key, and the process of key exchange. Scope The key is what is used to encrypt data from plaintext to ciphertext. There are different methods for utilizing keys and encryption. Symmetric cryptography Symmetric cryptography refers to the practice of the same key being used for both encryption and decryption. Asymmetric cryptography Asymmetric cryptography has separate keys for encrypting and decrypting. These keys are known as the public and private keys, respectively. Purpose Since the key pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brute Force Attack
In cryptography, a brute-force attack consists of an attacker submitting many passwords or passphrases with the hope of eventually guessing correctly. The attacker systematically checks all possible passwords and passphrases until the correct one is found. Alternatively, the attacker can attempt to guess the key which is typically created from the password using a key derivation function. This is known as an exhaustive key search. A brute-force attack is a cryptanalytic attack that can, in theory, be used to attempt to decrypt any encrypted data (except for data encrypted in an information-theoretically secure manner). Such an attack might be used when it is not possible to take advantage of other weaknesses in an encryption system (if any exist) that would make the task easier. When password-guessing, this method is very fast when used to check all short passwords, but for longer passwords other methods such as the dictionary attack are used because a brute-force search ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
O Notation
Big ''O'' notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation. The letter O was chosen by Bachmann to stand for ''Ordnung'', meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their run time or space requirements grow as the input size grows. In analytic number theory, big O notation is often used to express a bound on the difference between an arithmetical function and a better understood approximation; a famous example of such a difference is the remainder term in the prime number theorem. Big O notation is also used in many other fields to provide similar estimates. Big O notation characterizes functions according to their growth rates: diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Logarithm Problem
In mathematics, for given real numbers ''a'' and ''b'', the logarithm log''b'' ''a'' is a number ''x'' such that . Analogously, in any group ''G'', powers ''b''''k'' can be defined for all integers ''k'', and the discrete logarithm log''b'' ''a'' is an integer ''k'' such that . In number theory, the more commonly used term is index: we can write ''x'' = ind''r'' ''a'' (mod ''m'') (read "the index of ''a'' to the base ''r'' modulo ''m''") for ''r''''x'' ≡ ''a'' (mod ''m'') if ''r'' is a primitive root of ''m'' and gcd(''a'',''m'') = 1. Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution. Definition Let ''G'' be any group. Denote its group operation by mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boaz Barak
Boaz Barak (בועז ברק, born 1974) is an Israeli-American professor of computer science at Harvard University. Early life and education He graduated in 1999 with a B.Sc. in mathematics and computer science from Tel Aviv University. In 2004, he received his Ph.D. from the Weizmann Institute of Science with thesis ''Non-Black-Box Techniques in Cryptography'' under the supervision of Oded Goldreich. Barak was at the Institute for Advanced Study for two years from 2003 to 2005. He was an assistant professor in the computer science department of Princeton University from 2005 to 2010 and an associate professor from 2010 to 2011. From 2010 to 2016, he was a researcher at Microsoft's New England research laboratory. Since 2016, he is the Gordon McKay Professor of Computer Science in the Harvard John A. Paulson School of Engineering and Applied Sciences. He is a citizen of both Israel and the United States. Career He co-authored, with Sanjeev Arora, ''Computational Complexity: A Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
