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Hash Chain
A hash chain is the successive application of a cryptographic hash function to a piece of data. In computer security, a hash chain is a method to produce many one-time keys from a single key or password. For non-repudiation a hash function can be applied successively to additional pieces of data in order to record the chronology of data's existence. Definition A hash chain is a successive application of a cryptographic hash function h to a string x. For example, h(h(h(h(x)))) gives a hash chain of length 4, often denoted h^(x) Applications Leslie LamportL. Lamport, “Password Authentication with Insecure Communication”, Communications of the ACM 24.11 (November 1981), pp 770-772/ref> suggested the use of hash chains as a password protection scheme in an insecure environment. A server which needs to provide authentication may store a hash chain rather than a plain text password and prevent theft of the password in transmission or theft from the server. For example, ...
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Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output result ( hash value) for a random input string ("message") is 2^ (like for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is unfeasible, unless the value is selected from a known pre-calculated dictionary (" rainbow table"). The ''resistance'' to such search is quantified as security strength, a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits. A ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known; * finding any pair of different m ...
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Hash-based Cryptography
Hash-based cryptography is the generic term for constructions of cryptographic primitives based on the security of hash functions. It is of interest as a type of post-quantum cryptography. So far, hash-based cryptography is used to construct digital signatures schemes such as the Merkle signature scheme, zero knowledge and computationally integrity proofs, such as the zk-STARKScalable, transparent, and post-quantum secure computational integrity
Ben-Sasson, Eli and Bentov, Iddo and Horesh, Yinon and Riabzev, Michael, 2018
proof system and range proofs over issued credentials via the HashWires protocol. Hash-based signature schemes combine a one-time signature scheme, such as a

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Linked Timestamping
Linked timestamping is a type of trusted timestamping where issued time-stamps are related to each other. Description Linked timestamping creates time-stamp tokens which are dependent on each other, entangled in some authenticated data structure. Later modification of the issued time-stamps would invalidate this structure. The temporal order of issued time-stamps is also protected by this data structure, making backdating of the issued time-stamps impossible, even by the issuing server itself. The top of the authenticated data structure is generally ''published'' in some hard-to-modify and widely witnessed media, like printed newspaper or public blockchain. There are no (long-term) private keys in use, avoiding PKI-related risks. Suitable candidates for the authenticated data structure include: * Linear hash chain * Merkle tree (binary hash tree) * Skip list The simplest linear hash chain-based time-stamping scheme is illustrated in the following diagram: The linking-based ...
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Key Stretching
In cryptography, key stretching techniques are used to make a possibly weak key, typically a password or passphrase, more secure against a brute-force attack by increasing the resources (time and possibly space) it takes to test each possible key. Passwords or passphrases created by humans are often short or predictable enough to allow password cracking, and key stretching is intended to make such attacks more difficult by complicating a basic step of trying a single password candidate. Key stretching also improves security in some real-world applications where the key length has been constrained, by mimicking a longer key length from the perspective of a brute-force attacker. There are several ways to perform key stretching. One way is to apply a cryptographic hash function or a block cipher repeatedly in a loop. For example, in applications where the key is used for a cipher, the key schedule in the cipher may be modified so that it takes a specific length of time to perform. ...
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Hash List
In computer science, a hash list is typically a list of hashes of the data blocks in a file or set of files. Lists of hashes are used for many different purposes, such as fast table lookup (hash tables) and distributed databases (distributed hash tables). A hash list is an extension of the concept of hashing an item (for instance, a file). A hash list is a subtree of a Merkle tree. Root hash Often, an additional hash of the hash list itself (a ''top hash'', also called ''root hash'' or ''master hash'') is used. Before downloading a file on a p2p network, in most cases the top hash is acquired from a trusted source, for instance a friend or a web site that is known to have good recommendations of files to download. When the top hash is available, the hash list can be received from any non-trusted source, like any peer in the p2p network. Then the received hash list is checked against the trusted top hash, and if the hash list is damaged or fake, another hash list from another ...
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Challenge–response Authentication
In computer security, challenge–response authentication is a family of protocols in which one party presents a question ("challenge") and another party must provide a valid answer ("response") to be authenticated. The simplest example of a challenge–response protocol is password authentication, where the challenge is asking for the password and the valid response is the correct password. An adversary who can eavesdrop on a password authentication can then authenticate itself by reusing the intercepted password. One solution is to issue multiple passwords, each of them marked with an identifier. The verifier can then present an identifier, and the prover must respond with the correct password for that identifier. Assuming that the passwords are chosen independently, an adversary who intercepts one challenge–response message pair has no clues to help with a different challenge at a different time. For example, when other communications security methods are unavailable, th ...
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Bitcoin
Bitcoin (abbreviation: BTC; sign: ₿) is a decentralized digital currency that can be transferred on the peer-to-peer bitcoin network. Bitcoin transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. The cryptocurrency was invented in 2008 by an unknown person or group of people using the name Satoshi Nakamoto. The currency began use in 2009, when its implementation was released as open-source software. The word "''bitcoin''" was defined in a white paper published on October 31, 2008. It is a compound of the words ''bit'' and ''coin''. The legality of bitcoin varies by region. Nine countries have fully banned bitcoin use, while a further fifteen have implicitly banned it. A few governments have used bitcoin in some capacity. El Salvador has adopted Bitcoin as legal tender, although use by merchants remains low. Ukraine has accepted cryptocurrency donations to fund the resistance to the 2022 Rus ...
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Blockchain
A blockchain is a type of distributed ledger technology (DLT) that consists of growing lists of records, called ''blocks'', that are securely linked together using cryptography. Each block contains a cryptographic hash of the previous block, a timestamp, and transaction data (generally represented as a Merkle tree, where data nodes are represented by leaves). The timestamp proves that the transaction data existed when the block was created. Since each block contains information about the previous block, they effectively form a ''chain'' (compare linked list data structure), with each additional block linking to the ones before it. Consequently, blockchain transactions are irreversible in that, once they are recorded, the data in any given block cannot be altered retroactively without altering all subsequent blocks. Blockchains are typically managed by a peer-to-peer (P2P) computer network for use as a public distributed ledger, where nodes collectively adhere to a conse ...
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Extended Merkle Signature Scheme
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar Fields a ...
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Cryptographic Hash
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with fixed size of n bits) that has special properties desirable for cryptography: * the probability of a particular n-bit output result ( hash value) for a random input string ("message") is 2^ (like for any good hash), so the hash value can be used as a representative of the message; * finding an input string that matches a given hash value (a ''pre-image'') is unfeasible, unless the value is selected from a known pre-calculated dictionary ("rainbow table"). The ''resistance'' to such search is quantified as security strength, a cryptographic hash with n bits of hash value is expected to have a ''preimage resistance'' strength of n bits. A ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of finding a second message that matches the given hash value when one message is already known; * finding any pair of different mes ...
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Security Strength
In cryptography, security level is a measure of the strength that a cryptographic primitive — such as a cipher or hash function — achieves. Security level is usually expressed as a number of " bits of security" (also security strength), where ''n''-bit security means that the attacker would have to perform 2''n'' operations to break it, but other methods have been proposed that more closely model the costs for an attacker. This allows for convenient comparison between algorithms and is useful when combining multiple primitives in a hybrid cryptosystem, so there is no clear weakest link. For example, AES-128 ( key size 128 bits) is designed to offer a 128-bit security level, which is considered roughly equivalent to a RSA using 3072-bit key. In this context, security claim or target security level is the security level that a primitive was initially designed to achieve, although "security level" is also sometimes used in those contexts. When attacks are found that ha ...
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