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Memory-hard Function
In cryptography, a memory-hard function (MHF) is a function that costs a significant amount of memory to evaluate. It differs from a memory-bound function, which incurs cost by slowing down computation through memory latency. MHFs can be used as proof of work. Memory hard measure There are different ways to measure the memory hardness of a function, and a commonly seen measure is Cumulative Memory Complexity (CMC). In a parallel model, CMC is the sum of the memory required to compute a function over every time step of the computation. Other viable measures are integrating memory against physical time., and measuring memory bandwidth consumption on a memory bus. Functions requiring high memory bandwidth are sometimes referred to as "bandwidth-hard functions." Motivation MHFs were designed to use a lot of memory instead of a different resource, such as CPU cycles. Bitcoin's proof-of-work used repeated evaluation of the SHA-2 function, but modern general-purpose processors, suc ...
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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 ...
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Random-access Memory
Random-access memory (RAM; ) is a form of computer memory that can be read and changed in any order, typically used to store working Data (computing), data and machine code. A Random access, random-access memory device allows data items to be read (computer), read or written in almost the same amount of time irrespective of the physical location of data inside the memory, in contrast with other direct-access data storage media (such as hard disks, CD-RWs, DVD-RWs and the older Magnetic tape data storage, magnetic tapes and drum memory), where the time required to read and write data items varies significantly depending on their physical locations on the recording medium, due to mechanical limitations such as media rotation speeds and arm movement. RAM contains multiplexer, multiplexing and demultiplexing circuitry, to connect the data lines to the addressed storage for reading or writing the entry. Usually more than one bit of storage is accessed by the same address, and RAM ...
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Memory-bound Function
Memory bound refers to a situation in which the time to complete a given computational problem is decided primarily by the amount of free memory required to hold the working data. This is in contrast to algorithms that are compute-bound, where the number of elementary computation steps is the deciding factor. Memory and computation boundaries can sometimes be traded against each other, e.g. by saving and reusing preliminary results or using lookup tables. Memory-bound functions and memory functions Memory-bound functions and memory functions are related in that both involve extensive memory access, but a distinction exists between the two. Memory functions use a dynamic programming technique called memoization in order to relieve the inefficiency of recursion that might occur. It is based on the simple idea of calculating and storing solutions to subproblems so that the solutions can be reused later without recalculating the subproblems again. The best known example that tak ...
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Proof Of Work
Proof of work (PoW) is a form of Cryptography, cryptographic proof (truth), proof in which one party (the ''prover'') proves to others (the ''verifiers'') that a certain amount of a specific computational effort has been expended. Verifiers can subsequently confirm this expenditure with minimal effort on their part. The concept was invented by Moni Naor and Cynthia Dwork in 1993 as a way to deter denial-of-service attacks and other service abuses such as spam (electronic), spam on a network by requiring some work from a service requester, usually meaning processing time by a computer. The term "proof of work" was first coined and formalized in a 1999 paper by Markus Jakobsson and Ari Juels. Proof of work was later popularized by Bitcoin as a foundation for Consensus (computer science), consensus in a permissionless decentralized network, in which miners compete to append blocks and mint new currency, each miner experiencing a success probability proportional to the computationa ...
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Bandwidth (computing)
In computing, bandwidth is the maximum rate of data transfer across a given path. Bandwidth may be characterized as network bandwidth, data bandwidth, or digital bandwidth. This definition of ''bandwidth'' is in contrast to the field of signal processing, wireless communications, modem data transmission, digital communications, and electronics, in which ''bandwidth'' is used to refer to analog signal bandwidth measured in hertz, meaning the frequency range between lowest and highest attainable frequency while meeting a well-defined impairment level in signal power. The actual bit rate that can be achieved depends not only on the signal bandwidth but also on the noise on the channel. Network capacity The term ''bandwidth'' sometimes defines the net bit rate 'peak bit rate', 'information rate,' or physical layer 'useful bit rate', channel capacity, or the maximum throughput of a logical or physical communication path in a digital communication system. For example, bandwidth test ...
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Cryptology EPrint Archive
The Cryptology ePrint Archive is an electronic archive (eprint) of new results in the field of cryptography, maintained by the International Association for Cryptologic Research. It contains articles covering many of the most recent advances in cryptography, that did not necessarily undergo any refereeing process (yet). See also * arXiv * Electronic Colloquium on Computational Complexity The Electronic Colloquium on Computational Complexity (ECCC) is an electronic archive of research papers in computational complexity theory, a branch of computer science.... The intention of the ECCC is to provide a fast publication service interme ... External links ePrint Archive Cryptography journals Publications with year of establishment missing Eprint archives Open-access archives {{International Association for Cryptologic Research ...
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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 Russ ...
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SHA-2
SHA-2 (Secure Hash Algorithm 2) is a set of cryptographic hash functions designed by the United States National Security Agency (NSA) and first published in 2001. They are built using the Merkle–Damgård construction, from a one-way compression function itself built using the Davies–Meyer structure from a specialized block cipher. SHA-2 includes significant changes from its predecessor, SHA-1. The SHA-2 family consists of six hash functions with digests (hash values) that are 224, 256, 384 or 512 bits: SHA-224, SHA-256, SHA-384, SHA-512, SHA-512/224, SHA-512/256. SHA-256 and SHA-512 are novel hash functions computed with eight 32-bit and 64-bit words, respectively. They use different shift amounts and additive constants, but their structures are otherwise virtually identical, differing only in the number of rounds. SHA-224 and SHA-384 are truncated versions of SHA-256 and SHA-512 respectively, computed with different initial values. SHA-512/224 and SHA-512/256 are also trunca ...
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Central Processing Unit
A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, and input/output (I/O) operations specified by the instructions in the program. This contrasts with external components such as main memory and I/O circuitry, and specialized processors such as graphics processing units (GPUs). The form, design, and implementation of CPUs have changed over time, but their fundamental operation remains almost unchanged. Principal components of a CPU include the arithmetic–logic unit (ALU) that performs arithmetic and logic operations, processor registers that supply operands to the ALU and store the results of ALU operations, and a control unit that orchestrates the fetching (from memory), decoding and execution (of instructions) by directing the coordinated operations of the ALU, registers and other co ...
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Application-specific Integrated Circuit
An application-specific integrated circuit (ASIC ) is an integrated circuit (IC) chip customized for a particular use, rather than intended for general-purpose use, such as a chip designed to run in a digital voice recorder or a high-efficiency video codec. Application-specific standard product (ASSP) chips are intermediate between ASICs and industry standard integrated circuits like the 7400 series or the 4000 series. ASIC chips are typically fabricated using metal-oxide-semiconductor (MOS) technology, as MOS integrated circuit chips. As feature sizes have shrunk and design tools improved over the years, the maximum complexity (and hence functionality) possible in an ASIC has grown from 5,000 logic gates to over 100 million. Modern ASICs often include entire microprocessors, memory blocks including ROM, RAM, EEPROM, flash memory and other large building blocks. Such an ASIC is often termed a SoC (system-on-chip). Designers of digital ASICs often use a hardware descrip ...
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Scrypt
In cryptography, scrypt (pronounced "ess crypt") is a password-based key derivation function created by Colin Percival in March 2009, originally for the Tarsnap online backup service. The algorithm was specifically designed to make it costly to perform large-scale custom hardware attacks by requiring large amounts of memory. In 2016, the scrypt algorithm was published by IETF as RFC 7914. A simplified version of scrypt is used as a proof-of-work scheme by a number of cryptocurrencies, first implemented by an anonymous programmer called ArtForz in Tenebrix and followed by Fairbrix and Litecoin soon after. Introduction A password-based key derivation function (password-based KDF) is generally designed to be computationally intensive, so that it takes a relatively long time to compute (say on the order of several hundred milliseconds). Legitimate users only need to perform the function once per operation (e.g., authentication), and so the time required is negligible. However ...
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Argon2
Argon2 is a key derivation function that was selected as the winner of the 2015 Password Hashing Competition. It was designed by Alex Biryukov, Daniel Dinu, and Dmitry Khovratovich from the University of Luxembourg. The reference implementation of Argon2 is released under a Creative Commons CC0 license (i.e. public domain) or the Apache License 2.0, and provides three related versions: *Argon2d maximizes resistance to GPU cracking attacks. It accesses the memory array in a password dependent order, which reduces the possibility of time–memory trade-off (TMTO) attacks, but introduces possible side-channel attacks. *Argon2i is optimized to resist side-channel attacks. It accesses the memory array in a password independent order. *Argon2id is a hybrid version. It follows the Argon2i approach for the first half pass over memory and the Argon2d approach for subsequent passes. The RFC recommends using Argon2id if you do not know the difference between the types or you consider side ...
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