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JH (hash Function)
JH is a cryptographic hash function submitted to the NIST hash function competition by Hongjun Wu. Though chosen as one of the five finalists of the competition, in 2012 JH ultimately lost to NIST hash candidate Keccak. JH has a 1024-bit state, and works on 512-bit input blocks. Processing an input block consists of three steps: # XOR the input block into the left half of the state. # Apply a 42-round unkeyed permutation (encryption function) to the state. This consists of 42 repetitions of: ## Break the input into 256 4-bit blocks, and map each through one of two 4-bit S-boxes, the choice being made by a 256-bit round-dependent key schedule. Equivalently, combine each input block with a key bit, and map the result through a 5→4 bit S-box. ## Mix adjacent 4-bit blocks using a maximum distance separable code over GF(24). ## Permute 4-bit blocks so that they will be adjacent to different blocks in following rounds. # XOR the input block into the right half of the state. The re ...
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Hongjun Wu
Hongjun Laozu () lit. "Ancestor of the Great Balance" is a deity in Chinese folk religion and Taoism, teacher of the Three Pure Ones in Taoist mythology. ''Hongjun'' is a graphic variant of ''hungjun'' () "primordial nature", as used in the Chinese idiom ''Xian you hongjun hou you tian'' "First there was Hongjun and then there was Heaven". Daoists mythologize Hongjun Laozu as the ancestor of ''xian'' "trancendents; immortals" and use the honorific name Hongyuan Laozu () "Great Primal Ancestor". In Chinese creation myths, ''hongyuan'' or is a cosmological term for "the universe before the separation of heaven and earth". Some myths about the creator Pangu refer to Hongjun Laozu as Xuanxuan Shangren () "Mystery of Mysteries Saint" (a reference to the ''Daodejing'', "Mystery or mysteries, the gate of all wonders!"). Hongjun Laozu is also referred to as Hunyuan Laozu ( - "Ancestor of Original Chaos"). Myth Hongjun Laozu has hardly been the subject of academic studies and th ...
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Sponge Function
Sponges or sea sponges are primarily marine invertebrates of the animal phylum Porifera (; meaning 'pore bearer'), a basal clade and a sister taxon of the diploblasts. They are sessile filter feeders that are bound to the seabed, and are one of the most ancient members of macrobenthos, with many historical species being important reef-building organisms. Sponges are multicellular organisms consisting of jelly-like mesohyl sandwiched between two thin layers of cells, and usually have tube-like bodies full of pores and channels that allow water to circulate through them. They have unspecialized cells that can transform into other types and that often migrate between the main cell layers and the mesohyl in the process. They do not have complex nervous, digestive or circulatory systems. Instead, most rely on maintaining a constant water flow through their bodies to obtain food and oxygen and to remove wastes, usually via flagella movements of the so-called " collar ce ...
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Cycles Per Byte
Encryption software is software that uses cryptography to prevent unauthorized access to digital information. Cryptography is used to protect digital information on computers as well as the digital information that is sent to other computers over the Internet. Classification There are many software products which provide encryption. Software encryption uses a cipher to obscure the content into ciphertext. One way to classify this type of software is the type of cipher used. Ciphers can be divided into two categories: public key ciphers (also known as asymmetric ciphers), and symmetric key ciphers. Encryption software can be based on either public key or symmetric key encryption. Another way to classify software encryption is to categorize its purpose. Using this approach, software encryption may be classified into software which encrypts " data in transit" and software which encrypts "data at rest". Data in transit generally uses public key ciphers, and data at rest generally uses ...
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Core 2
Intel Core 2 is a processor family encompassing a range of Intel's mainstream 64-bit x86-64 single-, dual-, and quad-core microprocessors based on the Core microarchitecture. The single- and dual-core models are single- die, whereas the quad-core models comprise two dies, each containing two cores, packaged in a multi-chip module. The Core 2 range is the last flagship range of Intel desktop processors to use a front-side bus (FSB). The introduction of Core 2 relegated the Pentium brand to the mid-range market, and reunified laptop and desktop CPU lines for marketing purposes under the same product name, which were formerly divided into the Pentium 4, Pentium D, and Core Solo/Duo brands. The ''Core 2'' processor line was introduced on July 27, 2006, comprising the ''Duo'' ( dual-core) and ''Extreme'' (dual- or quad-core CPUs for enthusiasts), and in 2007, the ''Quad'' ( quad-core) and ''Solo'' ( single-core) sub-brands. Intel Core 2 processors with vPro technology (desig ...
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Preimage Attack
In cryptography, a preimage attack on cryptographic hash functions tries to find a message that has a specific hash value. A cryptographic hash function should resist attacks on its preimage (set of possible inputs). In the context of attack, there are two types of preimage resistance: * ''preimage resistance'': for essentially all pre-specified outputs, it is computationally infeasible to find any input that hashes to that output; i.e., given , it is difficult to find an such that . * ''second-preimage resistance'': for a specified input, it is computationally infeasible to find another input which produces the same output; i.e., given , it is difficult to find a second input such that . These can be compared with a collision resistance, in which it is computationally infeasible to find any two distinct inputs , that hash to the same output; i.e., such that . Collision resistance implies second-preimage resistance. Second-preimage resistance implies preimage resistance only ...
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Cryptographic Hash Function
A cryptographic hash function (CHF) is a hash algorithm (a map (mathematics), map of an arbitrary binary string to a binary string with a fixed size of n bits) that has special properties desirable for a cryptography, cryptographic application: * the probability of a particular n-bit output result (hash value) for a random input string ("message") is 2^ (as 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 infeasible, ''assuming all input strings are equally likely.'' 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, unless the space of possible input values is significantly smaller than 2^ (a practical example can be found in ); * a ''second preimage'' resistance strength, with the same expectations, refers to a similar problem of f ...
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NIST Hash Function Competition
The NIST hash function competition was an open competition held by the US National Institute of Standards and Technology (NIST) to develop a new hash function called SHA-3 to complement the older SHA-1 and SHA-2. The competition was formally announced in the ''Federal Register'' on November 2, 2007. "NIST is initiating an effort to develop one or more additional hash algorithms through a public competition, similar to the development process for the Advanced Encryption Standard (AES)." The competition ended on October 2, 2012, when NIST announced that Keccak would be the new SHA-3 hash algorithm. The winning hash function has been published as NIST FIPS 202 the "SHA-3 Standard", to complement FIPS 180-4, the '' Secure Hash Standard''. The NIST competition has inspired other competitions such as the Password Hashing Competition. Process Submissions were due October 31, 2008 and the list of candidates accepted for the first round was published on December 9, 2008. NIST held ...
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Keccak
SHA-3 (Secure Hash Algorithm 3) is the latest member of the Secure Hash Algorithm family of standards, released by NIST on August 5, 2015. Although part of the same series of standards, SHA-3 is internally different from the MD5-like structure of SHA-1 and SHA-2. SHA-3 is a subset of the broader cryptographic primitive family Keccak ( or ), designed by Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche, building upon RadioGatún. Keccak's authors have proposed additional uses for the function, not (yet) standardized by NIST, including a stream cipher, an authenticated encryption system, a "tree" hashing scheme for faster hashing on certain architectures, and AEAD ciphers Keyak and Ketje. Keccak is based on a novel approach called sponge construction. Sponge construction is based on a wide random function or random permutation, and allows inputting ("absorbing" in sponge terminology) any amount of data, and outputting ("squeezing") any amount of data, ...
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NIST
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into physical science laboratory programs that include nanoscale science and technology, engineering, information technology, neutron research, material measurement, and physical measurement. From 1901 to 1988, the agency was named the National Bureau of Standards. History Background The Articles of Confederation, ratified by the colonies in 1781, provided: The United States in Congress assembled shall also have the sole and exclusive right and power of regulating the alloy and value of coin struck by their own authority, or by that of the respective states—fixing the standards of weights and measures throughout the United States. Article 1, section 8, of the Constitution of the United States, ratified in 1789, granted these powers to the new Co ...
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S-box
In cryptography, an S-box (substitution-box) is a basic component of symmetric key algorithms which performs substitution. In block ciphers, they are typically used to obscure the relationship between the key and the ciphertext, thus ensuring Claude Shannon, Shannon's property of confusion and diffusion, confusion. Mathematically, an S-box is a nonlinear vectorial Boolean function. In general, an S-box takes some number of input bits, ''m'', and transforms them into some number of output bits, ''n'', where ''n'' is not necessarily equal to ''m''. An ''m''×''n'' S-box can be implemented as a lookup table with 2''m'' words of ''n'' bits each. Fixed tables are normally used, as in the Data Encryption Standard (DES), but in some ciphers the tables are generated dynamically from the cryptographic key, key (e.g. the Blowfish (cipher), Blowfish and the Twofish encryption algorithms). Example One good example of a fixed table is the S-box from DES (S5), mapping 6-bit input into a 4-bi ...
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Maximum Distance Separable Code
In coding theory, the Singleton bound, named after the American mathematician Richard Collom Singleton (1928–2007), is a relatively crude upper bound on the size of an arbitrary block code C with block length n, size M and minimum distance d. It is also known as the Joshibound proved by and even earlier by Komamiya. Statement of the bound The minimum distance of a set C of codewords of length n is defined as d = \min_ d(x,y) where d(x,y) is the Hamming distance between x and y. The expression A_(n,d) represents the maximum number of possible codewords in a q-ary block code of length n and minimum distance d. Then the Singleton bound states that A_q(n,d) \leq q^. Proof First observe that the number of q-ary words of length n is q^n, since each letter in such a word may take one of q different values, independently of the remaining letters. Now let C be an arbitrary q-ary block code of minimum distance d. Clearly, all codewords c \in C are distinct. If we puncture the co ...
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Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field (mathematics), field that contains a finite number of Element (mathematics), elements. As with any field, a finite field is a Set (mathematics), set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are the integers mod n, integers mod p when p is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number p and every positive integer k there are fields of order p^k. All finite fields of a given order are isomorphism, isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set that is a fiel ...
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