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Movements, leaders, victories and the continuing fight for equality.
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Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In cryptography, a sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length. Sponge functions have both theoretical and practical uses. They can be used to model or implement many cryptographic primitives, including cryptographic hashes, message authentication codes, mask generation functions, stream ciphers, pseudo-random number generators, and authenticated encryption.[1]
A sponge function is built from three components:[2]
S is divided into two sections: one of size r (the bitrate) and the remaining part of size c (the capacity). These sections are denoted R and C respectively.
f produces a pseudorandom permutation of the states from S.
P appends enough bits to the input string so that the length of the padded input is a whole multiple of the bitrate, r. This means the input is segmented into blocks of r bits.
The sponge function "absorbs" (in the sponge metaphor) all blocks of a padded input string as follows:
The sponge function output is now ready to be produced ("squeezed out") as follows:
If less than r bits remain to be output, then R will be truncated (only part of R will be output).
Another metaphor describes the state memory as an "entropy pool", with input "poured into" the pool, and the transformation function referred to as "stirring the entropy pool".[3]
Note that input bits are never XORed into the C portion of the state memory, nor are any bits of C ever output directly. The extent to which C is altered by the input depends entirely on the transformation function f. In hash applications, resistance to collision or preimage attacks depends on C, and its size (the "capacity" c) is typically twice the desired resistance level.
It is also possible to absorb and squeeze in an alternating fashion.[1] This operation is called the duplex construction or duplexing. It can be the basis of a single pass authenticated encryption system. This have also been used as an efficient variant of the Fiat-Shamir transformation for some protocols.[4]
It is possible to omit the XOR operations during absorption, while still maintaining the chosen security level.[1] In this mode, in the absorbing phase, the next block of the input overwrites the R part of the state. This allows keeping a smaller state between the steps. Since the R part will be overwritten anyway, it can be discarded in advance, only the C part must be kept.
Sponge functions have both theoretical and practical uses. In theoretical cryptanalysis, a random sponge function is a sponge construction where f is a random permutation or transformation, as appropriate. Random sponge functions capture more of the practical limitations of cryptographic primitives than does the widely used random oracle model, in particular the finite internal state.[5]
The sponge construction can also be used to build practical cryptographic primitives. For example, the Keccak cryptographic sponge with a 1600-bit state has been selected by NIST as the winner in the SHA-3 competition. The strength of Keccak derives from the intricate, multi-round permutation f that its authors developed.[6] The RC4-redesign called Spritz refers to the sponge-construct to define the algorithm.
For other examples, a sponge function can be used to build authenticated encryption with associated data (AEAD),[3] as well as password hashing schemes.[7]
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Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In cryptography, a sponge function or sponge construction is any of a class of algorithms with finite internal state that take an input bit stream of any length and produce an output bit stream of any desired length. Sponge functions have both theoretical and practical uses. They can be used to model or implement many cryptographic primitives, including cryptographic hashes, message authentication codes, mask generation functions, stream ciphers, pseudo-random number generators, and authenticated encryption.
Sponges or sea sponges are primarily marine invertebrates of the animal phylum Porifera (; meaning 'pore bearer'). They are filter feeders that are typically bound to the seabed, being sessile. Sponges are one of the most ancient members of living seabed community (macrobenthos), with many species being important reef-builders. Some sponge species inhabit freshwater. 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 sponges rely on maintaining a constant water flow through their bodies to obtain food and oxygen and to remove waste products, usually via flagellar movements of the so-called "collar cells". Sponges may be the sister group to all other animals, although the evidence for this relationship remains inconclusive, and different studies may recover different placements between sponges and other animal clades. Fossil evidence of primitive sponges such as Otavia dates to as early as the Tonian period (around 800 Mya). The branch of zoology that studies sponges is spongiology. Historically, the skeletons of sea sponges were used as the cleaning tool of the same name, though this is no longer a common practice.
A cryptographic hash function (CHF) is a hash algorithm (a map of an arbitrary binary string to a binary string with a fixed size of n {\displaystyle n} bits) that has special properties desirable for cryptographic applications. Hashing is a one-directional mathematical operation which is quick to calculate, yet hard to reverse. Common uses include password storage and digital signatures. Even a small change in the input results in a very different hash, meaning that it functions as an efficient and consistent way to check if two copies of data or software match. Typically, the operation works on a block of input data; the hash output is then hashed with the next block, creating a new hash reflecting everything to that point; this action is repeated until the hash reflects everything through the final block. More technically: the probability of a particular n {\displaystyle n} -bit output result (hash value) for a random input string ("message") is 2 − n {\displaystyle 2^{-n}} (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 {\displaystyle n} bits of hash value is expected to have a preimage resistance strength of n {\displaystyle n} bits, unless the space of possible input values is significantly smaller than 2 n {\displaystyle 2^{n}} (a practical example can be found in § Attacks on hashed passwords); 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 messages that yield the same hash value (a collision) is also infeasible: a cryptographic hash is expected to have a collision resistance strength of n / 2 {\displaystyle n/2} bits (lower because of the birthday paradox). Cryptographic hash functions have many information-security applications, notably in digital signatures, message authentication codes (MACs), and other forms of authentication. They can also be used as ordinary hash functions, to index data in hash tables, for fingerprinting, to detect duplicate data or uniquely identify files, and as checksums to detect accidental data corruption. Indeed, in information-security contexts, cryptographic hash values are sometimes called (digital) fingerprints, checksums, (message) digests, or just hash values, even though all these terms stand for more general functions with rather different properties and purposes. Non-cryptographic hash functions are used in hash tables and to detect accidental errors; their constructions frequently provide no resistance to a deliberate attack. For example, a denial-of-service attack on hash tables is possible if the collisions are easy to find, as in the case of linear cyclic redundancy check (CRC) functions.
Skein is a cryptographic hash function and one of five finalists in the NIST hash function competition. Entered as a candidate to become the SHA-3 standard, the successor of SHA-1 and SHA-2, it ultimately lost to NIST hash candidate Keccak. The name Skein refers to how the Skein function intertwines the input, similar to a skein of yarn. Skein was designed to natively support arbitrary, variable-length outputs, so it can be considered an extendable-output function (XOF).
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.
