###### Pseudorandom Functions

- Keyed cryptographic hash functions are popular examples of pseudorandom functions used for key derivation. (wikipedia.org)

###### Mathematics

- In mathematics, more specifically differential algebra, a p-derivation (for p a prime number) on a ring R, is a mapping from R to R that satisfies certain conditions outlined directly below. (wikipedia.org)
- In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. (wikipedia.org)
- The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M). Derivations occur in many different contexts in diverse areas of mathematics. (wikipedia.org)
- The format was originally introduced as a way for presenting proofs in programming logic, but was later adapted to provide a practical approach to presenting proofs and derivations in mathematics education including exact formalisms. (wikipedia.org)
- Structured derivations: a unified proof style for teaching mathematics. (wikipedia.org)
- An Empirical Evaluation of Structured Derivations in High School Mathematics. (wikipedia.org)

###### Derivative

- The partial derivative with respect to a variable is an R-derivation on the algebra of real-valued differentiable functions on Rn. (wikipedia.org)
- The Pincherle derivative is an example of a derivation in abstract algebra. (wikipedia.org)
- Examples of anti-derivations include the exterior derivative and the interior product acting on differential forms. (wikipedia.org)

###### differential algebra

- The notion of a p-derivation is related to that of a derivation in differential algebra. (wikipedia.org)
- If the algebra A is noncommutative, then the commutator with respect to an element of the algebra A defines a linear endomorphism of A to itself, which is a derivation over K. An algebra A equipped with a distinguished derivation d forms a differential algebra, and is itself a significant object of study in areas such as differential Galois theory. (wikipedia.org)

###### proofs

- Structured derivations (SD) is a logic-based format for presenting mathematical solutions and proofs created by Prof. Ralph-Johan Back and Joakim von Wright at Åbo Akademi University, Turku, Finland. (wikipedia.org)

###### Examples

- Examples of such key derivation functions include KDF1, defined in IEEE Std 1363-2000, and similar functions in ANSI X9.42. (wikipedia.org)
- The following three examples will be used to illustrate the most central features of structured derivations. (wikipedia.org)

###### displaystyle

- If ( R , δ ) {\displaystyle (R,\delta )} is a ring with a p-derivation, then the map σ ( x ) := x p + p δ ( x ) {\displaystyle \sigma (x):=x^{p}+p\delta (x)} defines a ring endomorphism which is a lift of the frobenius endomorphism. (wikipedia.org)
- If R is any p-torsion free ring and σ : R → R {\displaystyle \sigma :R\to R} is a lift of the Frobenius endomorphism then δ ( x ) = σ ( x ) − x p p {\displaystyle \delta (x)={\frac {\sigma (x)-x^{p}}{p}}} defines a p-derivation. (wikipedia.org)
- Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: D ( a b ) = D ( a ) b + a D ( b ) . {\displaystyle D(ab)=D(a)b+aD(b). (wikipedia.org)
- If A is a K-algebra, for K a ring, and D : A → A {\displaystyle D:A\to A} is a K-derivation, then If A has a unit 1, then D(1)=D(12)=2D(1), so that D(1)=0. (wikipedia.org)
- There is an A-module Ω A / K {\displaystyle \Omega _{A/K}} (called the Kähler differentials) with a K-derivation d : A → Ω A / K {\displaystyle d:A\to \Omega _{A/K}} through which any derivation D : A → M {\displaystyle D:A\to M} factors. (wikipedia.org)

###### derive

- A derivation-relevant character argument of an operation is an argument used to derive the collation of the operator's result. (oracle.com)
- State derivation has been understood since the 1970s as an attempt within Marxism and neo-Marxism to explain the emergence and extent of the state and its law within the bourgeois, modern economic system and therewith to derive the relationship between economics and politics from the structure of capitalist production. (wikipedia.org)
- Key derivation functions are also used in applications to derive keys from secret passwords or passphrases, which typically do not have the desired properties to be used directly as cryptographic keys. (wikipedia.org)

###### mathematical

- In computer science, program derivation is the derivation of a program from its specification, by mathematical means. (wikipedia.org)
- A structured derivation has a precise mathematical interpretation, and the syntax and the layout are precisely defined. (wikipedia.org)

###### Functions

- citation needed] Modern password-based key derivation functions, such as PBKDF2 (specified in RFC 2898), use a cryptographic hash, such as SHA-2, more salt (e.g. 64 bits and greater) and a high iteration count (often tens or hundreds of thousands). (wikipedia.org)

###### occur

- Derivation can also occur without any change of form:telephone (noun) and to telephone. (wikipedia.org)
- It may involve the use of an affix (such as with happy → happiness, employ → employee), or it may occur via conversion (such as with the derivation of the noun run from the verb to run). (wikipedia.org)

###### Guidelines

- James, J. and Ramanathan, R., "Spacecraft Water Exposure Guidelines: Derivation by Toxicological Risk Assessment Methods," SAE Technical Paper 2002-01-2536, 2002, https://doi.org/10.4271/2002-01-2536 . (sae.org)

###### Definition

- For each guideline discussed, a definition and description of the derivation and applicability or intended use are provided to enable you to determine if a comparison value is appropriate to use for evaluating site-specific conditions. (cdc.gov)
- Definition/Derivation. (cdc.gov)

###### example

- Generally speaking, inflection applies in more or less regular patterns to all members of a part of speech (for example, nearly every English verb adds -s for the third person singular present tense), while derivation follows less consistent patterns (for example, the nominalizing suffix -ity can be used with the adjectives modern and dense, but not with open or strong). (wikipedia.org)
- For example, when the affix -er, is added to an adjective, as in small-er, it acts as an inflection, but when added to a verb, as in cook-er, it acts as a derivation. (wikipedia.org)

###### Table

- In order to assist Code users in the transition to the new Code's organization, the Derivation Table indicates where chapters and articles of the 1975 Code have been included in the 2011 Code, or the reason for exclusion. (ecode360.com)
- An argument that is a format model, a pattern, a flag string, or a key into a virtual table of system information is not considered a derivation-relevant argument. (oracle.com)

###### important

- However, it is important to note that derivations and inflections can share homonyms, that being, morphemes that have the same sound, but not the same meaning. (wikipedia.org)
- The intent of this article is to document the important steps in these derivations. (wikipedia.org)
- The intent of this article is to highlight the important points of the derivation of the Navier-Stokes equations as well as its application and formulation for different families of fluids. (wikipedia.org)

###### exact

- The derivation is exact and axonal delays and memory effects such as refractory behavior are taken into account. (springer.com)

###### simple

- Solving a simple equation illustrates the basic structure of a structured derivation. (wikipedia.org)

###### values

- The following are the collation derivation rules for operations that return character values and have derivation-relevant arguments. (oracle.com)

###### zero

- An operator may have zero or more derivation-relevant character arguments, and zero or more other character arguments, such as flags or other control information not directly interacting with the derivation-relevant arguments. (oracle.com)
- That is known as conversion, or zero derivation. (wikipedia.org)

###### order

- I'm hoping to get a further insight on the derivation of the variation of parameters method used in ordinary differential equations to solve linear second order equations. (physicsforums.com)

###### known

- When writing a proof or a solution as a structured derivation, all known information is listed in the beginning as assumptions. (wikipedia.org)

###### process

- The process of determining the collation of a character result of an SQL operation is called collation derivation. (oracle.com)

###### Program

- Terms that are roughly synonymous with program derivation are: transformational programming, algorithmics, deductive programming. (wikipedia.org)
- The Bird-Meertens Formalism is an approach to program derivation. (wikipedia.org)

###### follows

- It follows that the adjoint representation of a Lie algebra is a derivation on that algebra. (wikipedia.org)

###### respect

- In that respect, derivation differs from compounding by which free morphemes are combined (lawsuit, Latin professor). (wikipedia.org)

###### word

- Derivation can be contrasted with inflection, in that derivation produces a new word (a distinct lexeme), whereas inflection produces grammatical variants of the same word. (wikipedia.org)
- Derivation can be contrasted with other types of word formation such as compounding. (wikipedia.org)

###### original

- Such use may be expressed as DK=KDF(Key, Salt, Iterations) where DK is the derived key, KDF is the key derivation function, Key is the original key or password, Salt is a random number which acts as cryptographic salt, and Iterations refers to the number of iterations of a sub-function. (wikipedia.org)

###### approach

- The calculational approach is limited to writing proof fragments, and longer derivations are commonly decomposed into several separate subproofs. (wikipedia.org)

###### generally

- In such applications, it is generally recommended that the key derivation function be made deliberately slow so as to frustrate brute-force attack or dictionary attack on the password or passphrase input value. (wikipedia.org)
- More generally, if M is an A-bimodule, a K-linear map D : A → M that satisfies the Leibniz law is also called a derivation. (wikipedia.org)
- more generally it is a derivation on the tensor algebra of a manifold. (wikipedia.org)

###### time

- This derivation only uses the star's coordinates at the time of emission, and therefore has the formal advantage there is no place for the relative velocity of the star towards the astronomer and therefore it is evident that the observed position doesn't depend on the star's velocity - provided that the resultant change of position is much smaller than the distance between star and Earth. (wikipedia.org)

###### seen

- Within the state-derivation debate the state is seen as a "structural component of the capitalist relations of production itself, its specific political form. (wikipedia.org)