In mathematics, a negligible function is a function μ : N → R {\displaystyle \mu :\mathbb {N} \to \mathbb {R} } such that for every positive integer c...

null sets can be ignored when studying the integral of a measurable function. Negligible sets define several useful concepts that can be applied in various...

which is negligible (for the Lebesgue measure). Thomae's function, a variation that is discontinuous only at the rational numbers "Dirichlet-function", Encyclopedia...

denotes some negligible function, and n is the security parameter. There are two different types of collision resistance. A hash function has weak collision...

{1}{2}}+\gamma }} . Definition (negligible function): In the proof of this theorem, we need a definition of a negligible function. A function ϵ ( n ) {\displaystyle...

collision—distinct values x, y such that f(x) = f(y)—with non-negligible probability. If f is a one-way function, then the inversion of f would be a problem whose...

In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if X {\displaystyle X} is a set, "almost all elements of X...

close if Δ ( X k , Y k ) {\displaystyle \Delta (X_{k},Y_{k})} is a negligible function in k {\displaystyle k} . Total variation distance (sometimes just...

sub-systems with negligible interaction energy, that is, we can assume the particles are essentially non-interacting. If the partition functions of the sub-systems...

probabilistic polynomial time algorithm A, the following quantity is a negligible function in n: δ ( n ) = | Pr x ← D n [ A ( x ) = 1 ] − Pr x ← E n [ A ( x...

statistically close, meaning that their statistical difference is a negligible function. We speak of computational zero-knowledge if no efficient algorithm...

will only win with negligible probability in the statistical security parameter since it only engages in the protocol once. Key size Negligible function...

\epsilon (k)} is a negligible function in the security parameter k {\displaystyle k} , i.e., for every (nonzero) polynomial function poly() there exists...

which kind of oracle is given to her is negligible in n {\displaystyle n} . In an oblivious pseudorandom function, abbreviated OPRF, information is concealed...

{\displaystyle G=M/N} of "moderate" modulo "negligible" nets of functions, where "moderateness" and "negligibility" refers to growth with respect to the index...

1\}^{k}}[A(G(x))=1]-\Pr _{r\gets \{0,1\}^{p(k)}}[A(r)=1]\right|<\mu (k)} for some negligible function μ {\displaystyle \mu } . (The notation x ← X {\displaystyle x\gets...

cryptography a universal one-way hash function (UOWHF, often pronounced "woof") is a type of universal hash function of particular importance to cryptography...

In mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric...

possible to amplify soundness until the soundness error becomes negligible function relative to the running time of the verifier. This is achieved by...

real-valued random variable. The general form of its probability density function is f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac...

In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b x 4 + c x 3 + d x 2 + e x + f , {\displaystyle g(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f...

given fk(x), find a pre-image x' such that fk(x' ) = fk(x)) is negligible. If each function in the collection above is a one-way permutation, then the collection...

polynomial-time adversary A, there is a negligible function ε ( k ) {\displaystyle \varepsilon (k)} (i.e., a function that eventually grows slower than 1...

equivalence class [ f ] {\displaystyle [f]} of bounded measurable functions modulo negligible functions a representative— which is henceforth written T ( [ f ]...

more likely to abuse a resource if the cost of abusing the resource is negligible: the underlying reason spam has become so rampant is that sending an e-mail...

etc.), called fermions, in thermodynamic equilibrium. For the case of negligible interaction between particles, the system can be described in terms of...

correlation functions, the equal-time correlation function is non-zero for all lattice points below the critical temperature, and is non-negligible for only...

A head-related transfer function (HRTF) is a response that characterizes how an ear receives a sound from a point in space. As sound strikes the listener...

Multiscale Green's function (MSGF) is a generalized and extended version of the classical Green's function (GF) technique for solving mathematical equations...

source of the gravitational field, this variation in field strength is negligible and we can assume that the force of gravity on a particular object is...