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Questions tagged [negligible]

Negligible means that something is so unimportant, that it isn't worth considering. For example, if a flaw in a cryptographic algorithm is considered to be negligible, it is insignificant to both the algorithm as well as it's security.

Negligible means that something is so unimportant, that it isn't worth considering. For example, if a flaw in a cryptographic algorithm is considered to be negligible, it is insignificant to both the algorithm as well as it's security.

In the complexity-based modern cryptography, a security scheme is provably secure if the probability of security failure (e.g., inverting a one-way function, distinguishing cryptographically strong pseudorandom bits from truly random bits) is negligible in terms of the input x cryptographic key length n.

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Property of negligible functions

Suppose that $\mu(n)$ is a negligible function, which means that for every $c>0$ there is some $N$ such that for all $n>N$ it holds that $\mu(n)\leq n^{-c}$. Now, imagine that some encryption scheme, signature scheme, or some cryptographic…
Daniel
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What does "overwhelming" mean in cryptography?

I found the term "overwhelming" when I study cryptography. According to the definition, we call $f$ overwhelming if $1-f$ is negligible. I already know the negligible function and its way to use but I don't understand why we consider the…
iomat
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Polynomial sum of negligible functions need not be negligible

Let $\{\epsilon_i\}_{n \in \mathbb{N}}$ be a sequence of negligible functions and $q(n)$ be a polynomial in $n$. Then $f(n) = \sum_{i = 1}^{q(n)} \epsilon_i(n)$ need not be a negligible function. Ideas A typical negligible function is $2^{-n}$.…
user1868607
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Unpacking the definition of negligible & non-negligible

There are several threads on this topic including: How is an epsilon of 1/1000 non-negligible? How to calculate if probability is negligible or not (and others) but I do not fully understand the answers in those threads. My question is: I would…
Max
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What are not non-negligible functions?

I had a brief look at "On Defining Proofs of Knowledge" by Bellare and Goldreich and I am a little confused by their definitions. I was under the impression a negligible function $f$ was defined as something like $$\forall\ polynomials\ p\ \exists…
Elias
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Is power of non-negligible function non-negligible?

If I have a probability which is > negl(n), i.e., non-negligible, will be this probability raised to the power of n also non-negligible?
JenyaKh
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Product of Negligible and Non-Negligible Functions

I know that the product of two negligible functions will always be negligible, but I'm wondering if it's possible for the product of two non-negligible functions to be a negligible function?
opposite-people
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Is inverse of a combination function negligible?

Can anyone help me in determining whether $1/{n\choose a}$ negligible function for sufficiently large value of $n$, say for example $n=p^2$ and $a=p$, for an integer $p$?
Gryel
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Negligible function defined as product of polynomial and a negligible function

How do I prove that a function $f_2$, defined as the product of a negligible function $f_1$ and a polynomial $p$, is itself negligible? $$f_2(n)= p_1(n)f_1(n)$$ I see $f_2$ as negligible simply because I know that if you have something that has a…
Nooby
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Is $\operatorname{negl}_1(n)-\operatorname{negl}_2(n) \leq \operatorname{negl}_3(n)$?

Is this statement $\operatorname{negl}_1(n)-\operatorname{negl}_2(n)\leq \operatorname{negl}_3(n)$ true for some negligible function $\operatorname{negl}_3$ and security parameter $n$?
Amir Amir
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How do you prove that if f(x) and g(x) are negligible, then f(x)/g(x) is not?

I can use an example: the case where we have $x$ such that $f(x)=g(x)$. The quotient is $1$, a non-negligible function. However, we can't conclude that all functions $f(x)/g(x)$ are also negligible. How can I formally prove this?
Akhil Dhir
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Proving negligible function

I was reading the following: The functions $2^{-n}, 2^{-\sqrt{n}}$ are negligible. However they approach zero at different rates. For example, we can look at the minimum value of $n$ for which each function is smaller than $\frac{1}{n^5}$ Solving…
MR.-c
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When is $p^n$ negligible? ($p$ may depend on $n$)

For what $p \in [0,1]$ would the function $p^n$ be negligible? Specifically; if $p$ is allowed to depend on $n$. If $p$ is a constant between 0 and 1, (say $p = \frac{1}{2}$), then it clearly is negligible. Judging from this plot, if one chooses $p…
Borage
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Why is repeating for polynomial time still negligible if one execution has negligible chance?

Goldreich justifies why we work with the term negligible by saying among other things "events that occur with negligible (in n) probability remain negligible even if the experiment is repeated for polynomially (in n) many times.". Now I want to…
killertoge
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