Questions tagged [statistical-distance]
The statistical-distance tag has no usage guidance.
11
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Noise flooding in Lattices
I noticed that in the paper [HLL24], the authors used the noise flooding technique to choose parameters and complete the proof.
But I am confused that why set $\sigma \ge 2^{\kappa+6}y$ to guarantee ...
- 31
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Prove equivalence of definitions of statistical distance
Let $P$ and $Q$ be two distributions over a finite set $U$.
Given I already proved the following definitions are equilivant:
$$
SD(P, Q) = \underset{S⊆U}{max} \ \left\{ \underset{x←P}{Pr} [x ∈ S] − \...
- 33
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A Smudging Lemma in Lattice
I saw a paper LLW21 in EUROCRYPT 2021 that used this lemma, but there was no proof or references.
How should this lemma be proved ？
- 311
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Modulo bias: How to compute statistical distance?
Assume we have two uniform distributions $X=U(\mathbb{Z}_m)$ and $Y=U(\mathbb{Z}_n) \bmod m$, for $m,n \in \mathbb{N}$.
The statistical distance is defined as:
$$
\Delta(X, Y) = \frac{1}{2} \sum_{a \...
- 687
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Statistical distance for multiplicative blinding
A common way to mask an integer $x$ in a range is to add a uniformly random integer $r$ from a much larger range. More formally, if $x$ lies in $[0,...,2^k)$ and $r$ in $[0,...,2^{k + l})$, then
$$\...
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What is a reasonable statistical distance bound in a SZK construction?
Many works, such as [YCX21] cite that $2^{-40}$ is a reasonable statistical distance for zero-knowledge proof based signatures, even when the security level is $\lambda = 128$.. I was wondering if ...
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ddh and statistical distance
Let $\mathbb{G}$ be a cyclic group of prime order q and generated by g. Let $D$ be the uniform distribution over $\mathbb{G}^3$. Let $D_{dh}$ be the uniform distribution over the set of all DH-triples ...
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Can two ciphertexts that decrypt to the same plaintext be statistically "distant"?
It might be a little dumb: I think it should be possible, if I encrypt a plaintext using the same public key twice, it should be possible to end up with two ciphertexts that for whom the statistical ...
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1
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Statistical Distance and Learning with Rounding
Given an integer $b$ modulo a prime $q$, one can define a `rounding’ function $\lfloor b\rceil_p$ for a prime $p$, $p<q$, as follows: $$\lfloor b\rceil_p = \lfloor \frac{p}{q}\cdot b\rceil\bmod p.$$...
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How to complete this proof of statistically indistinguishable distributions?
Given that:
$$ SD\bigg( (r, \langle r, s \rangle),(r, b) \bigg) < \mathrm{negl}(n)$$
where $SD$ stands for statistical distance, $r$ is random uniform in $\{0,1\}^n$, $s$ is random uniform in $S \...
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About the definition of distinguishing advantage and computational indistinguishability
Given a polynomial-time adversary $A$ with binary output, the distinguishing advantage of $A$ with respect two games $G, H$ is defined as
$$
\newcommand{\adv}{\mathbf{Adv}}
\newcommand{\pr}{\mathbf{Pr}...
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