差异性隐私的界限：理论到实践的探索
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"探索差异性隐私的隐私约束：从理论到实践"
本文主要探讨了差异性隐私（Differential Privacy）这一隐私保护的新范式，并着重分析了其隐私约束的理论与实践应用。差异性隐私旨在在保护个体数据的同时，允许数据分析和挖掘的进行，无论对手具有何种先验知识。近年来，尽管已经提出了一些方法来确定特定隐私风险的上限，但这些方法仍存在局限性，如依赖数据规模或提供的保护可能过于宽松，这限制了它们在实际中的应用。
作者Xianmang He、Yuan Hong和Yindong Chen分别来自东莞理工大学、伊利诺伊理工学院和汕头大学的计算机科学与工程领域，他们提出了一种创新的方法，将差异性隐私中的隐私约束（epsilon，通常表示为ε）转换为普通用户可以理解的隐私风险。这种方法有望解决现有方法的不足，使得数据所有者能更好地理解和选择适合的ε值。
在理论部分，文章深入研究了如何通过数学模型和统计分析来量化ε的边界，以及它如何影响数据发布后的隐私泄露程度。此外，作者还可能讨论了ε的选择对数据可用性和隐私保护之间的权衡，这对于在保护个人隐私的同时确保数据集的实用性至关重要。
在实践方面，文章可能涉及了如何在真实世界的数据发布场景中应用这种新的转换方法，包括如何评估和调整ε值以适应不同情境下的隐私需求。此外，还可能介绍了如何通过实验和案例研究验证该方法的有效性，以及它在实际数据处理中的性能和效果。
这篇研究论文为数据所有者提供了一个更直观的框架，帮助他们理解差异性隐私的隐私约束，并做出更为明智的决策，以达到理想的隐私保护水平。同时，这也为未来的研究和开发提供了新的思路，以便进一步改进和优化差异性隐私的实施策略。
Exploring the Privacy Bound for Differential Privacy: From Theory to Practice
probability of successfully identifying the individuals
from the counting queries to be no greater than
ρ ≤
1
10
(maximum inference probability). In order to
achieve this protection goal with the existing theoretical
result [15] (more details will be given in Section
3), we thus have: the upper bound of differential
privacy budget should satisfy ≤
∆f
∆v
ln
(n−1)ρ
1−ρ
, where
n represents the number of records, ∆f is the sensitivity
of query, ∆v is the maximum distance between function
values of every possible world (the same information
needed to calculate global sensitivity) [15], and ρ is the
maximum inference probability. Then, if given n =
600, 000 records, the bound yields
≤
1
1
ln
(600, 000 − 1)(
1
10
)
1 −
1
10
≈ 11.1 (1)
where ∆v is no greater than 1 for count queries.
In the above example, the upper bound of would
be 11.1, which might exceed our expectation. In
other words, such large can satisfy ρ ≤
1
10
in their
interpretive inference model but can be vulnerable in
other cases (for instance, in our proposed interpretive
inference model, =11.1 would result in ρ >
1
10
) (higher
privacy risks than the data owners’ demand).
Furthermore, in the interpretive inference model
proposed in [15], is proportional to ln(n) where n is
data size. As n increases, the upper bound of also
increases. In case of a large or small n, the derived
bound would be meaningless (unbounded or negative).
From the above examples, we can see that existing
solutions have their inherent drawbacks. Motivated
by such observations, we propose a novel interpretive
inference model, which can be used to evaluate the
probability or confidence that the adversary will
be able to identify any individual from the noise-
injected queries over the dataset. This enables us to
understand the privacy implications of differentially
private techniques in a much clearer way.
1.3. Our Contributions
The major contributions of this paper are summarized
as follows.
• This paper presents a novel interpretive inference
model to convert the privacy bound in
differential privacy to inference probabilities that
any individual is included in the input data
(for queries). The proposed interpretive inference
model and converted inference probabilities have
addressed the drawbacks of the existing models
[15, 24].
• Based on the proposed interpretive inference
model, we present an instantiation for choosing
appropriate (maximum privacy bound in dif-
ferential privacy), which should effectively bound
the risks of inferring the presence/absence of indi-
viduals (given the maximum inference probabil-
ity) in generic differentially private algorithms.
• An in-depth theoretical analysis of our approach
is provided, and a set of experiments are
conducted to confirm the effectiveness of our
approach.
The rest of the paper is organized as follows. In
Section 2, we describe the preliminaries for differential
privacy. In Section 3, we present the analysis for two
representative existing works. Then, in Section 4, we
propose our interpretive inference model and the upper
bound for in differential privacy (given the maximum
inference probability). Section 5 demonstrates the
experimental results, and Section 6 reviews related
work. Finally, Section 7 gives the concluding remarks.
2. Preliminaries
In this section, we will first describe the basic
mechanism of differential privacy, and then present
the Laplace distribution which contributes to a generic
differentially private approach.
2.1. Differential Privacy
The most commonly-used definition of differential
privacy is -differential privacy, which guarantees that
any individual tuple has negligible influence on the
published statistical results, in a probabilistic sense.
Specifically, a randomized algorithm A satisfies -
differential privacy if and only if for any two databases
D
1
, D
2
that differ in exactly one record, and any possible
output O of A, the ratio between the probability that A
outputs O on D
1
and the probability that A outputs O
on D
2
is bounded by a constant. Formally, we have
|P rob(A(D
1
) = O)|
|P rob(A(D
2
) = O)|
≤ e
(2)
where is a constant specified by the user, D
1
, D
2
differ in at most one element, and e is the base of
the natural logarithms. Intuitively, given the output
O of A, it is hard for the adversary to infer whether
the original data is D
1
or D
2
, if the parameter is
sufficiently small. Similarly, -differential privacy also
provides any individual with plausible deniability that
her/his record was in the databases.
The earliest and most widely-adopted approach
for enforcing -differential privacy is the Laplace
mechanism [4], which works by injecting random noise
x ∝ lap(λ) that follows a Laplace distribution into
the output of the original O, and the deterministic
algorithm A obtains its randomized version O + x, that
is, A(D) = O + x, where λ =
4f
.
3
EAI Endorsed Transactions on
Security and Safety
12 2018 - 01 2019 | Volume 5 | Issue 18 | e2
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