The emerging technologies for large scale data analysis raise new challenges
to the security and privacy of sensitive user data. In this work we investigate
the problem of private statistical analysis of time-series data in the
distributed and semi-honest setting. In particular, we study some properties of
Private Stream Aggregation (PSA), first introduced by Shi et al. 2017. This is
a computationally secure protocol for the collection and aggregation of data in
a distributed network and has a very small communication cost. In the
non-adaptive query model, a secure PSA scheme can be built upon any
key-homomorphic weak pseudo-random function as shown by Valovich 2017, yielding
security guarantees in the standard model which is in contrast to Shi et. al.
We show that every mechanism which preserves $(\epsilon,\delta)$-differential
privacy in effect preserves computational $(\epsilon,\delta)$-differential
privacy when it is executed through a secure PSA scheme. Furthermore, we
introduce a novel perturbation mechanism based on the symmetric Skellam
distribution that is suited for preserving differential privacy in the
distributed setting, and find that its performances in terms of privacy and
accuracy are comparable to those of previous solutions. On the other hand, we
leverage its specific properties to construct a computationally efficient
prospective post-quantum protocol for differentially private time-series data
analysis in the distributed model. The security of this protocol is based on
the hardness of a new variant of the Decisional Learning with Errors (DLWE)
problem. In this variant the errors are taken from the symmetric Skellam
distribution. We show that this new variant is hard based on the hardness of
the standard Learning with Errors (LWE) problem where the errors are taken from
the discrete Gaussian distribution. Thus, we provide a variant of the LWE
problem that is hard...

本研究探讨大数据分析所带来的安全和隐私问题，研究了私有时间序列数据在分布式和半诚信环境下的统计分析问题，并提出了一种基于对称 Skellam 分布的扰动机制，可用于保护分布式数据的差分隐私性，并构建了一个计算有效的量子后学协议，该协议的安全性基于一种新型决策学习问题。