Related papers: Birthday attack to discrete logarithm
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
In this paper, we consider continuous-variable quantum key distribution with a discrete modulation, either binary or quaternary. We establish the security of these protocols against the class of collective attacks that induce a linear…
Privacy is a major issue in learning from distributed data. Recently the cryptographic literature has provided several tools for this task. However, these tools either reduce the quality/accuracy of the learning algorithm---e.g., by adding…
This article presents an efficient algorithm to generate a discrete uniform distribution on a set of $p$ elements using a biased random source for $p$ prime. The algorithm generalizes Von Neumann's method and improves computational…
In this paper, we propose to use a skew dihedral group ring given by the group $D_{2n}$ and the finite field $\mathbb{F}_{q^2}$ for public-key cryptography. Using the ambient space $\mathbb{F}_{q^{2}}^{\theta} D_{2n}$ and a group…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is…
As a staple of data analysis and unsupervised learning, the problem of private clustering has been widely studied under various privacy models. Centralized differential privacy is the first of them, and the problem has also been studied for…
Key-value data is a naturally occurring data type that has not been thoroughly investigated in the local trust model. Existing local differentially private (LDP) solutions for computing statistics over key-value data suffer from the…
While pursuing better utility by discovering knowledge from the data, individual's privacy may be compromised during an analysis. To that end, differential privacy has been widely recognized as the state-of-the-art privacy notion. By…
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by several groups is to use this representation…
Due to the capability of tolerating high error rate and generating more key bits per trial, high-dimensional quantum key distribution attracts wide interest. Despite great progresses in high-dimensional quantum key distribution, there are…
Differential privacy (DP) provides formal guarantees that the output of a database query does not reveal too much information about any individual present in the database. While many differentially private algorithms have been proposed in…
We present an online voting architecture based on partitioning the election in small clusters of voters and using a new Multi-party Computation algorithm for obtaining voting results from the clusters. This new algorithm has some practical…
This text provides an introduction to distributed local algorithms -- an area at the intersection of theoretical computer science and discrete mathematics. We collect recent results in the area and demonstrate how they lead to a clean…
Recent breakthrough methods \cite{gggz,joux,bgjt} on computing discrete logarithms in small characteristic finite fields share an interesting feature in common with the earlier medium prime function field sieve method \cite{jl}. To solve…
In this paper, we consider the problem of responding to a count query (or any other integer-valued queries) evaluated on a dataset containing sensitive attributes. To protect the privacy of individuals in the dataset, a standard practice is…
It has been found that an algorithm can generate true random numbers on classical computer. The algorithm can be used to generate unbreakable message PIN (personal identification number) and password.
This study is mainly about the discrete logarithm problem in the ElGamal cryptosystem over the abelian group U(n) where n is one of the following forms p^m, or 2p^m where p is an odd large prime and m is a positive integer. It is another…
We generalize the continuous observation privacy setting from Dwork et al. '10 and Chan et al. '11 by allowing each event in a stream to be a subset of some (possibly unknown) universe of items. We design differentially private (DP)…