Oliver Wilhelm Gnilke

Aalto University · Department of Mathematics and Systems Analysis

Large matrix multiplications commonly take place in large-scale machine-learning applications. Often, the sheer size of these matrices prevent carrying out the multiplication at a single server. Therefore, these operations are typically offloaded to a distributed computing platform with a master server and a large amount of workers in the cloud, op...

This work considers the problem of privately outsourcing the computation of a matrix product over a finite field ${\mathbb {F}}_{q}$ to $N$ helper servers. These servers are considered to be honest but curious, i.e. , they behave according to the protocol but will try to deduce information about the user’s data. Furthermore, any set of up to...

This work considers the problem of privately outsourcing the computation of a matrix product over a finite field $\mathbb{F}_q$ to $N$ helper servers. These servers are considered to be honest but curious, i.e., they behave according to the protocol but will try to deduce information about the user's data. Furthermore, any set of up to $X$ servers...

A major drawback of many PIR schemes is the highcomputational cost at the servers. We present a scheme that usesonly operations in the prime field during response generation.For binary extension fields this leads to schemes that only needXOR operations at the servers to calculate the responses. This isachieved by restricting the queries to a subfie...

The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper’s correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper’s lattice, which we f...

Generalized concatenated codes were introduced in the 1970s by Zinoviev. There are many types of codes in the literature that are known by other names that can be viewed as generalized concatenated codes. Examples include matrix-product codes, multilevel codes and generalized cascade codes. Decoding algorithms for generalized concatenated codes wer...

The problem of Private Information Retrieval (PIR) from coded storage systems with colluding, Byzantine, and unresponsive servers is considered. An explicit scheme using an [n,k] Reed-Solomon storage code is designed, protecting against t-collusion and handling up to b Byzantine and r unresponsive servers, when n > k+t+2b+r–1. This scheme achieves...

In a User-Private Information Retrieval (UPIR) scheme, a set of users collaborate to retrieve files from a database without revealing to observers which participant in the scheme requested the file. Protocols have been proposed based on pairwise balanced designs and symmetric designs. Wepropose a new class of UPIR schemes based on generalised quadr...

The problem of Private Information Retrieval (PIR) from coded storage systems with colluding, byzantine, and unresponsive servers is considered. An explicit scheme using an $[n,k]$ Reed-Solomon storage code is designed, protecting against $t$-collusion and handling up to $b$ byzantine and $r$ unresponsive servers, when $n>k+t+2b+r-1$. %, for some i...

The problem of providing privacy, in the private information retrieval (PIR) sense, to users requesting data from a distributed storage system (DSS), is considered. The DSS is coded by an (n, k, d) Maximum Distance Separable (MDS) code to store the data reliably on unreliable storage nodes. Some of these nodes can be spies which report to a third p...

A private information retrieval (PIR) scheme on coded storage systems with colluding, byzantine, and non-responsive servers is presented. Furthermore, the scheme can also be used for symmetric PIR in the same setting. An explicit scheme using an $[n,k]$ generalized Reed-Solomon storage code is designed, protecting against $t$-collusion and handling...

Looking at incidence matrices of $t$-$(v,k,\lambda)$ designs as $v \times b$ matrices with $2$ possible entries, each of which indicates incidences of a $t$-design, we introduce the notion of a $c$-mosaic of designs, having the same number of points and blocks, as a matrix with $c$ different entries, such that each entry defines incidences of a des...

This paper presents private information retrieval (PIR) schemes for coded storage with colluding servers, which are not restricted to maximum distance separable (MDS) codes. PIR schemes for general linear codes are constructed and the resulting PIR rate is calculated explicitly. It is shown that codes with transitive automorphism groups yield the h...

We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on a Frobenius bimodule are viewed as a module over the semigroup ring of the multiplicative semigroup of the co...

We present private information retrieval protocols for coded storage with colluding servers. While previous schemes require field sizes that grow with the number of servers and files in the system, we restrict the field size and focus especially on the binary case. Reed-Muller codes are shown to be especially useful in this regard and explicit para...

In Private Information Retrieval (PIR), one wants to download a file from a database without revealing to the database which file is being downloaded. Much attention has been paid to the case of the database being encoded across several servers, subsets of which can collude to attempt to deduce the requested file. With the goal of studying the achi...

The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior per...

We present a general framework for Private Information Retrieval (PIR) from arbitrary coded databases, that allows one to adjust the rate of the scheme according to the suspected number of colluding servers. If the storage code is a generalized Reed-Solomon code of length n and dimension k, we design PIR schemes which simultaneously protect against...

The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior per...

In the wiretap setting it is assumed that the same message is transmitted over two different channels, a channel to an intended/legitimate receiver Bob and a different channel to an eavesdropper Eve. Three contradicting objectives are simultaneously tried to be achieved: A high information rate between the sender and Bob, high reliability at the le...

Vector perturbation is an encoding method for broadcast channels in which the transmitter solves a shortest vector problem in a lattice to create a perturbation vector, which is then added to the data before transmission. In this work, we introduce nested lattice codes into vector perturbation systems, resulting in a strategy which we deem matrix p...