Related papers: Private Polynomial Computation for Noncolluding Co…
We consider the problem of distributedly computing a general class of functions, referred to as gradient-type computation, while maintaining the privacy of the input dataset. Gradient-type computation evaluates the sum of some `partial…
In this paper, we present a coded computation (CC) scheme for distributed computation of the inference phase of machine learning (ML) tasks, specifically, the task of image classification. Building upon Agrawal et al.~2022, the proposed…
Federated Learning (FL) is an interesting strategy that enables the collaborative training of an AI model among different data owners without revealing their private datasets. Even so, FL has some privacy vulnerabilities that have been…
In distributed matrix multiplication, a common scenario is to assign each worker a fraction of the multiplication task, by partitioning the input matrices into smaller submatrices. In particular, by dividing two input matrices into…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
Delegating large-scale computations to service providers is a common practice which raises privacy concerns. This paper studies information-theoretic privacy-preserving delegation of data to a service provider, who may further delegate the…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
Nonclassical symmetries and reductions of polynomial equations and systems of polynomial equations are considered. It is shown that specific polynomial equations having "hidden" symmetries can be reduced to classical symmetric systems of…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
In this paper, we study the problem of \emph{private and secure distributed matrix multiplication (PSDMM)}, where a user having a private matrix $A$ and $N$ non-colluding servers sharing a library of $L$ ($L>1$) matrices $B^{(0)},…
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…
In this work, we consider the problem of secure multi-party computation (MPC), consisting of $\Gamma$ sources, each has access to a large private matrix, $N$ processing nodes or workers, and one data collector or master. The master is…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
The problem of private information retrieval gets renewed attentions in recent years due to its information-theoretic reformulation and applications in distributed storage systems. PIR capacity is the maximal number of bits privately…
We show that polynomial codes (and some related codes) used for distributed matrix multiplication are interleaved Reed-Solomon codes and, hence, can be collaboratively decoded. We consider a fault tolerant setup where $t$ worker nodes…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
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…
As society becomes more reliant on computers, cryptographic security becomes increasingly important. Current encryption schemes include the ElGamal signature scheme, which depends on the complexity of the discrete logarithm problem. It is…
Large language models (LLMs) have achieved remarkable success, yet aligning their generations with human preferences remains a critical challenge. Existing approaches to preference modeling often rely on an explicit or implicit reward…
In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density…