Related papers: Injective Rank Metric Trapdoor Functions with Homo…
We formalize and study the notion of a quantum trapdoor function. This is an efficiently computable unitary that takes as input a "public" quantum state and a classical string $x$, and outputs a quantum state. This map is such that (i) it…
One open problem in source coding is to characterize the limits of representing losslessly a non-identity discrete function of the data encoded independently by the encoders of several correlated sources with memory. This paper investigates…
This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
The key encapsulation mechanism Edon-K was proposed in response to the call for post-quantum cryptography standardization issued by the National Institute of Standards and Technologies (NIST). This scheme is inspired by the McEliece scheme…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
The matrix rank minimization problem has applications in many fields such as system identification, optimal control, low-dimensional embedding, etc. As this problem is NP-hard in general, its convex relaxation, the nuclear norm minimization…
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system…
Model Inversion (MI) attacks pose a significant threat to the privacy of Deep Neural Networks by recovering training data distribution from well-trained models. While existing defenses often rely on regularization techniques to reduce…
This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…
Every day, millions of credit cards are swiped and transactions are carried out across the world. Due to numerous forms of unethical digital activities, users are vulnerable to credit card fraud, phishing, identity theft, etc. This paper…
P vs NP problem is the most important unresolved problem in the field of computational complexity. Its impact has penetrated into all aspects of algorithm design, especially in the field of cryptography. The security of cryptographic…
Multi-dimensional data completion is a critical problem in computational sciences, particularly in domains such as computer vision, signal processing, and scientific computing. Existing methods typically leverage either global low-rank…
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory…
Sparse coding, which represents a data point as a sparse reconstruction code with regard to a dictionary, has been a popular data representation method. Meanwhile, in database retrieval problems, learning the ranking scores from data points…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
Several applications in communication, control, and learning require approximating target distributions to within small informational divergence (I-divergence). The additional requirement of invertibility usually leads to using encoders…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
In this paper, we develop a geometric framework for matrix rank-metric codes based on generator tensors and their slice spaces. To every nondegenerate matrix rank-metric code, we associate two systems, which translate metric properties of…
The iterative conditional branchings appear in various sensitive algorithms, like the modular exponentiation in the RSA cryptosystem or the scalar multiplication in ellipticcurve cryptography. In this paper, we abstract away the desirable…