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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…

Combinatorics · Mathematics 2026-05-20 Gianira N. Alfarano , Martino Borello , Alessandro Neri

Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…

Quantum Physics · Physics 2014-11-19 Li Yu , Carlos A. Perez-Delgado , Joseph F. Fitzsimons

Recht, Fazel, and Parrilo provided an analogy between rank minimization and $\ell_0$-norm minimization. Subject to the rank-restricted isometry property, nuclear norm minimization is a guaranteed algorithm for rank minimization. The…

Numerical Analysis · Mathematics 2009-05-01 Kiryung Lee , Yoram Bresler

We theoretically propose a symmetric encryption scheme based on Restricted Boltzmann Machines that functions as a probabilistic Enigma device, encoding information in the marginal distributions of visible states while utilizing bias…

Statistical Mechanics · Physics 2025-07-24 Bin Chen , Weichao Yu

Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today's world as the information to be sent might be of invaluable importance…

Cryptography and Security · Computer Science 2015-06-19 Arjun Puri , Sudesh Kumar

This paper considers a new secure gradient coding problem with uncoded groupwise keys, formalized as a (K, N, N_r, M, S) secure gradient coding model, where a user aims to compute the sum of the gradients from K datasets with the assistance…

Information Theory · Computer Science 2026-04-15 Xudong You , Kai Wan , Xiang Zhang , Wenbo Huang , Robert Caiming Qiu , Giuseppe Caire

The proposed hybrid message embedded scheme consists of hill cipher combined with message embedded chaotic scheme. Message-embedded scheme using non-linear feedback shift register as non-linear function and 1-D logistic map as chaotic map…

Cryptography and Security · Computer Science 2012-09-13 Mina Mishra , V. H. Mankar

This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random…

Information Theory · Computer Science 2015-03-19 Vincent Y. F. Tan , Laura Balzano , Stark C. Draper

Researchers in the past have shown that Symmetric key cryptography is generally considered infeasible and public key cryptography, at times, fails to provide sufficient security and integrity to data. In contrast to this prejudice, our…

Cryptography and Security · Computer Science 2020-12-24 Ananth Vishnu Bhaskar , Ankit Baingane , Ryan Jahnige , Qingquan Zhang , Ting Zhu

We show that in device independent quantum key distribution protocols the privacy of randomness is of crucial importance. For sublinear test sample sizes even the slightest guessing probability by an eavesdropper will completely compromise…

Quantum Physics · Physics 2013-09-12 Marcus Huber , Marcin Pawlowski

Due to the weakness of public key cryptosystems encounter of quantum computers, the need to provide a solution was emerged. The McEliece cryptosystem and its security equivalent, the Niederreiter cryptosystem, which are based on Goppa…

Cryptography and Security · Computer Science 2023-10-11 Arash Khalvan , Amirhossein Zali , Mahmoud Ahmadian Attari

In this paper, an anti-eavesdropping estimation problem is investigated. A linear encryption scheme is utilized, which first linearly transforms innovation via an encryption matrix and then encrypts some components of the transformed…

Systems and Control · Electrical Eng. & Systems 2024-06-18 Zhongyao Hu , Bo Chen , Pindi Weng , Jianzheng Wang , Li Yu

The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…

Information Theory · Computer Science 2024-10-22 Thomas Jerkovits , Hannes Bartz , Antonia Wachter-Zeh

Device-independent quantum key distribution does not need a precise quantum mechanical model of employed devices to guarantee security. Despite of its beauty, it is still a very challenging experimental task. We compare a recent proposal by…

Quantum Physics · Physics 2015-05-28 Marcos Curty , Tobias Moroder

Research in logic encryption over the last decade has resulted in various techniques to prevent different security threats such as Trojan insertion, intellectual property leakage, and reverse engineering. However, there is little agreement…

Cryptography and Security · Computer Science 2020-07-31 Yinghua Hu , Vivek V. Menon , Andrew Schmidt , Joshua Monson , Matthew French , Pierluigi Nuzzo

Fully homomorphic encryption is an encryption method with the property that any computation on the plaintext can be performed by a party having access to the ciphertext only. Here, we formally define and give schemes for quantum homomorphic…

Quantum Physics · Physics 2016-01-11 Anne Broadbent , Stacey Jeffery

This letter presents a cryptanalysis of the modified McEliece cryptosystem recently proposed by Moufek, Guenda and Gulliver [24]. The system is based on the juxtaposition of quasi-cyclic LDPC and quasi-cyclic MDPC codes. The idea of our…

Cryptography and Security · Computer Science 2017-12-07 Vlad Dragoi , Hervé Talé Kalachi

Many algorithms are specified with respect to a fixed but unspecified parameter. Examples of this are especially common in cryptography, where protocols often feature a security parameter such as the bit length of a secret key. Our aim is…

Logic in Computer Science · Computer Science 2025-10-28 Alessandro Di Giorgio , Pawel Sobocinski , Niels Voorneveld

In this paper, security analysis of block ciphers with key length greater than block length is proposed. When key length is significantly greater than block length and the statistical distribution of cipher system is like a uniform…

Cryptography and Security · Computer Science 2013-05-21 Maghsood Parviz , Seyed Hassan Mousavi , Saeed Mirahmadi

Computationally hard problems based on coding theory, such as the syndrome decoding problem, have been used for constructing secure cryptographic schemes for a long time. Schemes based on these problems are also assumed to be secure against…

Cryptography and Security · Computer Science 2024-09-12 Puja Mondal , Supriya Adhikary , Suparna Kundu , Angshuman Karmakar