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The problem of finding short vectors in Euclidean lattices is a central hard problem in complexity theory. The case of module lattices (i.e., lattices which are also modules over a number ring) is of particular interest for cryptography and…

Number Theory · Mathematics 2025-11-18 Koen de Boer , Aurel Page , Radu Toma , Benjamin Wesolowski

In this work, we study the solution of shortest vector problems (SVPs) arising in terms of learning with error problems (LWEs). LWEs are linear systems of equations over a modular ring, where a perturbation vector is added to the right-hand…

Cryptography and Security · Computer Science 2025-02-10 Tobias Köppl , René Zander , Louis Henkel , Nikolay Tcholtchev

Large-scale quantum computing is a significant threat to classical public-key cryptography. In strong "quantum access" security models, numerous symmetric-key cryptosystems are also vulnerable. We consider classical encryption in a model…

Quantum Physics · Physics 2021-05-14 Gorjan Alagic , Stacey Jeffery , Maris Ozols , Alexander Poremba

Design efficient lattice-based cryptosystem secure against adaptive chosen ciphertext attack (IND-CCA2) is a challenge problem. To the date, full CCA2-security of all proposed lattice-based PKE schemes achieved by using a generic…

Cryptography and Security · Computer Science 2013-03-04 Roohallah Rastaghi

Lattice-based cryptography relies on generating random bases which are difficult to fully reduce. Given a lattice basis (such as the private basis for a cryptosystem), all other bases are related by multiplication by matrices in…

Cryptography and Security · Computer Science 2021-05-20 Tamar Lichter Blanks , Stephen D. Miller

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…

Machine Learning · Computer Science 2019-04-12 Maksim Tsikhanovich , Malik Magdon-Ismail , Muhammad Ishaq , Vassilis Zikas

We construct a public-key encryption scheme from the hardness of the (planted) MinRank problem over uniformly random instances. This corresponds to the hardness of decoding random linear rank-metric codes. Existing constructions of…

Cryptography and Security · Computer Science 2025-10-07 Rohit Chatterjee , Changrui Mu , Prashant Nalini Vasudevan

We present an efficient reduction from the Bounded integer programming (BIP) to the Subspace avoiding problem (SAP) in lattice theory. The reduction has some special properties with some interesting consequences. The first is the new upper…

Computational Complexity · Computer Science 2008-08-12 Thân Quang Khoát

Efficiently solving the Shortest Vector Problem (SVP) in two-dimensional lattices holds practical significance in cryptography and computational geometry. While simpler than its high-dimensional counterpart, two-dimensional SVP motivates…

Computational Geometry · Computer Science 2025-07-02 Lihao Zhao , Chengliang Tian , Jingguo Bi , Guangwu Xu , Jia Yu

Post-quantum cryptography has gained attention due to the need for secure cryptographic systems in the face of quantum computing. Code-based and lattice-based cryptography are two prominent approaches, both heavily studied within the NIST…

Cryptography and Security · Computer Science 2024-10-16 Anna-Lena Horlemann , Karan Khathuria , Marc Newman , Amin Sakzad , Carlos Vela Cabello

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

Machine Learning · Computer Science 2022-11-14 Edith Cohen , Xin Lyu , Jelani Nelson , Tamás Sarlós , Uri Stemmer

Recently, a novel public key edcryption technique based on multiple chaotic systems has been proposed. The scheme employs m-chaotic systmes and a set of linear functions for key exchange over an insecure channel. The security of the…

Chaotic Dynamics · Physics 2009-11-11 K. wang , W. J. Pei , Z. L. Hua , Z. Y. He

Group ring NTRU (GR-NTRU) provides a general structure to design different variants of NTRU-like schemes by employing different groups. Although, most of the schemes in literature are built over cyclic groups, nonabelian groups can also be…

Cryptography and Security · Computer Science 2023-09-18 Vikas Kumar , Ali Raya , Sugata Gangopadhyay , Aditi Kar Gangopadhyay

Key Encapsulation Mechanisms (KEMs) are a set of cryptographic techniques that are designed to provide symmetric encryption key using asymmetric mechanism (public key). In the current study, we concentrate on design and analysis of key…

Cryptography and Security · Computer Science 2024-12-09 Reza Hooshmand

The Learning with Errors (\LWE) problem has been widely utilized as a foundation for numerous cryptographic tools over the years. In this study, we focus on an algebraic variant of the \LWE problem called \emph{Group ring} \LWE ($\GRLWE$).…

Cryptography and Security · Computer Science 2026-03-11 Jiaqi Liu , Fang-Wei Fu

In order to research the security of the knapsack problem under quantum algorithm attack, we study the quantum algorithm for knapsack problem over Z_r based on the relation between the dimension of the knapsack vector and r. First, the…

Cryptography and Security · Computer Science 2014-02-28 Xiangqun Fu , Wansu Bao , Jianhong Shi , Fada Li , Yuchao Zhang

The paper analyzes a new public key cryptosystem whose security is based on a matrix version of the discrete logarithm problem over an elliptic curve. It is shown that the complexity of solving the underlying problem for the proposed system…

Cryptography and Security · Computer Science 2007-05-23 J. J. Climent , E. Gorla , J. Rosenthal

In this paper, the authors give the definitions of a coprime sequence and a lever function, and describe the five algorithms and six characteristics of a prototypal public key cryptosystem which is used for encryption and signature, and…

Cryptography and Security · Computer Science 2014-11-04 Shenghui Su , Shuwang Lv

Quantum computers are expected to break today's public key cryptography within a few decades. New cryptosystems are being designed and standardised for the post-quantum era, and a significant proportion of these rely on the hardness of…

Quantum Physics · Physics 2021-03-31 David Joseph , Adam Callison , Cong Ling , Florian Mintert

A signcryption, which is an integration of a public key encryption and a digital signature, can provide confidentiality and authenticity simultaneously. Additionally, a signcryption associated with equality test allows a third party (e.g.,…

Cryptography and Security · Computer Science 2021-01-01 Huy Quoc Le , Dung Hoang Duong , Partha Sarathi Roy , Willy Susilo , Kazuhide Fukushima , Shinsaku Kiyomoto