Related papers: Ring Learning With Errors: A crossroads between po…
Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with…
The "Ring Learning with Errors" (RLWE) problem was formulated as a variant of the "Learning with Errors" (LWE) problem, with the purpose of taking advantage of an additional algebraic structure in the underlying considered lattices; this…
Machine learning techniques have had a long list of applications in recent years. However, the use of machine learning in information and network security is not new. Machine learning and cryptography have many things in common. The most…
In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisentr\"ager-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] gives rise to…
The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and…
Quantum algorithms have demonstrated promising speed-ups over classical algorithms in the context of computational learning theory - despite the presence of noise. In this work, we give an overview of recent quantum speed-ups, revisit the…
The Learning with Errors (LWE) problem is the fundamental backbone of modern lattice based cryptography, allowing one to establish cryptography on the hardness of well-studied computational problems. However, schemes based on LWE are often…
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 ($\GRLWE$).…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has…
This paper surveys various results in the field of Quantum Learning theory, specifically focusing on learning quantum-encoded classical concepts in the Probably Approximately Correct (PAC) framework. The cornerstone of this work is the…
With the growing processing power of computing systems and the increasing availability of massive datasets, machine learning algorithms have led to major breakthroughs in many different areas. This development has influenced computer…
Public-key cryptography has become a popular way to motivate the teaching of concepts in elementary number theory, abstract algebra, and introduction to proof courses, as well as in cryptography courses. Unfortunately, many experts expect…
Quantum computing poses fundamental risks to classical blockchain systems by undermining widely used cryptographic primitives. In response, two major research directions have emerged: post-quantum blockchains, which integrate…
We present cyber-security problems of high importance. We show that in order to solve these cyber-security problems, one must cope with certain machine learning challenges. We provide novel data sets representing the problems in order to…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
This paper builds a novel bridge between algebraic coding theory and mathematical knot theory, with applications in both directions. We give methods to construct error-correcting codes starting from the colorings of a knot, describing…
As quantum computing advances rapidly, guaranteeing the security of cryptographic protocols resistant to quantum attacks is paramount. Some leading candidate cryptosystems use the Learning with Errors (LWE) problem, attractive for its…
Machine learning in quantum computing and communication provides intensive opportunities for revolutionizing the field of Physics, Mathematics, and Computer Science. There exists an aperture of understanding behind this interdisciplinary…
The quality and correct functioning of software components embedded in electronic systems are of utmost concern especially for safety and mission-critical systems. Model-based testing and formal verification techniques can be employed to…