Lattice Based Cryptosystems

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Lattice Based Cryptosystems

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Author : Jiang Zhang
language : en
Publisher: Springer Nature
Release Date : 2020-10-14

Lattice Based Cryptosystems written by Jiang Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-14 with Computers categories.

This book focuses on lattice-based cryptosystems, widely considered to be one of the most promising post-quantum cryptosystems and provides fundamental insights into how to construct provably secure cryptosystems from hard lattice problems. The concept of provable security is used to inform the choice of lattice tool for designing cryptosystems, including public-key encryption, identity-based encryption, attribute-based encryption, key change and digital signatures. Given its depth of coverage, the book especially appeals to graduate students and young researchers who plan to enter this research area.

Complexity Of Lattice Problems

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Author : Daniele Micciancio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Complexity Of Lattice Problems written by Daniele Micciancio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Lattices are geometric objects that can be pictorially described as the set of intersection points of an infinite, regular n-dimensional grid. De spite their apparent simplicity, lattices hide a rich combinatorial struc ture, which has attracted the attention of great mathematicians over the last two centuries. Not surprisingly, lattices have found numerous ap plications in mathematics and computer science, ranging from number theory and Diophantine approximation, to combinatorial optimization and cryptography. The study of lattices, specifically from a computational point of view, was marked by two major breakthroughs: the development of the LLL lattice reduction algorithm by Lenstra, Lenstra and Lovasz in the early 80's, and Ajtai's discovery of a connection between the worst-case and average-case hardness of certain lattice problems in the late 90's. The LLL algorithm, despite the relatively poor quality of the solution it gives in the worst case, allowed to devise polynomial time solutions to many classical problems in computer science. These include, solving integer programs in a fixed number of variables, factoring polynomials over the rationals, breaking knapsack based cryptosystems, and finding solutions to many other Diophantine and cryptanalysis problems.

Lattice Based Cryptography

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Author : Jonathan Katz
language : en
Publisher: CRC Press
Release Date : 2018-06-15

Lattice Based Cryptography written by Jonathan Katz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-15 with categories.

The main focus of the book will graduate level courses on the techniques used in obtaining lattice-based cryptosystems. The book will first cover the basics of lattices and then introduce the more advanced material (e.g. Gaussian distributions, sampling, algebraic number theory, etc.) in a "natural" way, motivated by cryptographic constructions. There will also be a fair amount of mathematics that will be introduced gradually and will be motivated by cryptographic constructions.

A Decade Of Lattice Cryptography

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Author : Chris Peikert
language : en
Publisher:
Release Date : 2016-03-07

A Decade Of Lattice Cryptography written by Chris Peikert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Computer networks categories.

Surveys most of the major developments in lattice cryptography over the past ten years. The main focus is on the foundational short integer solution (SIS) and learning with errors (LWE) problems, their provable hardness assuming the worst-case intractability of standard lattice problems, and their many cryptographic applications.

Lattices And Their Application In Cryptography

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Author : Merve Cakir
language : en
Publisher: GRIN Verlag
Release Date : 2017-01-23

Lattices And Their Application In Cryptography written by Merve Cakir and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Computers categories.

Bachelor Thesis from the year 2014 in the subject Engineering - Computer Engineering, grade: 1,0, Hamburg University of Technology (Institut für Eingebettete Systeme), language: English, abstract: The aim of this thesis is to identify the characteristics of lattice-based cryptosystems. The use of encryption and signature schemes can be insecure considering attacks by a quantum computer and inefficient in the computation time. An alternative cryptography is proposed, which is based on worst-case lattice problems. The security and the hardness of the underlying computational problems will be analyzed by providing collaboration between the linear-algebra, complexity-theory and the public-key cryptography.

The Lll Algorithm

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Author : Phong Q. Nguyen
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-02

The Lll Algorithm written by Phong Q. Nguyen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-02 with Computers categories.

The first book to offer a comprehensive view of the LLL algorithm, this text surveys computational aspects of Euclidean lattices and their main applications. It includes many detailed motivations, explanations and examples.

An Introduction To Mathematical Cryptography

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Author : Jeffrey Hoffstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15

An Introduction To Mathematical Cryptography written by Jeffrey Hoffstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.

An Introduction to Mathematical Cryptography provides an introduction to public key cryptography and underlying mathematics that is required for the subject. Each of the eight chapters expands on a specific area of mathematical cryptography and provides an extensive list of exercises. It is a suitable text for advanced students in pure and applied mathematics and computer science, or the book may be used as a self-study. This book also provides a self-contained treatment of mathematical cryptography for the reader with limited mathematical background.

Computational Cryptography

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Author : Joppe Bos
language : en
Publisher:
Release Date : 2021-12-09

Computational Cryptography written by Joppe Bos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-09 with Language Arts & Disciplines categories.

The area of computational cryptography is dedicated to the development of effective methods in algorithmic number theory that improve implementation of cryptosystems or further their cryptanalysis. This book is a tribute to Arjen K. Lenstra, one of the key contributors to the field, on the occasion of his 65th birthday, covering his best-known scientific achievements in the field. Students and security engineers will appreciate this no-nonsense introduction to the hard mathematical problems used in cryptography and on which cybersecurity is built, as well as the overview of recent advances on how to solve these problems from both theoretical and practical applied perspectives. Beginning with polynomials, the book moves on to the celebrated Lenstra-Lenstra-Lovász lattice reduction algorithm, and then progresses to integer factorization and the impact of these methods to the selection of strong cryptographic keys for usage in widely used standards.

Handbook Of Applied Cryptography

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Author : Alfred J. Menezes
language : en
Publisher: CRC Press
Release Date : 1996-10-16

Handbook Of Applied Cryptography written by Alfred J. Menezes and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-16 with Mathematics categories.

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an important discipline that is not only the subject of an enormous amount of research, but provides the foundation for information security in many applications. Standards are emerging to meet the demands for cryptographic protection in most areas of data communications. Public-key cryptographic techniques are now in widespread use, especially in the financial services industry, in the public sector, and by individuals for their personal privacy, such as in electronic mail. This Handbook will serve as a valuable reference for the novice as well as for the expert who needs a wider scope of coverage within the area of cryptography. It is a necessary and timely guide for professionals who practice the art of cryptography. The Handbook of Applied Cryptography provides a treatment that is multifunctional: It serves as an introduction to the more practical aspects of both conventional and public-key cryptography It is a valuable source of the latest techniques and algorithms for the serious practitioner It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit It provides a mathematical treatment to accompany practical discussions It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.

Advances In Cryptology Crypto 2006

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Author : Cynthia Dwork
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-08

Advances In Cryptology Crypto 2006 written by Cynthia Dwork and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-08 with Business & Economics categories.

Constitutes the refereed proceedings of the 26th Annual International Cryptology Conference, CRYPTO 2006, held in California, USA in 2006. These papers address the foundational, theoretical and research aspects of cryptology, cryptography, and cryptanalysis as well as advanced applications.