Cryptography And Lattices

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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.

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.

Lattice Based Public Key Cryptography In Hardware

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Author : Sujoy Sinha Roy
language : en
Publisher: Springer
Release Date : 2019-11-25

Lattice Based Public Key Cryptography In Hardware written by Sujoy Sinha Roy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with Technology & Engineering categories.

This book describes the efficient implementation of public-key cryptography (PKC) to address the security challenges of massive amounts of information generated by the vast network of connected devices, ranging from tiny Radio Frequency Identification (RFID) tags to powerful desktop computers. It investigates implementation aspects of post quantum PKC and homomorphic encryption schemes whose security is based on the hardness of the ring-learning with error (LWE) problem. The work includes designing an FPGA-based accelerator to speed up computation on encrypted data in the cloud computer. It also proposes a more practical scheme that uses a special module called recryption box to assist homomorphic function evaluation, roughly 20 times faster than the implementation without this module.

Post Quantum Cryptography

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Author : Michele Mosca
language : en
Publisher: Springer
Release Date : 2014-09-23

Post Quantum Cryptography written by Michele Mosca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-23 with Computers categories.

This book constitutes the refereed proceedings of the 6th International Workshop on Post-Quantum Cryptography, PQCrypto 2014, held in Waterloo, ON, Canada, in October 2014. The 16 revised full papers presented were carefully reviewed and selected from 37 submissions. The papers cover all technical aspects of cryptographic research related to the future world with large quantum computers such as code-based cryptography, lattice-based cryptography, multivariate cryptography, isogeny-based cryptography, security proof frameworks, cryptanalysis and implementations.

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.

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.

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.

Lattice Basis Reduction

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Author : Murray R. Bremner
language : en
Publisher: CRC Press
Release Date : 2011-08-12

Lattice Basis Reduction written by Murray R. Bremner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-12 with Computers categories.

First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.

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.

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.