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E-grāmata: Computational Cryptography: Algorithmic Aspects of Cryptology

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Computational Cryptography: Algorithmic Aspects of CryptologyPalielināt
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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 LenstraLenstraLovįsz 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.

Recenzijas

'This volume celebrates the research career of Arjen Lenstra. The volume covers the latest research in many areas of applied cryptography: from algorithms for factoring and discrete log, to fast implementations of computer algebra, to the selection of cryptographic key sizes. Each topic is masterfully covered by a top researcher in the respective area. The information covered in this volume will serve readers for many years to come, and is sure to inspire further research on these topics.' Dan Boneh, Stanford University 'This book demonstrates the breathtaking diversity of Arjen Lenstra's research over the last forty years, and the deep influence his work has had on computational aspects of cryptography. Each chapter is written by a leading domain expert and provides an in a nutshell overview of a specific topic. The book is sure to become an important reference for experts and beginners alike.' Kenneth Paterson, ETH Zurich 'With highly accessible surveys by leading cryptographers, this book hits all pins with a single strike: framing the important area of "computational cryptography" through its fascinating history, peeking into its (no less prominent) future, and celebrating the impactful research career of one of its principal architects, Arjen Lenstra.' Ronald Cramer, CWI Amsterdam and Leiden University

Papildus informācija

A guide to cryptanalysis and the implementation of cryptosystems, written for students and security engineers by leading experts.
List of Contributors
x
Preface xi
1 Introduction Joppe W. Bos and Martijn Stam
1(14)
1.1 Biographical Sketch
1(8)
1.2 Outline
9(6)
Part I Cryptanalysis
2 Lattice Attacks on NTRU and LWE: A History of Refinements Martin R. Albrecht and Leo Ducas
15(26)
2.1 Introduction
15(2)
2.2 Notation and Preliminaries
17(1)
2.3 Lattice Reduction: Theory
18(2)
2.4 Practical Behaviour on Random Lattices
20(9)
2.5 Behaviour on LWE Instances
29(5)
2.6 Behaviour on NTRU Instances
34(7)
3 History of Integer Factorisation Samuel S. Wagstaff, Jr
41(37)
3.1 The Dark Ages: Before RS A
41(6)
3.2 The Enlightenment: RSA
47(3)
3.3 The Renaissance: Continued Fractions
50(5)
3.4 The Reformation: A Quadratic Sieve
55(3)
3.5 The Revolution: A Number Field Sieve
58(4)
3.6 An Exquisite Diversion: Elliptic Curves
62(5)
3.7 The Future: How Hard Can Factoring Be?
67(11)
4 Lattice-Based Integer Factorisation: An Introduction to Coppersmith's Method Alexander May
78(28)
4.1 Introduction to Coppersmith's Method
79(1)
4.2 Useful Coppersmith-Type Theorems
80(5)
4.3 Applications in the Univariate Case
85(10)
4.4 Multivariate Applications: Small Secret Exponent RSA
95(5)
4.5 Open Problems and Further Directions
100(6)
5 Computing Discrete Logarithms Robert Granger and vAntoine Joux
106(34)
5.1 Introduction
106(4)
5.2 Elliptic Curves
110(8)
5.3 Some Group Descriptions with Easier Discrete Logarithms
118(4)
5.4 Discrete Logarithms for XTR and Algebraic Tori
122(8)
5.5 Discrete Logarithms in Finite Fields of Fixed Characteristic
130(9)
5.6 Conclusion
139(1)
6 RSA, DH and DSA in the Wild Nadia Heninger
140(42)
6.1 Introduction
140(1)
6.2 RSA
141(13)
6.3 Diffie--Hellman
154(16)
6.4 Elliptic-Curve Diffie--Hellman
170(4)
6.5 (EC)DSA
174(7)
6.6 Conclusion
181(1)
7 A Survey of Chosen-Prefix Collision Attacks Marc Stevens
182(41)
7.1 Cryptographic Hash Functions
182(4)
7.2 Chosen-Prefix Collisions
186(4)
7.3 Chosen-Prefix Collision Abuse Scenarios
190(22)
7.4 MD5 Collision Attacks
212(11)
Part II Implementations
8 Efficient Modular Arithmetic Joppe W. Bos, Thorsten Kleinjung and Dan Page
223(28)
8.1 Montgomery Multiplication
224(1)
8.2 Arithmetic for RSA
225(12)
8.3 Arithmetic for ECC
237(6)
8.4 Special Arithmetic
243(8)
9 Arithmetic Software Libraries Victor Shoup
251(42)
9.1 Introduction
251(3)
9.2 Long-Integer Arithmetic
254(5)
9.3 Number-Theoretic Transforms
259(11)
9.4 Arithmetic in Zp[ X] for Multi-Precision p
270(12)
9.5 Arithmetic in Zp[ X] for Single-Precision p
282(4)
9.6 Matrix Arithmetic over Zp
286(3)
9.7 Polynomial and Matrix Arithmetic over Other Finite Rings
289(1)
9.8 Polynomial and Matrix Arithmetic over Z
289(2)
9.9 The Future of NTL
291(2)
10 XTR and Tori Martijn Stam
293(21)
10.1 The Birth of XTR
293(4)
10.2 The Magic of XTR
297(7)
10.3 The Conservative Use of Tori
304(4)
10.4 Pairings with Elliptic Curves
308(3)
10.5 Over the Edge: Cyclotomic Subgroups Recycled
311(3)
11 History of Cryptographic Key Sizes Nigel P. Smart and Emmanuel Thome
314(21)
11.1 Introduction
314(1)
11.2 Attacking Symmetric Algorithms with Software and Hardware
315(3)
11.3 Software Attacks on Factoring and Discrete Logarithms
318(5)
11.4 Hardware for Factoring
323(2)
11.5 Attacking Cryptosystems Based on Elliptic Curves
325(4)
11.6 Post-Quantum Cryptography
329(3)
11.7 Key-Size Recommendation
332(3)
References 335(48)
Index 383
Joppe W. Bos is a cryptographic researcher in the Competence Center for Crypto & Security at NXP Semiconductors, Leuven, Belgium. Previously, he was a post-doctoral researcher in the Cryptography Research Group at Microsoft Research and obtained his PhD at EPFL, Lausanne, Switzerland. His research focuses on computational number theory and high-performance arithmetic as used in (post-quantum) public-key cryptography. He is the editor of the book Topics in Computational Number Theory Inspired by Peter L. Montgomery and serves as the Editor of the Cryptology ePrint Archive, and he is elected as the Secretary of the International Association for Cryptologic Research. Martijn Stam is a Chief Research Scientist in cryptology at Simula UiB, Bergen, Norway. Previously, he was a Reader in Cryptology at the University of Bristol, UK and a postdoc at EPFL Switzerland. He obtained his PhD at the TU Eindhoven in the Netherlands. His research ranges a wide area of cryptologic research, with an emphasis on a mathematical and algorithmic perspective. He has won two FSE Best Paper Awards and served as elected Secretary of the IACR from 2011 to 2016.
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