Modern cryptography, probabilistic proofs and pseudorandomness
著者
書誌事項
Modern cryptography, probabilistic proofs and pseudorandomness
(Algorithms and combinatorics, 17)
Springer-Verlag, c1999
大学図書館所蔵 全60件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Cryptography is one of the most active areas in current mathematics research and applications. This book focuses on cryptography along with two related areas: the study of probabilistic proof systems, and the theory of computational pseudorandomness. Following a common theme that explores the interplay between randomness and computation, the important notions in each field are covered, as well as novel ideas and insights.
目次
Preface Chapter 1: The Foundations of Modern Cryptography 1.1 Introduction Part I: Basic Tools 1.2 Central Paradigms 1.2.1 Computational Difficulty 1.2.2 Computational Indistinguishability 1.2.3 The Simulation Paradigm 1.3 Pseudorandomness 1.3.1 The Basics 1.3.2 Pseudorandom Functions 1.4 Zero-Knowledge 1.4.1 The Basics 1.4.2 Some Variants Part II: Basic Utilities 1.5 Encryption 1.5.1 Definitions 1.5.2 Constructions 1.5.3 Beyond eavesdropping security 1.6 Signatures 1.6.1 Definitions 1.6.2 Constructions 1.6.3 Two variants 1.7 Cryptographic Protocols 1.7.1 Definitions 1.7.2 Constructions Part III: Concluding Comments 1.8 Some Notes 1.8.1 General notes 1.8.2 Specific notes 1.9 Historical Perspective 1.10 Two Suggestions for Future Research 1.11 Some Suggestions for Further Reading Chapter 2: Probabilistic Proof Systems 2.1 Introduction 2.2 Interactive Proof Systems 2.2.1 Definition 2.2.2 The Role of Randomness 2.2.3 The Power of Interactive Proofs 2.2.4 The Interactive Proof System Hierarchy 2.2.5 How Powerful Should the Prover be? 2.3 Zero-Knowledge Proof Systems 2.3.1 A Sample Definition 2.3.2 The Power of Zero-Knowledge 2.3.3 The Role of Randomness 2.4 Probabilistically Checkable Proof Systems 2.4.1 Definition 2.4.2 The Power of Probabilistically Checkable Proofs 2.4.3 PCP and Approximation 2.4.4 More on PCP itself 2.4.5 The Role of Randomness 2.5 Other Probabilistic Proof Systems 2.5.1 Restricting the Provers Strategy 2.5.2 Non-Interactive Probabilistic Proofs 2.5.3 Proofs of Knowledge 2.5.4 Refereed Games 2.6 Concluding Remarks 2.6.1 Comparison among the various systems 2.6.2 The Story 2.6.3 Open Problems Chapter 3: Pseudorandom Generators 3.1 Introduction 3.2 The General Paradigm 3.3 The Archetypical Case 3.3.1 A Short Discussion 3.3.2 Some Basic Observations 3.3.3 Constructions 3.3.4 Pseudorandom Functions 3.4 Derandomization of time-complexity classes 3.5 Space Pseudorandom Generators 3.6 Special Purpose Generators 3.6.1 Pairwise-Independence Generators 3.6.2Small-Bias Generators 3.6.3 Random Walks on Expanders 3.6.4 Samplers 3.6.5 Dispersers, Extractors and Weak Random Sources 3.7 Concluding Remarks 3.7.1 Discussion 3.7.2 Historical Perspective 3.7.3 Open Problems Appendix A: Background on Randomness and Computation A.1 Probability Theory -- Three Inequalities A.2 Computational Models and Complexity classes A.2.1 P, NP, and more A.2.2 Probabilistic Polynomial-Time A.2.3 Non-Uniform Polynomial-Time A.2.4 Oracle Machines A.2.5 Space Bounded Machines A.2.6 Average-Case Complexity A.3 Complexity classes -- Glossary A.4 Some Basic Cryptographic Settings A.4.1 Encryption Schemes A.4.2 Digital Signatures and Message Authentication A.4.3 The RSA and Rabin Functions Appendix B: Randomized Computations B.1 Randomized Algorithms B.1.1 Approx. Counting of DNF satisfying assignments B.1.2 Finding a perfect matching B.1.3 Testing whether polynomials are identical B.1.4 Randomized Rounding applied to MaxSAT B.1.5 Primality Testing B.1.6 Testing Graph Connectivity via a random walk B.1.7 Finding minimum cuts in graphs B.2 Randomness in Complexity Theory B.2.1 Reducing (Approximate) Counting to Deciding B.2.2 Two-sided error versus one-sided error B.2.3 The permanent: Worst-Case vs Average Case B.3 Randomness in Distributed Computing B.3.1 Testing String Equality B.3.2 Routing in networks B.3.3 Byzantine Agreement B.4 Bibliographic Notes Appendix C: Notes on two proofs C.1 Parallel repetition of interactive proofs C.2 A generic Hard-Core Predicate C.2.1 A motivating discussion C.2.2 Back to the formal argument C.2.3 Improved Implementation of Algorithm $A Appendix D: Related Surveys by the Author Bibliography (over 300 entries) '
「Nielsen BookData」 より