Hashing in Computer Science
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Hashing in Computer Science: Fifty Years of Slicing and Dicing

Hashing in Computer Science: Fifty Years of Slicing and Dicing

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International Edition


About the Book

Written by one of the developers of the technology, Hashing is both a historical document on the development of hashing and an analysis of the applications of hashing in a society increasingly concerned with security. The material in this book is based on courses taught by the author, and key points are reinforced in sample problems and an accompanying instructor s manual. Graduate students and researchers in mathematics, cryptography, and security will benefit from this overview of hashing and the complicated mathematics that it requires.

Table of Contents:
PREFACE. PART I: MATHEMATICAL PRELIMINARIES. 1. Counting. 1.1: The Sum and Product Rules. 1.2: Mathematical Induction. 1.3: Factorial. 1.4: Binomial Coefficients. 1.5: Multinomial Coefficients. 1.6: Permutations. 1.7: Combinations. 1.8: The Principle of Inclusion-Exclusion. 1.9: Partitions. 1.10: Relations. 1.11: Inverse Relations. Appendix 1: Summations Involving Binomial Coefficients. 2. Recurrence and Generating Functions. 2.1: Recursions. 2.2: Generating Functions. 2.3: Linear Constant Coefficient Recursions. 2.4: Solving Homogeneous LCCRs Using Generating Functions. 2.5: The Catalan Recursion. 2.6: The Umbral Calculus. 2.7: Exponential Generating Functions. 2.8: Partitions of a Set: The Bell and Stirling Numbers. 2.9: Rouché’s Theorem and the Lagrange’s Inversion Formula. 3. Asymptotic Analysis. 3.1: Growth Notation for Sequences. 3.2: Asymptotic Sequences and Expansions. 3.3: Saddle Points. 3.4: Laplace’s Method. 3.5: The Saddle Point Method. 3.6: When Will the Saddle Point Method Work? 3.7: The Saddle Point Bounds. 3.8: Examples of Saddle Point Analysis. 4. Discrete Probability Theory. 4.1: The Origins of Probability Theory. 4.2: Chance Experiments, Sample Points, Spaces, and Events. 4.3: Random Variables. 4.4: Moments—Expectation and Variance. 4.5: The Birthday Paradox. 4.6: Conditional Probability and Independence. 4.7: The Law of Large Numbers (LLN). 4.8: The Central Limit Theorem (CLT). 4.9: Random Processes and Markov Chains. 5. Number Theory and Modern Algebra. 5.1: Prime Numbers. 5.2: Modular Arithmetic and the Euclidean Algorithm. 5.3: Modular Multiplication. 5.4: The Theorems of Fermat and Euler. 5.5: Fields and Extension Fields. 5.6: Factorization of Integers. 5.7: Testing Primality. 6. Basic Concepts of Cryptography. 6.1: The Lexicon of Cryptography. 6.2: Stream Ciphers. 6.3: Block Ciphers. 6.4: Secrecy Systems and Cryptanalysis. 6.5: Symmetric and Two-Key Cryptographic Systems. 6.6: The Appearance of Public Key Cryptographic systems. 6.7: A Multitude of Keys. 6.8: The RSA Cryptosystem. 6.9: Does PKC Solve the Problem of Key Distribution? 6.10: Elliptic Groups Over the Reals. 6.11: Elliptic Groups Over the Field Zm,2 . 6.12: Elliptic Group Cryptosystems. 6.13: The Menezes-Vanstone Elliptic Curve Cryptosystem. 6.14: Super-Singular Elliptic Curves. PART II: HASHING FOR STORAGE: DATA MANAGEMENT. 7. Basic Concepts. 7.1: Overview of the Records Management Problem. 7.2: A Simple Storage Management Protocol: Plain Vanilla Chaining. 7.3: Record-Management with Sorted Keys. 8. Hash Functions. 8.1: The Origin of Hashing. 8.2: Hash Tables. 8.3: A Statistical Model for Hashing. 8.4: The Likelihood of Collisions. 9. Hashing Functions: Examples and Evaluation. 9.1: Overview: The Tradeoff of Randomization Versus Computational Simplicity. 9.2: Some Examples of Hashing Functions. 9.3: Performance of Hash Functions: Formulation. 9.4: The X2-Test. 9.5: Testing a Hash Function. 9.6: The McKenzie et al. Results. 10. Record Chaining with Hash Tables. 10.1: Separate Chaining of Records. 10.2: Analysis of Separate Chaining Hashing Sequences and the Chains They Create. 10.3: A Combinatorial Analysis of Separate Chaining. 10.4: Coalesced Chaining. 10.5: The Pittel-Yu Analysis of EICH Coalesced Chaining. 10.6: To Separate or to Coalesce; and Which Version? That Is the Question. 11. Perfect Hashing. 11.1: Overview. 11.2: Chichelli’s Construction. 12. The Uniform Hashing Model. 12.1: An Idealized Hashing Model. 12.2: The Asymptotics of Uniform Hashing. 12.3: Collision-Free Hashing. 13. Hashing with Linear Probing. 13.1: Formulation and Preliminaries. 13.2: Performance Measures for LP Hashing. 13.3: All Cells Other than HTn-1 in the Hash-Table of n Cells are Occupied. 13.4: m-Keys Hashed into a Hash Table of n Cells Leaving Cell HTn-1 Unoccupied. 13.5: The Probability Distribution for the Length of a Search. 13.6: Asymptotics. 13.7: Hashing with Linear Open Addressing: Coda. 13.8: A Possible Improvement to Linear Probing. 14. Double Hashing. 14.1: Formulation of Double Hashing. 14.2: Progressions and Strides. 14.3: The Number of Progressions Which Fill a Hash-Table Cell. 14.3.1: Progression Graphs. 14.4: Dominance. 14.5: Insertion-Cost Bounds Relating Uniform and Double Hashing. 14.6: UsuallyDoubleHash. 14.7: The UDH Chance Experiment and the Cost to Insert the Next Key by Double Hashing. 14.8: Proof of Equation (14.12a). 14.9: UsuallyDoubleHash. 14.10: Proof of Equation (14.12b). 15. Optimum Hashing. 15.1: The Ullman–Yao Framework. 15.1.1: The Ullman–Yao Hashing Functions. 15.1.2: Ullman–Yao INSERT(k) and SEARCH(k). 15.1.3: The Ullman–Yao Statistical Model. 15.2: The Rates at Which a Cell is Probed and Occupied. 15.3: Partitions of (i)Scenarios, (i)Subscenarios, and Their Skeletons. 15.3.1: (i)Subscenarios. 15.3.2: Skeletons. 15.4: Randomly Generated m-Scenarios. 15.5: Bounds on Random Sums. 15.6: Completing the Proof of Theorem 15.1. PART III: SOME NOVEL APPLICATIONS OF HASHING. 16. Karp-Rabin String Searching. 16.1: Overview. 16.2: The Basic Karp-Rabin Hash-Fingerprint Algorithm. 16.3: The Plain Vanilla Karp-Rabin Fingerprint Algorithm. 16.4: Some Estimates on Prime Numbers. 16.5: The Cost of False Matches in the Plain Vanilla Karp-Rabin Fingerprint Algorithm. 16.6: Variations on the Plain Vanilla Karp-Rabin Fingerprint Algorithm. 16.7: A Nonhashing Karp-Rabin Fingerprint. 17. Hashing Rock and Roll. 17.1: Overview of Audio Fingerprinting . 17.2: The Basics of Fingerprinting Music. 17.3: Haar Wavelet Coding. 17.4: Min-Hash. 17.5: Some Commercial Fingerprinting Products. 18. Hashing in E-Commerce. 18.1: The Varied Applications of Cryptography. 18.2: Authentication. 18.3: The Need for Certificates. 18.4: Cryptographic Hash Functions. 18.5: X.509 Certificates and CCIT Standardization. 18.6: The Secure Socket Layer (SSL). 18.7: Trust on the Web ... Trust No One Over 40! 18.8: MD5. 18.9: Criticism of MD5. 18.10: The Wang-Yu Collision Attack. 18.11: Steven’s Improvement to the Wang-Yu Collision Attack. 18.12: The Chosen-Prefix Attack on MD5. 18.13: The Rogue CA Attack Scenario. 18.14: The Secure Hash Algorithms. 18.15: Criticism of SHA-1. 18.16: SHA-2. 18.17: What Now? Appendix 18: Sketch of the Steven’s Chosen Prefix Attack. 19. Hashing and the Secure Distribution of Digital Media. 19.1: Overview. 19.2: Intellectual Property (Copyrights and Patents). 19.3: Steganography. 19.4: Boil, Boil, Toil ... and But First, Carefully Mix. 19.5: Software Distribution Systems. 19.6: Watermarks. 19.7: An Image-Processing Technique for Watermarking. 19.8: Using Geometric Hashing to Watermark Images. 19.9: Biometrics and Hashing. 19.10: The Dongle. Appendix 19: Reed-Solomon and Hadamard Coding. Exercises and Solutions. INDEX.


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Product Details
  • ISBN-13: 9780470344736
  • Publisher: John Wiley & Sons Inc
  • Binding: Hardback
  • Language: English
  • Returnable: N
  • Spine Width: 25 mm
  • Weight: 979 gr
  • ISBN-10: 0470344733
  • Publisher Date: 25 Jun 2010
  • Height: 132 mm
  • No of Pages: 408
  • Returnable: N
  • Sub Title: Fifty Years of Slicing and Dicing
  • Width: 94 mm


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