About the Book

The Stony Brook Algorithm Repository

Steven Skiena
Stony Brook University
Dept. of Computer Science

• By Language
  • C
  • C++
  • C#
  • Java
  • FORTRAN
  • Python
  • Mathematica
  • Pascal
  • ADA
  • Lisp
  • Binary
• By Problem
  • 1.1 Data Structures
    • Dictionaries
    • Priority Queues
    • Suffix Trees and Arrays
    • Graph Data Structures
    • Set Data Structures
    • Kd-Trees
  • 1.2 Numerical Problems
    • Solving Linear Equations
    • Bandwidth Reduction
    • Matrix Multiplication
    • Determinants and Permanents
    • Constrained and Unconstrained Optimization
    • Linear Programming
    • Random Number Generation
    • Factoring and Primality Testing
    • Arbitrary Precision Arithmetic
    • Knapsack Problem
    • Discrete Fourier Transform
  • 1.3 Combinatorial Problems
    • Sorting
    • Searching
    • Median and Selection
    • Generating Permutations
    • Generating Subsets
    • Generating Partitions
    • Generating Graphs
    • Calendrical Calculations
    • Job Scheduling
    • Satisfiability
  • 1.4 Graph Problems -- polynomial-time problems
    • Connected Components
    • Topological Sorting
    • Minimum Spanning Tree
    • Shortest Path
    • Transitive Closure and Reduction
    • Matching
    • Eulerian Cycle / Chinese Postman
    • Edge and Vertex Connectivity
    • Network Flow
    • Drawing Graphs Nicely
    • Drawing Trees
    • Planarity Detection and Embedding
  • 1.5 Graph Problems -- hard problems
    • Clique
    • Independent Set
    • Vertex Cover
    • Traveling Salesman Problem
    • Hamiltonian Cycle
    • Graph Partition
    • Vertex Coloring
    • Edge Coloring
    • Graph Isomorphism
    • Steiner Tree
    • Feedback Edge/Vertex Set
  • 1.6 Computational Geometry
    • Robust Geometric Primitives
    • Convex Hull
    • Triangulation
    • Voronoi Diagrams
    • Nearest Neighbor Search
    • Range Search
    • Point Location
    • Intersection Detection
    • Bin Packing
    • Medial-Axis Transformation
    • Polygon Partitioning
    • Simplifying Polygons
    • Shape Similarity
    • Motion Planning
    • Maintaining Line Arrangements
    • Minkowski Sum
  • 1.7 Set and String Problems
    • Set Cover
    • Set Packing
    • String Matching
    • Approximate String Matching
    • Text Compression
    • Cryptography
    • Finite State Machine Minimization
    • Longest Common Substring
    • Shortest Common Superstring
• Algorithm Links
  • Algorithm Lectures
  • Algorithm Design Manual Information
  • CSE 373 Course page
  • NIST Dictory of Algorithms and Data Structures
  • World of Mathematics
  • Programming Challenges
  • Graduate Study Opportuinties

MIRACL is a Big Number Library which implements all of the primitives necessary to design Big Number Cryptography into your real-world application. It is primarily a tool for cryptographic system implementors. RSA public key cryptography, Diffie-Hellman Key exchange, DSA digital signature, they are all just a few procedure calls away. Support is also included for even more esoteric Elliptic Curves and Lucas function based schemes. The latest version offers full support for Elliptic Curve Cryptography over GF(p) and GF(2m) - see the links on this page for more details. Less well-known techniques can also be implemented as MIRACL allows you to work directly and efficiently with the big numbers that are the building blocks of number-theoretic cryptography. Although implemented as a C library, a well-thought out C++ wrapper is provided, which greatly simplifies program development. Most example programs (25+ of them) are provided in both C and C++ versions.