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Algorithms Analysis & Design
  • Algorithm Analysis & Design
  • 🚢Searching and Sorting
    • Introduction-Search
    • Linear Search
    • Binary Search
    • Interpolation Search
    • Introduction-Sorting
    • Bubble Sort
    • Selection Sort
    • Counting Sort
  • 💸Greedy Method
    • Introduction
    • Activity Selection
    • Fractional Knapsack Problem
    • Graph Colouring
  • 🚠Backtracking
    • Introduction
    • Hamiltonian Path/Cycle Problem
    • N Queen Problem
    • Rat in a Maze
    • Knight's Tour Problem
  • ⚔️Divide and Conquer
    • Introduction
    • Strassen's Matrix multiplication
    • Karatsuba algorithm
    • Tower of Hanoi
    • Closest Pair
  • 💣Dynamic Programming
    • Introduction
    • Longest Common Subsequence
    • Floyd-Warshall Algorithm
    • 0-1 Knapsack problem
    • Dice Throw
  • 📈Graph
    • Introduction
    • DFS
    • Dictionary Game
    • BFS
    • Flood Fill Algorithm
    • Minesweeper Lite
  • 🔢Number Theory
    • Introduction
    • GCD
    • Factorial
    • IsPrime | School Method
    • IsPrime | Fermat's Little Theorem
    • IsPrime | Miller-Rabin Method
  • 🌮References
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  1. Number Theory

Introduction

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Last updated 3 years ago

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Number theory was once viewed as a beautiful but largely useless subject in pure mathematics.

Today number-theoretic algorithms are used widely, due in part to the invention of cryptographic schemes based on large prime numbers.

The feasibility of these schemes rests on our ability to find large primes easily, while their security rests on our inability to factor the product of large primes. This chapter presents some of the number theory and associated algorithms that underlie such applications.

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