CryptoBook
  • CryptoBook
  • Book Plan
  • Style Guide
    • Sample Page
  • Contributors
  • Fundamentals
    • Mathematical Notation
    • Division and Greatest common divisor
      • Euclidean Algorithm
    • Modular Arithmetic
      • Theorems of Wilson, Euler, and Fermat
        • Fermat's Little Theorem in Detail
        • Euler's Theorem in Detail
      • Quadratic Residues
    • Continued Fractions
  • Number Theory
  • Ideals
  • Polynomials With Shared Roots
  • Integer Factorization
    • Pollard rho
    • Sieves
  • Abstract algebra
    • Groups
      • Another take on groups
      • Discrete Log Problem
    • Rings
    • Fields
    • Polynomials
  • Elliptic Curves
    • Untitled
  • Lattices
    • Introduction
    • LLL reduction
      • Gram-Schmidt Orthogonalization
      • Lagrange's algorithm
      • LLL reduction
    • Lattice reduction
      • Minkowski reduced
      • HKZ reduced
      • LLL reduced
    • Applications
      • Coppersmith algorithm
      • Extensions of Coppersmith algorithm
    • Hard lattice problems
    • Lattices of interest
    • Cryptographic lattice problems
      • Short integer solutions (SIS)
      • Learning with errors (LWE)
      • Ring-LWE
      • NTRU
    • Interactive fun
    • Resources and notations
  • Asymmetric Cryptography
  • RSA
    • Proof of correctness
    • RSA application
    • Low Private Component Attacks
      • Wiener's Attack
      • Boneh-Durfee Attack
    • Common Modulus Attack
    • Recovering the Modulus
  • Diffie-Hellman
    • MITM
  • Elliptic Curve Cryptography
  • Symmetric Cryptography
    • Encryption
    • The One Time Pad
    • AES
      • Rijndael Finite Field
      • Round Transformations
  • Hashes
    • Introduction / overview
    • The Birthday paradox / attack
  • Isogeny Based Cryptography
    • Introduction to Isogeny Cryptography
    • Isogenies
    • Isogeny and Ramanujan Graphs
  • Appendices
    • Sets and Functions
    • Probability Theory
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On this page
  • Introduction
  • Laws of Addition
  • Interesting Identity
  • Sage Example
  • Further Resources

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  1. Style Guide

Sample Page

A rough guideline to a page

Introduction

Give a description of the topic, and what you hope the reader will get from this. For example, this page will cover addition of the natural numbers. Talk about how this relates to something in cryptography, either through a protocol, or an attack. This can be a single sentence, or verbose.

Laws of Addition

For all integers, the addition operation is

  • Associative: a+(b+c)=(a+b)+ca + (b + c) = (a + b) + ca+(b+c)=(a+b)+c

  • Commutative: a+b=b+aa + b = b + aa+b=b+a

  • Distributive: a(b+c)=ab+aca(b + c) = ab + aca(b+c)=ab+ac

  • Contains an identity element: a+0=0+a=aa + 0 = 0 + a = aa+0=0+a=a

  • Has an inverse for every element: a+(−a)=(−a)+a=0a + (-a) = (-a) + a = 0a+(−a)=(−a)+a=0

  • Closed: ∀a,b∈Z,a+b∈Z\forall a, b \in \mathbb{Z}, a + b \in \mathbb{Z}∀a,b∈Z,a+b∈Z

Interesting Identity

(1+2+3+…+n)2=13+23+33+…+n3(1 + 2 + 3 + \ldots + n)^2 = 1^3 + 2^3 + 3^3 + \ldots + n^3(1+2+3+…+n)2=13+23+33+…+n3

Sage Example

sage: 1 + (2 + 3) == (1 + 2) + 3
True
sage: 1 + 2 == 2 + 1
True
sage: 5*(7 + 11) == 5*7 + 5*11
True
sage: sum(i for i in range(1000))^2 == sum(i^3 for i in range(1000))
True

Further Resources

  • Links to

  • Other interesting

  • Resources

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Last updated 4 years ago

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