Cryptography Tutorials - Herong's Tutorial Notes
Dr. Herong Yang, Version 4.00

Basic Concepts

Part:   1  2 

This chapter describes some basic concepts of cryptography:

  • What is cryptography?
  • Functions.
  • Encryptions.


Cryptography - The study of techniques related to all aspects of data security. The word "cryptography" is derived from the ancient Greek words "kryptos" (hidden) and "graphia" (writing).

Some aspects of data security:

  • Confidentiality - Keeping data secret.
  • Data Integrity - Ensuring data has not been altered.
  • Entity Authentication - Identifying parties involved.
  • Data Origin Authentication - Identifying the data origin.

Cryptanalysis - The study of techniques to defeat cryptographic techniques.


Function - Two sets of elements, X and Y, and a rule, f, which assigns to each element in X, to one element in Y. A function is denoted as f: X -> Y.

Domain - The set of elements, X, in the above definition.

Codomain - The set of elements, Y, in the above definition.

If x is element in X, and y is the element in Y assigned to x by a function f, y is called the image of x, and denoted as y = f(x).

If y = f(x), x is called a preimage of y.

Image of Function - The set of all elements in Y which has at least one preimage in X.

1-1 Function - A function that satisfies that "if x <> y, then f(x) <> f(y)". No two elements in the domain will have the same image for a 1-1 function.

Bijection - A 1-1 function that satisfies that "image of f is Y".

Inverses Function - The function g of a bijection f that satisfies that "if y = f(x), then x = g(y)".

One-way Function - A bijection that satisfies that "the computation of its inverse function is very hard, and close to infeasible".

Trapdoor One-way Function - A one-way function that satisfies that "the computation of its inverse function becomes feasible, if additional information is given".

Permutation - A bijection that satisfies "f: X -> X".

Involution - A permutation that satisfies that "inverse function of f is f".

(Continued on next part...)

Part:   1  2 

Dr. Herong Yang, updated in 2007
Cryptography Tutorials - Herong's Tutorial Notes - Basic Concepts