What Is Function?

This section describes what is function - Two sets of elements, X and Y, and a rule, f, which assigns to each element in X, to one element in Y.

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".

Table of Contents

 About This Book

 Cryptography Terminology

Cryptography Basic Concepts

 What Is Cryptography?

What Is Function?

 What Is Encryption?

 Introduction to AES (Advanced Encryption Standard)

 Introduction to DES Algorithm

 DES Algorithm - Illustrated with Java Programs

 DES Algorithm Java Implementation

 DES Algorithm - Java Implementation in JDK JCE

 DES Encryption Operation Modes

 DES in Stream Cipher Modes

 PHP Implementation of DES - mcrypt

 Blowfish - 8-Byte Block Cipher

 Secret Key Generation and Management

 Cipher - Secret Key Encryption and Decryption

 Introduction of RSA Algorithm

 RSA Implementation using java.math.BigInteger Class

 Introduction of DSA (Digital Signature Algorithm)

 Java Default Implementation of DSA

 Private key and Public Key Pair Generation

 PKCS#8/X.509 Private/Public Encoding Standards

 Cipher - Public Key Encryption and Decryption

 MD5 Mesasge Digest Algorithm

 SHA1 Mesasge Digest Algorithm

 OpenSSL Introduction and Installation

 OpenSSL Generating and Managing RSA Keys

 OpenSSL Managing Certificates

 OpenSSL Generating and Signing CSR

 OpenSSL Validating Certificate Path

 "keytool" and "keystore" from JDK

 "OpenSSL" Signing CSR Generated by "keytool"

 Migrating Keys from "keystore" to "OpenSSL" Key Files

 Certificate X.509 Standard and DER/PEM Formats

 Migrating Keys from "OpenSSL" Key Files to "keystore"

 Using Certificates in IE (Internet Explorer)

 Using Certificates in Firefox

 Using Certificates in Google Chrome

 Outdated Tutorials

 References

 PDF Printing Version