Cryptography Tutorials - Herong's Tutorial Examples - v5.42, by Herong Yang
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
Introduction to AES (Advanced Encryption Standard)
DES Algorithm - Illustrated with Java Programs
DES Algorithm Java Implementation
DES Algorithm - Java Implementation in JDK JCE
DES Encryption Operation Modes
PHP Implementation of DES - mcrypt
Blowfish - 8-Byte Block Cipher
Secret Key Generation and Management
Cipher - Secret Key Encryption and Decryption
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
OpenSSL Introduction and Installation
OpenSSL Generating and Managing RSA Keys
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"