**Cryptography Tutorials - Herong's Tutorial Examples** - v5.40, by Dr. Herong Yang

Introduction of RSA Algorithm

This chapter provides tutorial notes and example codes on RSA public key encryption algorithm. Topics include illustration of public key algorithm; proof of RSA encryption algorithm; security of public key; efficient way of calculating exponentiation and modulus; generating large prime numbers.

What Is Public Key Encryption?

RSA Public Key Encryption Algorithm

Illustration of RSA Algorithm: p,q=5,7

Illustration of RSA Algorithm: p,q=7,19

Proof of RSA Public Key Encryption

Efficient RSA Encryption and Decryption Operations

Conclusions:

- RSA (Rivest, Shamir and Adleman) uses public key and private key to encrypt and decrypt messages.
- RSA public keys are generated using 2 large prime numbers.
- RSA public key security is based the difficult level of factoring prime numbers. Given P and q to calculate n = p*q is easy. But given n to find p and q is very difficult.
- RSA encryption operation requires calculation of "C = M**e mod n", which can be done by loop of "C = C*C * M**e[i]".
- Most RSA tools are using public keys generated from large probable prime numbers, because generating large prime numbers is very expensive.

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

►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

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"