Cryptography Tutorials - Herong's Tutorial Examples - Version 5.36, by Dr. Herong Yang
RSA Keys Generated by RsaKeyGenerator.java
This section provides some RSA keys generated by my BigInteger implementation, RsaKeyGenerator.java, of RSA public key and private key generation algorithm.
Are you ready to see how my initial implementation of RSA public key and private key generation behaves? Here is the first test run using JDK 1.6:
C:\herong>javac RsaKeyGenerator.java C:\herong>java RsaKeyGenerator 4 Exception in thread "main" java.lang.ArithmeticException: bitLength < 2 at java.math.BigInteger.probablePrime(BigInteger.java:539) at RsaKeyGenerator.getCoprime(RsaKeyGenerator.java:35) at RsaKeyGenerator.main(RsaKeyGenerator.java:21)
Too bad. The program failed in the "getCoprime()" call to find a public key, "e". This is because the requested key size is too low, which does not give enough room to find a public key, "e".
Rerun the program with a higher key size. The problem should go away.
C:\herong>java RsaKeyGenerator 5 p: 3 q: 5 m: 8 Modulus: 15 Key size: 4 Public key: 5 Private key: 5
The program completed! But the result is not ideal. The private key is the same as the public key "5". This makes my private key not secure. The program could be enhanced to ensure the private key is different than the public key.
Rerun the program with a higher key size. Hope it will return a good pair of public key and private key.
C:\herong>java RsaKeyGenerator 7 p: 7 q: 11 m: 60 Modulus: 77 Key size: 7 Public key: 17 Private key: 53
Cool. The program generated a good pair of public key, {77,17} and {77,53}.
Rerun the program with different key sizes:
C:\herong>java RsaKeyGenerator 8 p: 11 q: 13 m: 120 Modulus: 143 Key size: 8 Public key: 53 Private key: 77 C:\herong>java RsaKeyGenerator 16 p: 151 q: 157 m: 23400 Modulus: 23707 Key size: 15 Public key: 10151 Private key: 4751 C:\herong>java RsaKeyGenerator 32 p: 34613 q: 34631 m: 1198613560 Modulus: 1198682803 Key size: 31 Public key: 756303523 Private key: 705860827 C:\herong>java RsaKeyGenerator 64 p: 2966449091 q: 2966449099 m: 8799820227293420820 Modulus: 8799820233226319009 Key size: 63 Public key: 3447872045926560979 Private key: 5997668047507921159 C:\herong>java RsaKeyGenerator 128 p: 17902136406704537069 q: 17902136406704537077 m: 320486487924256034368552058949822333168 Modulus: 320486487924256034404356331763231407313 Key size: 128 Public key: 138184930940463531660820083778072069237 Private key: 173448309040289888328993883042709949325 C:\herong>java RsaKeyGenerator 256 p: 248658744261550238073459677814507557459 q: 248658744261550238073459677814507557527 m: 618311710977310434529034534762836648859088873902738200302650613... Modulus: 618311710977310434529034534762836648864062048787969205064... Key size: 256 Public key: 394190853336940694532345943348534965939075733405768734... Private key: 21429568381701961014089098585280129682302896350728470...
Output looks good. But we need test them with the encryption and decryption process.
Last update: 2013.
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
Generating Prime Number with BigInteger Class
Performance of Prime Number Generation
RSA Encryption Implementation using BigInteger Class
RsaKeyGenerator.java for RSA Key Generation
►RSA Keys Generated by RsaKeyGenerator.java
RsaKeyValidator.java for RSA Key Validation
64-bit RSA Key Validated by RsaKeyValidator.java
Converting Byte Sequences to Positive Integers
Cleartext Block Size for RSA Encryption
Cleartext Message Padding and Revised Block Size
Ciphertext Block Size for RSA Encryption
RsaKeyEncryption.java for RSA Encryption Operation
RsaKeyDecryption.java for RSA Decryption Operation
Testing RsaKeyEncryption.java with a 16-bit Key
Testing RsaKeyEncryption.java with a 64-bit Key
Testing RsaKeyEncryption.java with a 3072-bit Key
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"
Using Certificates in IE (Internet Explorer)