When encrypting, you use their public key to write a message and they use their private key to read it.
When signing, you use your private key to write message's signature, and they use your public key to check if it's really yours.
I want to use my private key to generate messages so only I can possibly be the sender.
I want my public key to be used to read the messages and I do not care who reads them
This is signing, it is done with your private key.
I want to be able to encrypt certain information and use it as a product key for my software.
I only care that I am the only one who can generate these.
If you only need to know it to yourself, you don't need to mess with keys to do this. You may just generate random data and keep it in a database.
But if you want people to know that the keys are really yours, you need to generate random data, keep in it a database AND sign it with your key.
I would like to include my public key in my software to decrypt/read the signature of the key.
You'll probably need to purchase a certificate for your public key from a commercial provider like Verisign or Thawte, so that people may check that no one had forged your software and replaced your public key with theirs.
Share the password (a char[]) and salt (a byte[]—8 bytes selected by a SecureRandom makes a good salt—which doesn't need to be kept secret) with the recipient out-of-band. Then to derive a good key from this information:
/* Derive the key, given password and salt. */
SecretKeyFactory factory = SecretKeyFactory.getInstance("PBKDF2WithHmacSHA256");
KeySpec spec = new PBEKeySpec(password, salt, 65536, 256);
SecretKey tmp = factory.generateSecret(spec);
SecretKey secret = new SecretKeySpec(tmp.getEncoded(), "AES");
The magic numbers (which could be defined as constants somewhere) 65536 and 256 are the key derivation iteration count and the key size, respectively.
The key derivation function is iterated to require significant computational effort, and that prevents attackers from quickly trying many different passwords. The iteration count can be changed depending on the computing resources available.
The key size can be reduced to 128 bits, which is still considered "strong" encryption, but it doesn't give much of a safety margin if attacks are discovered that weaken AES.
Used with a proper block-chaining mode, the same derived key can be used to encrypt many messages. In Cipher Block Chaining (CBC), a random initialization vector (IV) is generated for each message, yielding different cipher text even if the plain text is identical. CBC may not be the most secure mode available to you (see AEAD below); there are many other modes with different security properties, but they all use a similar random input. In any case, the outputs of each encryption operation are the cipher text and the initialization vector:
/* Encrypt the message. */
Cipher cipher = Cipher.getInstance("AES/CBC/PKCS5Padding");
cipher.init(Cipher.ENCRYPT_MODE, secret);
AlgorithmParameters params = cipher.getParameters();
byte[] iv = params.getParameterSpec(IvParameterSpec.class).getIV();
byte[] ciphertext = cipher.doFinal("Hello, World!".getBytes(StandardCharsets.UTF_8));
Store the ciphertext and the iv. On decryption, the SecretKey is regenerated in exactly the same way, using using the password with the same salt and iteration parameters. Initialize the cipher with this key and the initialization vector stored with the message:
/* Decrypt the message, given derived key and initialization vector. */
Cipher cipher = Cipher.getInstance("AES/CBC/PKCS5Padding");
cipher.init(Cipher.DECRYPT_MODE, secret, new IvParameterSpec(iv));
String plaintext = new String(cipher.doFinal(ciphertext), StandardCharsets.UTF_8);
System.out.println(plaintext);
Java 7 included API support for AEAD cipher modes, and the "SunJCE" provider included with OpenJDK and Oracle distributions implements these beginning with Java 8. One of these modes is strongly recommended in place of CBC; it will protect the integrity of the data as well as their privacy.
A java.security.InvalidKeyException with the message "Illegal key size or default parameters" means that the cryptography strength is limited; the unlimited strength jurisdiction policy files are not in the correct location. In a JDK, they should be placed under ${jdk}/jre/lib/security
Based on the problem description, it sounds like the policy files are not correctly installed. Systems can easily have multiple Java runtimes; double-check to make sure that the correct location is being used.
Best Solution
Unless you are using something like ECB mode, the decryptor needs the initialization vector used by the encryptor.