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Encrypt and Decrypt Data with Public Private Keys

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To encrypt data with a public key: 

final Cipher rsa = Cipher.getInstance("RSA");

rsa.init(Cipher.ENCRYPT_MODE, keyPair.getPublic());
rsa.update(message.getBytes());
final byte[] result = rsa.doFinal();

System.out.println("Message: " + message);
System.out.println("Encrypted: " + DatatypeConverter.printHexBinary(result));

Produces output similar to: 

Message: Hello
Encrypted: 5641FBB9558ECFA9ED...

Note that when creating the Cipher object, you have to specify a transformation that is compatible with the type of key being used. (See JCA Standard Algorithm Names for a list of supported transformations.). For RSA encryption data message.getBytes() length must be smaller than the key size. See this SO Answer for detail.

To decrypt the data: 

final Cipher rsa = Cipher.getInstance("RSA");

rsa.init(Cipher.DECRYPT_MODE, keyPair.getPrivate());
rsa.update(cipherText);
final String result = new String(rsa.doFinal());

System.out.println("Decrypted: " + result);

Produces the following output: 

Decrypted: Hello
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Security and Cryptograhy:
* Security Cryptography
* Compute Cryptographic Hashes
* Generate Cryptographically Random Data
* Generate Public Private Key Pairs
* Compute and Verify Digital Signatures
* Encrypt and Decrypt Data with Public Private Keys
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