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Fast, simple to use symmetric cipher for integer encryption in Java

What is in Java a cipher function for integer encryption having these properties?:
Fast
Symmetric-key algorithm
Simple to use (i.e. a couple of lines of code to use it and no external library to include)
It is possible to specify the output length (e.g. 20 characters)
I need to use it only to encrypt/decrypt integers.

The requirement for no external library reduces the list to DES, 3DES and AES. DES and 3DES have a block size of 64 bits whereas AES has a block size of 128 bits. There are different aspects, one can examine this for.
Ciphertext size
DES and 3DES are best used for integers that are at most 56-bit wide (non-full long), because the result will be a single block of 8 byte, because of padding. If you encrypt a full long value, then an additional padding block will be added.
AES will always produce a 16 byte ciphertext for any int of long value.
Speed
According to this analysis AES (Rijndael-128) is more than twice as fast as DES/3DES with a bigger key size (more secure). AES can be even much faster than DES or 3DES when the CPU supports AES-NI. All current CPUs support this. This is my current result for taken from the openssl speed command.
AES achieves 127MB/s for 16 byte payloads whereas 3DES only achieves 27MB/s. Here's the data to poke around.
Security
Don't use DES for anything serious, because it only has a 56-bit key (64-bit with parity). Brute forcing cost is 256. 3DES is also not that good, because Brute forcing cost is 2112. Brute forcing cost for AES is 2128, 2192, 2256 depending on the used key size.
Code
Probably use AES:
private final String CIPHER_NAME = "AES/ECB/PKCS5Padding";
private final String ALGORITHM_NAME = "AES"; // keySizes 128, 192, 256
// private final String CIPHER_NAME = "DES/ECB/PKCS5Padding";
// private final String ALGORITHM_NAME = "DES"; // keySize 56
// private final String CIPHER_NAME = "DESede/ECB/PKCS5Padding";
// private final String ALGORITHM_NAME = "DESede"; // keySize 168
byte[] encrypt(SecretKey key, long num) {
BigInteger bignum = BigInteger.valueOf(num);
Cipher cipher = Cipher.getInstance(CIPHER_NAME);
cipher.init(Cipher.ENCRYPT_MODE, key);
return cipher.doFinal(bignum.toByteArray());
}
long decrypt(SecretKey key, byte[] ct) {
Cipher cipher = Cipher.getInstance(CIPHER_NAME);
cipher.init(Cipher.DECRYPT_MODE, key);
byte[] pt = cipher.doFinal(ct);
BigInteger bignum = new BigInteger(pt);
return bignum.longValue();
}
SecretKey keyGen(String algorithm, int keySize) {
KeyGenerator keygen = KeyGenerator.getInstance(algorithm);
keygen.init(keySize);
return keygen.generateKey();
}
Mode of operation
Here I use ECB mode. It is generally not a good idea to use it. It has a problem that encrypting the same plaintext with the same key results in the same ciphertext. This may not be a property that is acceptable. If it is not acceptable, then you need to use for example CBC mode with a new random IV. With will blow up the ciphertext by an additional block.

If you don't need a secure solution, but just fast one, consider the XOR cipher:
int key = ...
....
int b = a ^ key;
int c = b ^ key;
assert (c == a);

You should never implement a cipher yourself if you want any security. There's just too much what can get wrong.
But you can write your numbers into a byte[] and use a cipher provided with Java like described in this answer.

BigInteger implementation of RSA's key generation

I am having a bit of trouble getting the modulus's size to be consistently 128 bytes big. Sometimes the modulus's byte array has a size of 129 or even 130. I've searched for implementation online, and my implementation is really close to the one from this link: http://introcs.cs.princeton.edu/java/78crypto/RSA.java.html
Here is my implementation:
public static void genKey() throws NoSuchAlgorithmException, NoSuchProviderException {
int bitLength = 512;
SecureRandom srand = new SecureRandom();
BigInteger one = new BigInteger("1");
BigInteger p = BigInteger.probablePrime(bitLength, srand);
BigInteger q = BigInteger.probablePrime(bitLength, srand);
BigInteger phi = (p.subtract(one)).multiply(q.subtract(one));
BigInteger modulus = p.multiply(q); //Varies here
BigInteger publicKey = new BigInteger("65537");
BigInteger privateKey = publicKey.modInverse(phi);
byte[] modulusArray = modulus.toByteArray();
byte[] publicKeyArray = publicKey.toByteArray();
byte[] privateKeyArray = privateKey.toByteArray();
byte[] tmpArray = new byte[128];
for (int i = 0; i < publicKeyArray.length; i++) {
tmpArray[i] = publicKeyArray[i];
}
publicKeyArray = tmpArray;
byte[] publicKeyAndModulus = concat(modulusArray, publicKeyArray);
byte[] privateKeyAndModulus = concat(modulusArray, privateKeyArray);
}
In addition, the privateKey length would vary a bit too. Can I get more consistency with the size using java.Security library or is this not possible to achieve?

The BigInteger#bitLength() function has the necessary documentation:
Returns the number of bits in the minimal two's-complement representation of this BigInteger, excluding a sign bit.
When you generate a BigInteger with bitLength 512, the most significant bit will be 0 ~50% of the time in which case the sign bit will take its place and it will fit into 64 bytes, but in the other cases the most significant bit will be 1 which means that the sign bit will be put into a new byte.
This means that using 511 as the bitLength always results BigIntegers of 64 bytes and 128 bytes for the modulus.
You shouldn't really generate p, q, the modulus and all the other values yourself. It is best to use existing APIs such as Java's Cipher class which also provides proper padding to be used with RSA such as OAEP (PKCS#1 v1.5 is not good anymore): "RSA/ECB/OAEPWithSHA-256AndMGF1Padding".

I suggest you use BouncyCastle and create an AsymmetricCipherKeyPair; here is an example I adapted from RSA using BouncyCastle
public static AsymmetricCipherKeyPair generateKeys(int keySizeInBits) {
RSAKeyPairGenerator kpg = new RSAKeyPairGenerator();
kpg.init(new KeyGenerationParameters(new SecureRandom(), keySizeInBits));
return kpg.generateKeyPair();
}

RSA Authentication Issue

I'm making a system where I want to verify the server's identity via RSA, but I can't seem to get the server to properly decrypt the client's message.
The public and private keys are in slot 0 of the array, and mod is in slot 1, so they are setup correctly.
Client side code
int keyLength = 3072 / 8;//RSA key size
byte[] data = new byte[keyLength];
//Generate some random data. Note that
//Only the fist half of this will be used.
new SecureRandom().nextBytes(data);
int serverKeySize = in.readInt();
if (serverKeySize != keyLength) {//Definitely not the right heard
return false;
}
//Take the server's half of the random data and pass ours
in.readFully(data, keyLength / 2 , keyLength / 2);
//Encrypt the data
BigInteger[] keys = getKeys();
BigInteger original = new BigInteger(data);
BigInteger encrypted = original.modPow(keys[0], keys[1]);
data = encrypted.toByteArray();
out.write(data);
//If the server's hash doesn't match, the server has the wrong key!
in.readFully(data, 0, data.length);
BigInteger decrypted = new BigInteger(data);
return original.equals(decrypted);
Server side code
int keyLength = 3072 / 8;//Key length
byte[] data = new byte[keyLength];
//Send the second half of the key
out.write(data, keyLength / 2, keyLength / 2);
in.readFully(data);
BigInteger[] keys = getKeys();
BigInteger encrypted = new BigInteger(data);
BigInteger original = encrypted.modPow(keys[0], keys[1]);
data = original.toByteArray();
out.write(data);
AFAIK that implementation is correct however it doesn't seem to produce the correct output. Also no, I do not wish to use a Cipher for various reasons.

There are some critical details that are not being accounted for. The data you want to apply RSA to must be encoded as BigInteger x, with 0 <= x < n, where n is your modulus. You aren't doing that. In fact, because you are filling your entire data array with random data you cannot guarantee that. The PKCS#1 padding algorithm is designed to do this correctly, but since you are rolling your own you'll have to fix this in your code. Also, examine carefully how the BigInteger(byte[]) constructor and BigInteger.toByteArray() decode/encode integers. Naively many expect simply the base 256 encoding, and forget that BigInteger must accommodate negative integer also. It does so by using the ASN.1 DER integer rules. If the positive integer's high-order byte would be >= 128 then a leading zero byte is added.

Using secure random to generate a long number

I have seeded my secure random object with a long number. Now I want to extract another long number. But there is only a function called nextBytes(byte[] b) which gives a random byte[].
Is there any way to get a long number?
SecureRandom ranGen1 = new SecureRandom();
ranGen1.setSeed(1000);
SecureRandom ranGen2 = new SecureRandom();
ranGen2.setSeed(1000);
byte[] b1= new byte[3];
byte[] b2=new byte[3];
ranGen1.nextBytes(b1);
ranGen2.nextBytes(b2);
int a1=b1[0];
int a2=b1[1];
int a3=b1[2];
int c1=b2[0];
int c2=b2[1];
int c3=b2[2];
System.out.println(a1+", "+a2+", "+a3);//genearated by ranGen1
System.out.println(c1+", "+c2+", "+c3);//generated by ranGen2
System.out.println(ranGen1.nextLong());//genearated by ranGen1
System.out.println(ranGen2.nextLong());//generated by ranGen2
result:
4, -67, 69
4, -67, 69
-3292989024239613972 //this is using nextLong()
-3292989024239613972
The Output for Peter Lawrey's code:(Using secure random)
-7580880967916090810 -7580880967916090810
7364820596437092015 7364820596437092015
6152225453014145174 6152225453014145174
6933818190189005053 6933818190189005053
-2602185131584800869 -2602185131584800869
-4964993377763884762 -4964993377763884762
-3544990590938409243 -3544990590938409243
8725474288412822874 8725474288412822874
-8206089057857703584 -8206089057857703584
-7903450126640733697 -7903450126640733697
They are exaclty the same. How could you get different numbers?
This is the output that I am getting after using Peter Lawrey's second update(I am using windows operating system and he seems to be using some other operaing system which has created the confusion)
SHA1PRNG appears to produce the same values with the same seed
The default PRNG on this system is SHA1PRNG

Revised again, this is the correct answer! (and I should follow my own advice and read the documentation more carefully)
Is this what you're using? If so, it extends Random so it has an inherited nextLong() method. As it overrides next() all the typical Random methods will be using the SecureRandom PRNG method.
(see in the comments why my second answer is incorrect.. or rather unnecessary)
I would suggest creating a long by just composing it out of the next 8 bytes or of two ints (returned by next). There's no problem with doing that and I can't see any reason why you wouldn't be able to touch all the long values (think that either of the two 32-bit halves can have values from 0 to 2^32, with equal probability) or why one would be more probable than another (which would mean it's not pseudo-random).
I do not completely understand why the Random documentation indicates that limitation for nextLong(), but I believe it is a limitation of the linear algorithm that it uses (I think linear algorithms have a much shorter cycle - i.e. when they start repeating numbers - than modern PRNGs). I think that's worth exploring on crypto stack exchange for curiosity.

SecureRandom extends Random, and Random has a nextLong() method: http://docs.oracle.com/javase/6/docs/api/java/util/Random.html#nextLong%28%29

BigInteger randomNumber = new BigInteger(numBits, random);

Note: With Random, a given seed will always produce the same results. With SecureRandom it will not. The seed just adds to the randomness.
Have you ever user secure random? The whole point of seed is to produce the same sequesnce of numbers. This is also the case with secure random. Two secure random numbers seeded with the same value produce same sequence of random numbers.
public static void main(String... args) throws NoSuchProviderException, NoSuchAlgorithmException {
testRNG("NativePRNG");
testRNG("SHA1PRNG");
System.out.println("The default PRNG on this system is " + new SecureRandom().getAlgorithm());
}
private static void testRNG(String prng) throws NoSuchAlgorithmException, NoSuchProviderException {
SecureRandom sr1 = SecureRandom.getInstance(prng, "SUN");
SecureRandom sr2 = SecureRandom.getInstance(prng, "SUN");
sr1.setSeed(1);
sr2.setSeed(1);
for (int i = 0; i < 10; i++) {
if (sr1.nextLong() != sr2.nextLong()) {
System.out.println(prng + " does not produce the same values with the same seed");
return;
}
}
System.out.println(prng + " appears to produce the same values with the same seed");
}
prints
NativePRNG does not produce the same values with the same seed
SHA1PRNG appears to produce the same values with the same seed
The default PRNG on this system is NativePRNG
go and try it first
Good advice, but just trying it doesn't always give you the whole answer in this case.

Decrypting “long” message encrypted with RSA java

Hi this is the same question, that was asked two years ago:
Java/JCE: Decrypting “long” message encrypted with RSA
I had a large byte array and rsa keypair, initiated by value 1024.
Using rsa encryption and the specified size of the key is strong requirement, I can't change it. So I can't use symmetric encryption with asymetric encryption symmetric key. I can't use any other keys. I had a byte array and need ciphered byte array to be returned. I wonder if there is any ready tool, that can manage with this problem?
Sorry for such an amateurish question, but I really need a help.

As stated, your question has a single answer, and that's "no". RSA encryption is an algorithm which encrypts messages up to a given size, which depends on the key size; with a 1024-bit RSA key, and RSA as the standard describes it, the maximum size is 117 bytes, no more. There is no way to encrypt a larger message with RSA alone, and that's a definite, mathematical certainty.
If you really need to process longer messages, then you necessarily have to add something else. In that case, please, please, do not try to do anything fancy of your own devising with some oh-so-clever splitting of data into small blocks and the like. That path leads to doom. You might produce something which appears to compile and run, but which will be invariably weak in some way, like almost every other home-made variation on cryptography. That's because security cannot be tested: it is not a case of "works" or "does not work".
The well-trodden path of asymmetric encryption goes thus:
You select a random sequence of bytes of some appropriate length, e.g. 128 bits (that's 16 bytes). Let's call it K.
You encrypt K with the RSA public key; this yields E.
You encrypt the message with K using a symmetric encryption algorithm ("AES/CBC/PKCS5Padding"). Since this is a one-shot key, you can use an all-zeros IV. This yields a bunch of bytes, let's call it F.
The encrypted message is then the concatenation of E and F.
Decryption proceeds in the reverse order: the RSA private key is used to recover K from E, then K is used to decrypt F into the original message. The key K is never stored anywhere, and a new key K is generated every time (even if you encrypt the same message twice). That's important, do not change that unless you understand what you are doing (and if you do, then you already know that).
Given what you state about your problem, you have to do something else than "just RSA". The procedure I describe above is about the best "something else" that you could come up with, security-wise.
Assembling some cryptographic elements into such a protocol is a process fraught with pitfalls so you may have better luck using an already defined format and support library. Two common formats for asymmetric encryption are CMS and OpenPGP. A library which supports both and has good reputation is Bouncy Castle.

If you do need to encrypt/decrypt long strings using RSA, then you can break the bytes up in to smaller "chunks" and process each chunk of bytes through the cipher one at a time while storing the results in a ByteBuffer.
Encryption:
byte[] encData = null;
try {
// create public key
X509EncodedKeySpec publicKeySpec = new X509EncodedKeySpec(key);
KeyFactory kf = KeyFactory.getInstance("RSA");
PublicKey pk = kf.generatePublic(publicKeySpec);
Cipher pkCipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
pkCipher.init(Cipher.ENCRYPT_MODE, pk);
int chunkSize = 117; // 1024 / 8 - 11(padding) = 117
int encSize = (int) (Math.ceil(data.length/117.0)*128);
int idx = 0;
ByteBuffer buf = ByteBuffer.allocate(encSize);
while (idx < data.length) {
int len = Math.min(data.length-idx, chunkSize);
byte[] encChunk = pkCipher.doFinal(data, idx, len);
buf.put(encChunk);
idx += len;
}
// fully encrypted data
encData = buf.array();
} catch (Exception e) {
e.printStackTrace();
Decryption
Cipher rsaCipher = Cipher.getInstance("RSA/ECB/PKCS1Padding");
rsaCipher.init(Cipher.DECRYPT_MODE, rsaPk);
int chunkSize = 128;
int idx = 0;
ByteBuffer buf = ByteBuffer.allocate(data.length);
while(idx < data.length) {
int len = Math.min(data.length-idx, chunkSize);
byte[] chunk = rsaCipher.doFinal(data, idx, len);
buf.put(chunk);
idx += len;
}
// fully decrypted data
byte[] decryptedData = buf.array();