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Breaking down RSA/ECB/OAEPWithSHA-256AndMGF1Padding

Java has a mode called RSA/ECB/OAEPWithSHA-256AndMGF1Padding. What does that even mean?
RFC3447, Public-Key Cryptography Standards (PKCS) #1: RSA Cryptography Specifications Version 2.1, section 7.1.2 Decryption operation says Hash and MGF are both options for RSAES-OAEP-DECRYPT. MGF is it's own function, defined in Section B.2.1 MGF1 and that has it's own Hash "option" as well.
Maybe the Hash "option" in RSAES-OAEP-DECRYPT and MGF1 are supposed to be the same or maybe they're not, it is unclear to me. If they are then I guess when you have RSA/ECB/OAEPWITHSHA-256ANDMGF1PADDING that means sha256 should be used for both. But if they're not supposed to be the same then you could have sha256 used for RSAES-OAEP-DECRYPT and, for example, sha1 used for MGF1. And if that's the case then what function is sha256 supposed to be used for? And what hash algorithm is supposed to be used for the other function?
And what does ECB mean in this context? ECB is a symmetric block cipher mode. Electronic Code Book. Maybe it's supposed to mean how Java deals with plaintext's that are larger than the modulo? Like maybe splits the plaintext into chunks that are as big as the modulo and then encrypts each one with RSA and concatenates them together? I'm just guessing..

The default for OAEP is to use SHA-1 for MGF1 (but see the edit on the end of this answer). Note that the hash chosen doesn't have that much impact on the security of OAEP, so mostly it will be left to this default.
We can easily test this by testing it against "OAEPPadding" and OAEPParameterSpec:
// --- we need a key pair to test encryption/decryption
KeyPairGenerator kpg = KeyPairGenerator.getInstance("RSA");
kpg.initialize(1024); // speedy generation, but not secure anymore
KeyPair kp = kpg.generateKeyPair();
RSAPublicKey pubkey = (RSAPublicKey) kp.getPublic();
RSAPrivateKey privkey = (RSAPrivateKey) kp.getPrivate();
// --- encrypt given algorithm string
Cipher oaepFromAlgo = Cipher.getInstance("RSA/ECB/OAEPWITHSHA-256ANDMGF1PADDING");
oaepFromAlgo.init(Cipher.ENCRYPT_MODE, pubkey);
byte[] ct = oaepFromAlgo.doFinal("owlstead".getBytes(StandardCharsets.UTF_8));
// --- decrypt given OAEPParameterSpec
Cipher oaepFromInit = Cipher.getInstance("RSA/ECB/OAEPPadding");
OAEPParameterSpec oaepParams = new OAEPParameterSpec("SHA-256", "MGF1", new MGF1ParameterSpec("SHA-1"), PSpecified.DEFAULT);
oaepFromInit.init(Cipher.DECRYPT_MODE, privkey, oaepParams);
byte[] pt = oaepFromInit.doFinal(ct);
System.out.println(new String(pt, StandardCharsets.UTF_8));
The code will fail with a padding related exception if you substitute "SHA-256" for the MGF1 as parameter.
The reason why the extended algorithm is needed at all is compatibility with other Cipher algorithms. Code written for e.g. "RSA/ECB/PKCS1Padding" doesn't use any parameters, let alone OAEP parameters. So without the longer string OAEP cannot function as drop in replacement.
The mode of operation "ECB" doesn't mean anything in this context, it should have been "None" or it should have been left out completely. You can only encrypt a single block using the RSA implementation of the SunRSA provider.
If you want to encrypt more data, create a random (AES) symmetric key and encrypt that using OAEP. Then use the AES key to encrypt your specific data. This is called a hybrid cryptosystem as it uses both asymmetric and symmetric primitives to encrypt data.
Note that OAEP is not supported in JDK 7 (1.7) or earlier. OAEP is included in the implementation requirements for Java runtimes since Java 8:
RSA/ECB/OAEPWithSHA-1AndMGF1Padding (1024, 2048)
RSA/ECB/OAEPWithSHA-256AndMGF1Padding (1024, 2048)
Some protocols may require you to use SHA-256 or SHA-512 within the padding, as SHA-1 is being deprecated for most use - even if it is not directly vulnerable for this kind of purpose.
EDIT: this was written mostly with Java in mind. By now many other libraries seem to take a somewhat different approach and use the same hash for the (mostly empty) label and MGF1 - which does make more sense. If you have an invalid OAEP ciphertext you should first make sure that the right "default" is being used. It is impossible to wrong any library implementation for choosing their own default; in the end it is up to the protocol to define the hashes used. Unfortunately no mandatory default exists - which is especially a problem if protocol owners forget to fully specify a configuration for the algorithms.

Symmetric key generation after ECDHC using KDF with SHA-256

I want to generate a Symmetric key using Single-step Key Derivation Function (KDF) based on SHA-256.
I think key derivations are in the lightweight API of Bouncy Castle since 1.50.
I have successfully generated the secret key "Z".And have a code for generating KDF from Z.
Please kind the code below
byte[] data = new byte[16];
SecretKey secretKeyA = generateSharedSecretZ(keyPairA.getPrivate(),
keyPairB.getPublic());
System.out.println(bytesToHex(secretKeyA.getEncoded()));
//Single-Step KDF specification using SHA256
Digest digest = new SHA256Digest();
System.out.println(digest.getDigestSize());
HKDFBytesGenerator kDF1BytesGenerator = new HKDFBytesGenerator(digest);
kDF1BytesGenerator.init(new HKDFParameters(secretKeyA.getEncoded(),
generateSalt(), null));
kDF1BytesGenerator.generateBytes(data, 0, 16);
System.out.println(new String(data));
System.out.println(data.length);
Using the below method for generating the salt
private static byte[] generateSalt() throws NoSuchAlgorithmException {
SecureRandom random = SecureRandom.getInstance("SHA1PRNG");
byte[] salt = new byte[32];
random.nextBytes(salt);
return salt;
}
I am using org.bouncycastle.crypto.generators.HKDFBytesGenerator for generating the Symmetric key using sha-256. Is the above implemention, a single-step KDF? Am I missing any relevant steps in generating the Symmetric key using single-step KDF using sha-256 according to the NIST 800-56A document.
Is there any standard size for the Symmetric key. Iam using the Symmetric key for Generates the MAC as per GCM-GMAC specification.

Beware that you need to communicate the salt value if you use one in HKDF. For a KDF after Key Agreement - which should already provide you with enough entropy in the secret - I would consider it strictly optional.
Yes, it is a single step KDF (at least it doesn't use multiple iterations as would be expected for a Password Based Key Derivation Function.
No, you don't seem to be missing any steps (not that there are that many). You could consider using "GCM.GMAC".getBytes(StandardCharsets.US_ASCII) as value for info; this makes it easier to generate more keys later on.
There is no standard size for symmetric keys. Modern crypto would require at least 128 bits (16 bytes). AES uses 128, 192 or 256 bit keys, neither of which is a bad choice. AES-128 may be slightly faster and does not require the Unlimited Crypto files for Java. AES-256 may protect against some future attacks that uses Quantum Cryptoanalysis.

I'm confuse about KeyGenerator and encoded key in JCE

Now I'm studying about Cryptography and I'm interested in JCE but I am confused about the KeyGenerator class. I know this class can generate a key for a symmetric algorithm but I don't understand why I should use this class? since I can create a secret key by myself using SecretKeyFactory and use it to init the cipher object,right?
like this code below
// Create Key
DESKeySpec desKeySpec = new DESKeySpec(key);
SecretKeyFactory keyFactory = SecretKeyFactory.getInstance("DES");
SecretKey secretKey = keyFactory.generateSecret(desKeySpec);
// Create Cipher
Cipher desCipher = Cipher.getInstance("DES/ECB/PKCS5Padding");
desCipher.init(Cipher.ENCRYPT_MODE, secretKey);
and then compare with this code
KeyGenerator generator = KeyGenerator.getInstance("AES", "BC");
generator.init(192);
Key encryptionKey = generator.generateKey();
What is the difference between them? Do they do the same thing?
Also, In what situation should I choose to use the "getEncoded()" method??

KeyGenerator is a convenience class for generating keys. You can tell it what algorithm you will be using in your Cipher and it can generate a key that matches the algorithm without you having to provide anything.
You can of course do this manually, but it takes a few steps as you have have demonstrated in your question (and you don't even cover generating the key data in byte[] key).

There are some JCE providers where keys are treated more securely than byte arrays in that keys are used to encrypt and decrypt data, but are themselves never present in memory in the clear. For example, Smart Card and HSM-backed providers work like that.
When you create a byte array and then construct the key out of it, you're explicitly loading it into memory. When you use a KeyGenerator, the key might be created in a secure storage and not present in memory, eliminating one attack vector.

Too much data for RSA block fail. What is PKCS#7?

Talking about javax.crypto.Cipher
I was trying to encrypt data using Cipher.getInstance("RSA/None/NoPadding", "BC") but I got the exception:
ArrayIndexOutOfBoundsException: too much data for RSA block
Looks like is something related to the "NoPadding", so, reading about padding, looks like CBC is the best approach to use here.
I found at google something about "RSA/CBC/PKCS#7", what is this "PKCS#7"? And why its not listed on sun's standard algorithm names?
Update:
I'm wondering, if is a padding problem, why this example run just fine?
import java.math.BigInteger;
import java.security.KeyFactory;
import java.security.interfaces.RSAPrivateKey;
import java.security.interfaces.RSAPublicKey;
import java.security.spec.RSAPrivateKeySpec;
import java.security.spec.RSAPublicKeySpec;
import javax.crypto.Cipher;
/**
* Basic RSA example.
*/
public class BaseRSAExample
{
public static void main(
String[] args)
throws Exception
{
byte[] input = new byte[] { (byte)0xbe, (byte)0xef };
Cipher cipher = Cipher.getInstance("RSA/None/NoPadding", "BC");
KeyFactory keyFactory = KeyFactory.getInstance("RSA", "BC");
// create the keys
RSAPublicKeySpec pubKeySpec = new RSAPublicKeySpec(
new BigInteger("d46f473a2d746537de2056ae3092c451", 16),
new BigInteger("11", 16));
RSAPrivateKeySpec privKeySpec = new RSAPrivateKeySpec(
new BigInteger("d46f473a2d746537de2056ae3092c451", 16),
new BigInteger("57791d5430d593164082036ad8b29fb1", 16));
RSAPublicKey pubKey = (RSAPublicKey)keyFactory.generatePublic(pubKeySpec);
RSAPrivateKey privKey = (RSAPrivateKey)keyFactory.generatePrivate(privKeySpec);
// encryption step
cipher.init(Cipher.ENCRYPT_MODE, pubKey);
byte[] cipherText = cipher.doFinal(input);
// decryption step
cipher.init(Cipher.DECRYPT_MODE, privKey);
byte[] plainText = cipher.doFinal(cipherText);
}
}
Update 2:
I realized that even if I use just Cipher.getInstance("RSA", "BC") it throws the same exception.

If you use a block cipher, you input must be an exact multiple of the block bit length.
In order to encipher arbitrary length data, you need first to pad you data to a multiple of the block length. This can be done with any method, but there are a number of standards. PKCS7 is one which is quite common, you can see an overview on the wikipedia article on padding.
Since block cipers operate on blocks, you also need to come up with a way of concatenating the encrypted blocks. This is very important, since naive techniques greatly reduce the strength of the encryption. There is also a wikipedia article on this.
What you did was to try to encrypt (or decrypt) data of a length which didn't match the block length of the cipher, and you also explicitly asked for no padding and also no chaining mode of operation.
Consequently the block cipher could not be applied to your data, and you got the reported exception.
UPDATE:
As a response to your update and GregS's remark, I would like to acknowledge that GregS was right (I did not know this about RSA), and elaborate a bit:
RSA does not operate on bits, it operates on integer numbers. In order to use RSA you therefore need to convert your string message into an integer m: 0 < m < n, where n is the modulus of the two distinct primes chosen in the generation process. The size of a key in the RSA algorithm typically refers to n. More details on this can be found on the wikipedia article on RSA.
The process of converting a string message to an integer, without loss (for instance truncating initial zeroes), the PKCS#1 standard is usually followed. This process also adds some other information for message integrity (a hash digest), semantical security (an IV) ed cetera. With this extra data, the maximum number of bytes which can be supplied to the RSA/None/PKCS1Padding is (keylength - 11). I do not know how PKCS#1 maps the input data to the output integer range, but
my impression is that it can take any length input less than or equal to keylength - 11 and produce a valid integer for the RSA encryption.
If you use no padding, your input will simply be interpreted as a number. Your example input, {0xbe, 0xef} will most probably be interpreted as {10111110 +o 11101111} = 1011111011101111_2 = 48879_10 = beef_16 (sic!). Since 0 < beef_16 < d46f473a2d746537de2056ae3092c451_16, your encryption will succeed. It should succeed with any number less than d46f473a2d746537de2056ae3092c451_16.
This is mentioned in the bouncycastle FAQ. They also state the following:
The RSA implementation that ships with
Bouncy Castle only allows the
encrypting of a single block of data.
The RSA algorithm is not suited to
streaming data and should not be used
that way. In a situation like this you
should encrypt the data using a
randomly generated key and a symmetric
cipher, after that you should encrypt
the randomly generated key using RSA,
and then send the encrypted data and
the encrypted random key to the other
end where they can reverse the process
(ie. decrypt the random key using
their RSA private key and then decrypt
the data).

RSA is a one-shot asymmetric encryption with constraints. It encrypts a single "message" in one go, but the message has to fit within rather tight limits based on the public key size. For a typical 1024 bit RSA key, the maximum input message length (with RSA as described in the PKCS#1 standard) is 117 bytes, no more. Also, with such a key, the encrypted message has length 128 bytes, regardless of the input message length. As a generic encryption mechanism, RSA is very inefficient, and wasteful of network bandwidth.
Symmetric encryption systems (e.g. AES or 3DES) are much more efficient, and they come with "chaining modes" which allow them to process input messages of arbitrary length. But they do not have the "asymmetric" property of RSA: with RSA, you can make the encryption key public without revealing the decryption key. That's the whole point of RSA. With symmetric encryption, whoever has the power to encrypt a message also has all the needed information to decrypt messages, hence you cannot make the encryption key public because it would make the decryption key public as well.
Thus it is customary to use an hybrid system, in which a (big) message is symmetrically encrypted (with, e.g., AES), using a symmetric key (which is an arbitrary short sequence of random bytes), and have that key encrypted with RSA. The receiving party then uses RSA decryption to recover that symmetric key, and then uses it to decrypt the message itself.
Beyond the rather simplistic description above, cryptographic systems, in particular hybrid systems, are clock full of little details which, if not taken care of, may make your application extremely weak against attackers. So it is best to use a protocol with an implementation which already handles all that hard work. PKCS#7 is such a protocol. Nowadays, it is standardized under the name of CMS. It is used in several places, e.g. at the heart of S/MIME (a standard for encrypting and signing emails). Another well-known protocol, meant for encrypting network traffic, is SSL (now standardized under the name of TLS, and often used in combination with HTTP as the famous "HTTPS" protocol).
Java contains an implementation of SSL (see javax.net.ssl). Java does not contain a CMS implementation (at least not in its API) but Bouncy Castle has some code for CMS.

This error indicates that the input data size is greater than the key modulus size. You will need a bigger key size to encrypt the data. If changing the key length is not an option, alternatively you may need to investigate if you are really expecting that big input data.

RSA can only be used to encrypt, when the number of bits being used to encrypt is greater then the size of the thing you are tying to encrypt + 11 bytes
Public-Key Cryptography Standards - PKCS

Scroll down a bit and you'll see it. It's not an cypher algortihm (like RSA) or a cypher mode like CBC, but a description of the way the certificate is encoded as bytes (i.e., a data structure syntax). You can find the spec for it here.

PKCS#7 is listed (referring to your link). It's encoding is PKCS7
Description
A PKCS#7 SignedData object, with the
only significant field being
certificates.
Use java.security.cert.CertificateFactory or CertPath when using PKCS7.
RSA is a block cipher. It encrypts block of the same key size.
Therefore, BouncyCastle RSA gives an exception if you try to encrypt a block
which is longer than the key size.
That's all I can tell you so far.

You should not encrypt your data using RSA directly. Encrypt your data with a random symmetric key (i.e. AES/CBC/PKCS5Padding) and encrypt the symmetric key using RSA/None/PKCS1Padding.

How to implement Java 256-bit AES encryption with CBC

I've read the following threads and they've helped a little, but I'm looking for a little more info.
How to write AES/CBC/PKCS5Padding encryption and decryption with Initialization Vector Parameter for BlackBerry
Java 256bit AES Encryption
Basically, what I am doing is writing a program that will encrypt a request to be sent over TCP/IP, and then decrypted by a server program. The encryption will need to be AES, and doing some research I found out I need to use CBC and PKCS5Padding. So basically I need a secret key and an IV as well.
The application I'm developing is for a phone, so I want to use the java security packages to keep the size down. I've got the design done, but unsure of the implementation of the IV and the shared key.
Here's some code:
// My user name
byte[] loginId = "login".getBytes();
byte[] preSharedKey128 = "ACME-1234AC".getBytes();
byte[] preSharedKey192 = "ACME-1234ACME-1234A".getBytes();
// 256 bit key
byte[] preSharedKey256 = "ACME-1234ACME-1234ACME-1234".getBytes();
byte[] preSharedKey = preSharedKey256;
// Initialization Vector
// Required for CBC
byte[] iv ={0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00};
IvParameterSpec ips = new IvParameterSpec(iv);
byte[] encodedKey = new byte[loginId.length + preSharedKey.length];
System.arraycopy(loginId, 0, encodedKey, 0, loginId.length);
System.arraycopy(preSharedKey, 0, encodedKey, loginId.length, preSharedKey.length);
// The SecretKeySpec provides a mechanism for application-specific generation
// of cryptography keys for consumption by the Java Crypto classes.
// Create a key specification first, based on our key input.
SecretKey aesKey = new SecretKeySpec(encodedKey, "AES");
// Create a Cipher for encrypting the data using the key we created.
Cipher encryptCipher;
encryptCipher = Cipher.getInstance("AES/CBC/PKCS5Padding");
// Initialize the Cipher with key and parameters
encryptCipher.init(Cipher.ENCRYPT_MODE, aesKey, ips);
// Our cleartext
String clearString = "33,8244000,9999,411,5012022517,0.00,0,1,V330";
byte[] cleartext = clearString.getBytes();
// Encrypt the cleartext
byte[] ciphertext = encryptCipher.doFinal(cleartext);
// Now decrypt back again...
// Decryption cipher
Cipher decryptCipher = Cipher.getInstance("AES/CBC/PKCS5Padding");
// Initialize PBE Cipher with key and parameters
decryptCipher.init(Cipher.DECRYPT_MODE, aesKey, ips);
// Decrypt the cleartext
byte[] deciphertext = decryptCipher.doFinal(ciphertext);
In a nutshell what it should do is encrypt some message that can decrypted by the server without the server needing to get a key or IV from the phone. Is there a way I could do this where I could secure the IV and key on the phone, and still have the key and IV known by the server as well? Feel free to tell me to make things more clear if they're not.

There are a few problems with the code. First of all, you really should use a key generator to generate secret keys. Just using some text directly might work for some algorithms, but others have weak keys and so forth that need to be tested.
Even if you want to do password-based encryption, the password should be run through a key-derivation algorithm to produce a key, as shown in my answer to the question that you cited already.
Also, you shouldn't use the no-arg getBytes() method of String. This is platform dependent. If all of the strings that you are encoding contain only characters from the US-ASCII character set, make it clear by specifying that encoding explicitly. Otherwise, if the phone and server platforms use different character encodings, the key and IV won't turn out the same.
For CBC mode, it's best to use a new IV for every message you send. Usually, CBC IVs are generated randomly. Other modes like CFB and OFB require unique IVs for every message. IVs are usually sent with along the ciphertext—IVs don't need to be kept secret, but many algorithms will break if a predictable IV is used.
The server doesn't need to get the secret or IV directly from the phone. You can configure the server with the secret key (or password, from which the secret key is derived), but in many applications, this would be a bad design.
For example, if the application is going to be deployed to the phones of multiple people, it isn't a good idea for them to use the same secret key. One malicious user can recover the key and break the system for everyone.
A better approach is to generate new secret keys at the phone, and use a key agreement algorithm to exchange the key with the server. Diffie-Hellman key agreement can be used for this, or the secret key can be encrypted with RSA and sent to the server.
Update:
Diffie-Hellman in "ephemeral-static" mode (and "static-static" mode too, though that's less desirable) is possible without an initial message from the server to the phone, as long as the server's public key is embedded in the application.
The server public key doesn't pose the same risk as embedding a common secret key in the phone. Since it is a public key, the threat would be an attacker getting his hands on (or remotely hacking into) the phone and replacing the real public key with a fake key that allows him to impersonate the server.
Static-static mode could be used, but it's actually more complicated and a little less secure. Every phone would need its own unique key pair, or you fall back into the secret key problem. At least there would be no need for the server to keep track of which phone has which key (assuming there is some authentication mechanism at the application level, like a password).
I don't know how fast phones are. On my desktop, generating an ephemeral key pair takes about 1/3 of a second. Generating Diffie-Hellman parameters is very slow; you'd definitely want to re-use the parameters from the server key.

Done similar projects in a midlet before, I have following advice for you:
There is no secure way to store shared secret on the phone. You can use it but this falls into a category called Security through Obscurity. It's like a "key under mat" kind of security.
Don't use 256-bit AES, which is not widely available. You might have to install another JCE. 128-bit AES or TripleDES are still considered secure. Considering #1, you shouldn't worry about this.
Encryption using a password (different for each user) is much more secure. But you shouldn't use password as the key like you are showing in the example. Please use PBEKeySpec (password-based encryption) to generate the keys.
If you are just worried about MITM (man-in-the-middle) attacks, use SSL.