# Security of this scheme

I am developing a software and I am not sure if it is completely secure.

I have 22 Mb of data to encrypt used multiple times,
random IV (generated using RAND_bytes from OpenSSL lib)
and password which is $key = SHA3_{256}(PBKDF2(salt, password, 256000, SHA2-256))$.

SHA3_256 from Qt QCryptographicHash, PBKDF2 and SHA_256 from OpenSSL, salt is also generated from RAND_BYTE and 256 bits long.

Now I would like to know your opinion if this scheme is secure:

XOR key and IV together:

$$encryptionKey = IV \oplus key\\$$

encrypting IV:

$$firstBlock=E_{AES-EBC-256}(key, IV)$$

encrypting data:

$$secondBlock = E_{AES-GCM-256}(encryptionKey, IV, data)$$

and then:

$$output << firstBlock\\ output << secondBlock$$

I am not sure especially about this part $E_{AES-GCM-256}(IV \oplus key, IV, data)$.

• Is there any reason you aren't using Thomas Ptacek's Cryptographic Right Answers? – Jack O'Connor Dec 31 '15 at 16:22
• I cannot see connection with my question. I am using AES_GCM, 256 bits everywhere, PBKDF2 and SHA2_256 or SHA3_256. – MKAROL Dec 31 '15 at 16:34
• It just seems like you're doing some nonstandard things. I don't think your IV needs to be encrypted, using ECB mode is scary, and feeding related keys into AES is scary too. Compare to Ptacek's first recommendation: just use NaCl. You wouldn't need to worry about any of these decisions. – Jack O'Connor Dec 31 '15 at 17:04
• I am encrypting IV to avoid leaking information about changes in data (or lack of it) (IV exhaustion, if two ciphertexts are the same, data are the same). ECB mode on 16 byte long IV data (AES_BLOCK_SIZE == 16) is secure and data is random so even when decrypted the adversary doesn't know if he is successful. All I am worrying about are those related keys. What is more in C++ I am more willing to use OpenSSL. – MKAROL Dec 31 '15 at 17:42
• I think you have key and password flipped – Richie Frame Dec 31 '15 at 20:22

It's rather hard to answer the full question, but I'll try and answer as best as possible.

You try to derive a data encryption key using the IV, because you think the IV may be overused.

NIST SP 800-38D section 8.3 states (for a probability of non-repeation of $2^{-32}$ ):

The total number of invocations of the authenticated encryption function shall not exceed $2^{32}$, including all IV lengths and all instances of the authenticated encryption function with the given key.

Great, so unless you invoke GCM more than 4 billion times (short-scale), then you should be OK, and you may not need any special constructs.

Let's assume you don't want to limit the amount of GCM calls. In that case you to derive a key for each encryption. You can use a Key Based Key Derivation Function or KBKDF. Probably the best one you can use is HKDF. HKDF accepts a salt as well, and is able to generate as many bits from the input as needed. So you could use the following construct:

1. $salt = random()$
2. $seed = PBKDF2(salt, password, 256000, SHA2-256)$
3. $key = HKDF(seed, \text{"key"})$
4. $iv = HKDF(seed, \text{"iv"})$
5. $(ct, tag) = E_{AES-GCM-256}(key, iv, data)$
6. $output = encode(salt, (ct, tag))$

now say you don't want to perform those 256000 iterations for each file, and you want to encrypt/decrypt multiple files at a time, then you can do the following:

1. $salt = random()$
2. $seed = PBKDF2(salt, password, 256000, SHA2-256)$
3. $salt_2 = random()$
4. $key = HKDF(seed, salt_2, \text{"key"})$
5. $iv = HKDF(seed, salt_2, \text{"iv"})$
6. $(ct, tag) = E_{AES-GCM-256}(key, iv, data)$
7. $output = encode(salt, salt_2, (ct, tag))$

as HKDF can also use a salt. For each file, repeat steps 3 to 6.

A trick is to use just HKDF-expand and generate 512 bits for key and IV. Other, more simple KDF's such as KDF1 or KDF2 may also be used if HKDF is not available.

As for your scheme, I see some drawbacks.

1. the additional call to SHA-3 is spurious;
2. the IV of GCM is best set to 96 bits (12 bytes), but the XOR and encryption of the IV seems to suggest an IV of 128 bits;
3. the XOR'ing of key and IV is not a secure key derivation function;
4. the key length is now limited to the size of the IV or introduce additional complexities;
5. reusing the derived key for different, related algorithms is not recommended.

Here the combination of 3 and 5 is the biggest issue; you'd have to prove that the insecure key derivation doesn't hamper the security of the GCM algorithm. This is not something you should want to do.

As always, it may be advisable to use an existing protocol and library though; there are plenty secure ones available.

• 2. I am using code from OpenSSL template. (Is setting IV size to 16 bytes a problem?) Also I have a question about key=HKDF(seed,salt2,"key"). Is "key" simply a string? Finally, is it secure to use PBKDF2 with non-random salt (eg. hash of login)? – MKAROL Jan 1 '16 at 17:33
• 16 bytes is not the standard option and means additional processing, which doesn't help security either. "key" is indeed a string (say, ASCII encoded), it should be part of info as defined in RFC 5869 which handles labels. No, PBKDF2 should be used with a random salt. – Maarten Bodewes Jan 2 '16 at 0:53