Today I was doing some leisurely reading and stumbled upon Section 5.8 (on page 45) of Recommendation for Pair-Wise Key Establishment Schemes Using Discrete Logarithm Cryptography (Revised) (NIST Special Publication 800-56A). I was very confused by this:
An Approved key derivation function
(KDF) shall be used to derive secret
keying material from a shared secret.
The output from a KDF shall only be
used for secret keying material, such
as a symmetric key used for data
encryption or message integrity, a
secret initialization vector, or a
master key that will be used to
generate other keys (possibly using a
different process). Nonsecret keying
material (such as a non-secret
initialization vector) shall not be
generated using the shared secret.
Now I'm no Alan Turing, but I thought that initialization vectors need not be kept secret. Under what circumstances would one want a "secret initialization vector?"
Thomas Pornin says that IVs are public and he seems well-versed in cryptography. Likewise with caf.
An initialization vector needs not be secret (it is not a key) but it needs not be public either (sender and receiver must know it, but it is not necessary that the Queen of England also knows it).
A typical key establishment protocol will result in both involve parties computing a piece of data which they, but only they, both know. With Diffie-Hellman (or any Elliptic Curve variant thereof), the said shared piece of data has a fixed length and they have no control over its value (they just both get the same seemingly random sequence of bits). In order to use that shared secret for symmetric encryption, they must derive that shared data into a sequence of bits of the appropriate length for whatever symmetric encryption algorithm they are about to use.
In a protocol in which you use a key establishment algorithm to obtain a shared secret between the sender and the receiver, and will use that secret to symmetrically encrypt a message (possibly a very long streamed message), it is possible to use the KDF to produce the key and the IV in one go. This is how it goes in, for instance, SSL: from the shared secret (called "pre-master secret" in the SSL spec) is computed a big block of derived secret data, which is then split into symmetric keys and initialization vectors for both directions of encryption. You could do otherwise, and, for instance, generate random IV and send them along with the encrypted data, instead of using an IV obtained through the KDF (that's how it goes in recent versions of TLS, the successor to SSL). Both strategies are equally valid (TLS uses external random IV because they want a fresh random IV for each "record" -- a packet of data within a TLS connection -- which is why using the KDF was not deemed appropriate anymore).
Well, consider that if two parties have the same cryptographic function, but don't have the same IV, they won't get the same results. So then, it seems like the proposal there is that the two parties get the same shared secret, and each generate, deterministically, an IV (that will be the same) and then they can communicate. That's just how I read it; but I've not actually read the document, and I'm not completely sure that my description is accurate; but it's how I'd start investigating.
IV is public or private, it doesn't matter
let's consider IV is known to attacker, now by looking at encrypted packet/data,
and knowledge of IV and no knowledge on encryption key, can he/she can guess about input data ? (think for a while)
let's go slightly backwards, let's say there is no IV in used in encryption
AES (input, K)= E1
Same input will always produce the same encrypted text.
Attacker can guess Key "K" by looking at encrypted text and some prior knowledge of input data(i.e. initial exchange of some protocols)
So, here is what IV helps. its added with input value , your encrypted text changes even for same input data.
i.e. AES (input, IV, K)= E1
Hence, attacker sees encrypted packets are different (even with same input data) and can't guess easily. (even having IV knowledge)
The starting value of the counter in CTR mode encryption can be thought of as an IV. If you make it secret, you end up with some amount of added security over the security granted by the key length of the cipher you're using. How much extra is hard to say, but not knowing it does increase the work required to figure out how to decrypt a given message.
Related
Recently while learning Backend development (Node, Express, MongoDB), I discovered the crypto-js library. According to the docs, we can use the following code to encrypt a message using the AES Encryption -
const ciphertext = CryptoJS.AES.encrypt('my message', 'secret key 123').toString();
However, as I'm new to cryptography, the difference between an encryption algorithm and a secret key is not very clear to me.
I have a message, and I can use the AES encryption algorithm to encrypt/decrypt it. Same way, I can use the AES encryption algorithm to decrypt the message as well. Hence, I don't understand how does a secret key fit in here? How exactly do an encryption algorithm and a secret key work in tandem to secure a message?
I have gone through numerous videos, blogs, StackOverflow posts, etc. on the internet, however, I couldn't understand it completely through all the complex crypto jargon. I do have a faint idea, which I'll describe below with the help of Ceaser's cipher.
In Ceaser's Cipher, what I've understood is that the technique of shifting letters by a certain number (A shifted by 4 places is E) is the encryption algorithm, and the certain number (4) is the secret key.
Can somebody please tell me if I'm correct?
If I'm correct, can you please tell me how exactly this translates in the case of the AES encryption mentioned in the beginning?
If I'm not correct, can anyone explain this with the help of a simple analogy? Please try to minimize the use of crypto jargon, as otherwise I'll get lost again.
The algorithm is a series of steps that happen in processing the data with the secret key to produce the encrypted data.
There are two inputs into the algorithm - the key and the initial data. The algorithm takes those two inputs and produces the encrypted output.
+---------+ +---------+
| Key | | Data |
+---------+ +---------+
\ /
\ /
\ /
\ /
\ /
+-----------+
| Algorithm |
+-----------+
|
+-----------+
| Encrypted |
| Result |
+-----------+
The key and the data are separate from the algorithm. If you change either of them, you will get a different encrypted result without changing the algorithm.
In your example of the very simple Caesar Cipher, the algorithm is that each character in the input is going to be replaced by another character (a substitution cipher) that is offset in the alphabet by some amount.
The key would be what the amount is. So, if the key is 1, then a is replaced by b and b is replaced by c and so on. The code for the algorithm can be written to accept the key as an input parameter or function argument and the algorithm code does not have to be rewritten for a different key. The key is applied to the input data by the algorithm programmatically to produced the result. The same algorithm code works with all the different keys you can pass it.
Can somebody please tell me if I'm correct [in understanding the algorithm and key in the Caesar Cipher]?
Yes, your understanding of that is correct.
If I'm correct, can you please tell me how exactly this translates in the case of the AES encryption mentioned in the beginning?
The AES encryption is a much more complicated algorithm that again accepts input data and a key. In this case, the key is a block of data itself, not just a single number. If you want to know more about how it works, you can find many articles on the web about it so it's probably better to read those than try to repeat all that here. Here's one article: What is AES Encryption and How Does It Work?.
Note, you generally do not need to know how a given encryption algorithm works in order to use it successfully. You do need to know how secure it is, what kind of keys are required, what kind of output it generates and how you decrypt it. But, you don't need to know the details of how the algorithm works. And, you need to select the right type of algorithm (for example, symmetric encryption with the same key used for encryption and description vs. asymmetric encryption such as public key/private key pairs) because this determines how you generate/manage/share secrets.
In your code example:
const ciphertext = CryptoJS.AES.encrypt('my message', 'secret key 123').toString();
CryptoJS.AES.encrypt is a function that implements the algorithm. It accepts two arguments. The first argument is the data you want encrypted. The second argument is a key string where all the data in the key is used in the encryption and the key will need to be supplied again in order to descrypt the data.
The result of the call to CryptoJS.AES.encrypt() is a buffer of data.
As it stands, I have written a python3 project to encrypt a file (using AES) and a public/private key system (RSA) to encrypt the AES key.
My current predicament is as follows, what is the best approach to get the encrypted AES key to the recipient ? My program does NOT depend on the medium for sending of the files, rather just the files are securely encrypted. In other words, once a user chooses a public key of the recipient, there is no peer-to-peer communication.
Is naming the file the RSA encrypted AES key a bad idea ?
I dont have extensive knowledge of cryptography as such, so any suggestions are welcome
If you know the recipient public RSA key you can use RSA-KEM (KEM : Key Encapsulation Mechanism). RSA-KEM for a single recipient with AES-GCM simply as follows;
The Sender;
First generate a x in [2..n-1] uniformly randomly, n is the RSA modulus.
Use a Key Derivation Function (KDF) on x,
key= KDF(x)
for AES 128,192, or 256-bit depending on your need. Prefer 256.
Encrypt the x,
c = x^c mod n
Encrypt the message with AES-GCM generate an IV and
(IV,ciphertext,tag) = AES-GCM-Enc(IV,message, key)
Send (c,(IV,ciphertext,tag))
The receiver;
To get x, They are using their private exponent d,
x = c^d mod n
Uses the same (KDF) on x to derive same AES key,
key= KDF(x)
Decrypts the message with AES-GCM
message = AES-GCM-Dec(IV,ciphertext,tag, key)
Note 1: This is actually a composition of a KEM and a DEM (data encapsulation mechanism; an authenticated cipher serves as a DEM). This provides the standard of IND-CCA2/NM-CCA2—ciphertext indistinguishability and nonmalleability under adaptive chosen-ciphertext attack. That is the minimum requirement for modern Cryptography.
Note 2: If you want to send the key itself as you described, to prevent the attacks on textbook RSA, you will need a padding scheme like OAEP or PKCS#v1.5. RSA-KEM eliminates this by using the full modulus as a message.
Note 3: The above described RSA-KEM work for a single-user case. RSA-KEM for multiple users will fall into Håstad's broadcast attack. Instead use RSAES-OAEP, this makes it safe for multiple recipients with the same x encrypted for different recipients. This will make it very useful to send the message multiple recipients instead of creating a new x for every recipient and encrypting the message for each derived key (as PGP/GPG does).
I read that XOR encryption can be considered very safe as long as two conditions are fulfilled.
1. The length of the key is as long (or longer) than the data
2. The key is not following a notable pattern (i.e. it's a random jumble of characters)
In that case, how about this: Before the XOR operations you use the (short) key to generate a seed for a Random Number Generator. You then use this Generator to create characters which are added to the end of your key until it's as long as the data you want to encrypt.
Then you use this new key to XOR the data.
I have tested this and it does seem to have no problem working as intended (it can encrypt and decrypt without corruption of the data).
My question is how "secure" such an encryption would be. Anyone have an estimate of how hard it'd be to break/decrypt that data?
As others have said, your idea is a stream cipher. It fails to be completely secure, like a One Time Pad is provably secure, because of the first condition you state:
The length of the key is as long (or longer) than the data
You are using a "short key" to seed your RNG. That is a weakness, because that "short key" is the cryptographic key for the whole system. If an attacker knows the short key, she can plug it into a copy of the RNG, generate the entire keystream and decrypt the message. If the key is too short she can try every possible key and eventually decrypt the message -- a brute force attack.
You are right that this avoids the problems with the OTP, but in so doing it loses the absolute security. There are secure stream ciphers, see eSTREAM for some examples, or else a block cipher running in counter mode is effectively a stream cipher.
Your idea is a reasonable one, but it has been thought of before. Sorry.
I need to sign a small string with an asymmetric key encryption scheme.
The signature will be stored on a small chip together with the signed string. I have very little space to spare (about 60bytes for signature + string), so the generated signature should be as small as possible.
I looked around for how to do it, and what I found is that I could use RSA-SHA1, but the generated signature with a 512 bit key is 64 bytes. That is a bit much.
What secure algorithm could I use to generate a small asymmetric signature?
Would it still be secure if I store the SHA1 sum of the RSA-SHA1 signature, and later verify that instead?
What you're bumping up against here is one of the properties of a good hash function - the return value should be long to protect against birthday attacks (where two different inputs result in the same output hash). Generally 128-512 bits is preferred hence the SHA-1 signature gives you 512 bits.
As with all things in cryptography security is a trade off. As you are using asymmetric signing have you considered using RSA-MD5 as your signature option? This will give you a far shorter return of 128 bits but this comes with the caveat that MD5 is considered broken and is generally being moved away from.
Best practice is to use unique ivs, but what is unique? Is it unique for each record? or absolutely unique (unique for each field too)?
If it's per field, that sounds awfully complicated, how do you manage the storage of so many ivs if you have 60 fields in each record.
I started an answer a while ago, but suffered a crash that lost what I'd put in. What I said was along the lines of:
It depends...
The key point is that if you ever reuse an IV, you open yourself up to cryptographic attacks that are easier to execute than those when you use a different IV every time. So, for every sequence where you need to start encrypting again, you need a new, unique IV.
You also need to look up cryptographic modes - the Wikipedia has an excellent illustration of why you should not use ECB. CTR mode can be very beneficial.
If you are encrypting each record separately, then you need to create and record one IV for the record. If you are encrypting each field separately, then you need to create and record one IV for each field. Storing the IVs can become a significant overhead, especially if you do field-level encryption.
However, you have to decide whether you need the flexibility of field level encryption. You might - it is unlikely, but there might be advantages to using a single key but different IVs for different fields. OTOH, I strongly suspect that it is overkill, not to mention stressing your IV generator (cryptographic random number generator).
If you can afford to do encryption at a page level instead of the row level (assuming rows are smaller than a page), then you may benefit from using one IV per page.
Erickson wrote:
You could do something clever like generating one random value in each record, and using a hash of the field name and the random value to produce an IV for that field.
However, I think a better approach is to store a structure in the field that collects an algorithm identifier, necessary parameters (like IV) for that parameter, and the ciphertext. This could be stored as a little binary packet, or encoded into some text like Base-85 or Base-64.
And Chris commented:
I am indeed using CBC mode. I thought about an algorithm to do a 1:many so I can store only 1 IV per record. But now I'm considering your idea of storing the IV with the ciphertext. Can you give me more some more advice: I'm using PHP + MySQL, and many of the fields are either varchar or text. I don't have much experience with binary in the database, I thought binary was database-unfriendly so I always base64_encoded when storing binary (like the IV for example).
To which I would add:
IBM DB2 LUW and Informix Dynamic Server both use a Base-64 encoded scheme for the character output of their ENCRYPT_AES() and related functions, storing the encryption scheme, IV and other information as well as the encrypted data.
I think you should look at CTR mode carefully - as I said before. You could create a 64-bit IV from, say, 48-bits of random data plus a 16-bit counter. You could use the counter part as an index into the record (probably in 16 byte chunks - one crypto block for AES).
I'm not familiar with how MySQL stores data at the disk level. However, it is perfectly possible to encrypt the entire record including the representation of NULL (absence of) values.
If you use a single IV for a record, but use a separate CBC encryption for each field, then each field has to be padded to 16 bytes, and you are definitely indulging in 'IV reuse'. I think this is cryptographically unsound. You would be much better off using a single IV for the entire record and either one unit of padding for the record and CBC mode or no padding and CTR mode (since CTR does not require padding - one of its merits; another is that you only use the encryption mode of the cipher for both encrypting and decrypting the data).
Once again, appendix C of NIST pub 800-38 might be helpful. E.g., according to this
you could generate an IV for the CBC mode simply by encrypting a unique nonce with your encryption key. Even simpler if you would use OFB then the IV just needs to be unique.
There is some confusion about what the real requirements are for good IVs in the CBC mode. Therefore, I think it is helpful to look briefly at some of the reasons behind these requirements.
Let's start with reviewing why IVs are even necessary. IVs randomize the ciphertext. If the same message is encrypted twice with the same key then (but different IVs) then the ciphertexts are distinct. An attacker who is given two (equally long) ciphertexts, should not be able to determine whether the two ciphertexts encrypt the same plaintext or two different plaintext. This property is usually called ciphertext indistinguishablility.
Obviously this is an important property for encrypting databases, where many short messages are encrypted.
Next, let's look at what can go wrong if the IVs are predictable. Let's for example take
Ericksons proposal:
"You could do something clever like generating one random value in each record, and using a hash of the field name and the random value to produce an IV for that field."
This is not secure. For simplicity assume that a user Alice has a record in which there
exist only two possible values m1 or m2 for a field F. Let Ra be the random value that was used to encrypt Alice's record. Then the ciphertext for the field F would be
EK(hash(F || Ra) xor m).
The random Ra is also stored in the record, since otherwise it wouldn't be possible to decrypt. An attacker Eve, who would like to learn the value of Alice's record can proceed as follows: First, she finds an existing record where she can add a value chosen by her.
Let Re be the random value used for this record and let F' be the field for which Eve can submit her own value v. Since the record already exists, it is possible to predict the IV for the field F', i.e. it is
hash(F' || Re).
Eve can exploit this by selecting her value v as
v = hash(F' || Re) xor hash(F || Ra) xor m1,
let the database encrypt this value, which is
EK(hash(F || Ra) xor m1)
and then compare the result with Alice's record. If the two result match, then she knows that m1 was the value stored in Alice's record otherwise it will be m2.
You can find variants of this attack by searching for "block-wise adaptive chosen plaintext attack" (e.g. this paper). There is even a variant that worked against TLS.
The attack can be prevented. Possibly by encrypting the random before using putting it into the record, deriving the IV by encrypting the result. But again, probably the simplest thing to do is what NIST already proposes. Generate a unique nonce for every field that you encrypt (this could simply be a counter) encrypt the nonce with your encryption key and use the result as an IV.
Also note, that the attack above is a chosen plaintext attack. Even more damaging attacks are possible if the attacker has the possibility to do chosen ciphertext attacks, i.e. is she can modify your database. Since I don't know how your databases are protected it is hard to make any claims there.
The requirements for IV uniqueness depend on the "mode" in which the cipher is used.
For CBC, the IV should be unpredictable for a given message.
For CTR, the IV has to be unique, period.
For ECB, of course, there is no IV. If a field is short, random identifier that fits in a single block, you can use ECB securely.
I think a good approach is to store a structure in the field that collects an algorithm identifier, necessary parameters (like IV) for that algorithm, and the ciphertext. This could be stored as a little binary packet, or encoded into some text like Base-85 or Base-64.