# Should we MAC-then-encrypt or encrypt-then-MAC?

Most of the time, when some data must be encrypted, it must also be protected with a MAC, because encryption protects only against passive attackers. There are some nifty encryption modes which include a MAC (EAX, GCM...) but let's assume that we are doing old-style crypto, so we have a standalone encryption method (e.g. AES with CBC chaining and PKCS#5 padding) and a standalone MAC (e.g. HMAC with SHA-256). How should we assemble the encryption and the MAC?

• MAC-then-Encrypt: Compute the MAC on the cleartext, append it to the data, and then encrypt the whole? (That's what TLS does)
• Encrypt-and-MAC: Compute the MAC on the cleartext, encrypt the cleartext, and then append the MAC at the end of the ciphertext? (That's what SSH does)
• Encrypt-then-MAC: Encrypt the cleartext, then compute the MAC on the ciphertext, and append it to the ciphertext? (In that case, we do not forget to include the initialization vector (IV) and the encryption method identifier into the MACed data.)

The first two options are often called "MAC-then-encrypt" while the third is "encrypt-then-MAC". What are the arguments for or against either?

• I've heard the second method most commonly referred to as encrypt-and-mac. – Stavros Korokithakis Oct 12 '13 at 14:35
• I am a bit perplexed by the fact that this question seems highly related to crypto.stackexchange.com/questions/5458/…, but has diametrically opposed answers... – Clément Mar 24 '14 at 12:41
• @Clément: the confusion comes from the widespread (but wrong) habit of calling MAC "signatures". In fact MAC and signatures are very different things used in very different contexts. Sign-then-encrypt protocols also use a distinct encryption key for each message, which nullifies all padding oracle attacks; and the signature is meant to serve as proof (e.g. in a trial), so it MUST be applied on the plaintext message. In MAC+encrypt contexts, the same symmetric key is often reused, and there is no "proof" requirement. – Thomas Pornin Apr 3 '14 at 10:56
• @Clément one difference is that here the secrets are shared, while in the public-key setting, anyone knowing the public key of the recipient can do the encryption part well. – npouillard Jul 2 '15 at 8:29
• Moxie Marlinspike says, 'When it comes to designing secure protocols, I have a principle that goes like this: if you have to perform any cryptographic operation before verifying the MAC on a message you’ve received, it will somehow inevitably lead to doom'. See moxie.org/blog/the-cryptographic-doom-principle – mti2935 Dec 20 '17 at 18:01

I'm assuming you actually know all of this better than I do. Anyway, this paper neatly summarizes all these approaches, and what level of security they do or don't provide. I shall paraphrase it in English, rather than Mathematical notation, as I understand it.

• Encrypt-then-MAC:

• Provides integrity of Ciphertext. Assuming the MAC shared secret has not been compromised, we ought to be able to deduce whether a given ciphertext is indeed authentic or has been forged; for example, in public-key cryptography anyone can send you messages. EtM ensures you only read valid messages.
• Plaintext integrity.
• If the cipher scheme is malleable we need not be so concerned since the MAC will filter out this invalid ciphertext.
• The MAC does not provide any information on the plaintext since, assuming the output of the cipher appears random, so does the MAC. In other words, we haven't carried any structure from the plaintext into the MAC.
• MAC-then-Encrypt:

• Does not provide any integrity on the ciphertext, since we have no way of knowing until we decrypt the message whether it was indeed authentic or spoofed.
• Plaintext integrity.
• If the cipher scheme is malleable it may be possible to alter the message to appear valid and have a valid MAC. This is a theoretical point, of course, since practically speaking the MAC secret should provide protection.
• Here, the MAC cannot provide any information on the plaintext either, since it is encrypted.
• Encrypt-and-MAC:

• No integrity on the ciphertext again, since the MAC is taken against the plaintext. This opens the door to some chosen-ciphertext attacks on the cipher, as shown in section 4 of Breaking and provably repairing the SSH authenticated encryption scheme: A case study of the Encode-then-Encrypt-and-MAC paradigm.
• The integrity of the plaintext can be verified
• If the cipher scheme is malleable, the contents of the ciphertext could well be altered, but on decryption, we ought to find the plaintext is invalid. Of course, any implementation error that can be exploited in the decryption process has been by that point.
• May reveal information about the plaintext in the MAC. Theoretical, of course, but a less than ideal scenario. This occurs if the plaintext messages are repeated, and the MACed data does not include a counter (it does in the SSH 2 protocol, but only as a 32-bit counter, so you should take care to re-key before it overflows).

In short, Encrypt-then-MAC is the most ideal scenario. Any modifications to the ciphertext that do not also have a valid MAC can be filtered out before decryption, protecting against any attacks on the implementation. The MAC cannot, also, be used to infer anything about the plaintext. MAC-then-Encrypt and Encrypt-and-MAC both provide different levels of security, but not the complete set provided by Encrypt-then-MAC.

• Please also note the "padding oracle attack" in the answer from Thomas. – Maarten Bodewes Nov 29 '11 at 20:55
• For personal/future reference: Encrypt-then-MAC = Encrypt the plaintext, MAC the ciphertext + iv then append it to the ciphertext. MAC-then-Encrypt = MAC the plaintext then append the MAC to the plaintext then Encrypt it all. Encrypt-and-MAC = Encrypt and MAC the plaintext then append the MAC onto the ciphertext. – MD Kieran Jun 25 '13 at 21:23
• Could you perhaps comment on crypto.stackexchange.com/questions/5458/… ? It seems to be a closely related, but with diametrically opposed answers... – Clément Mar 24 '14 at 12:42
• @clement it is a good point although I don't think you'd use a mac for identity verification... but there are definitely those who disagree that encrypt-then-mac is the best solution and their arguments are very very valid too. – user46 Mar 30 '14 at 19:21
• @Clément I have had a go at explaining the difference via a separate question, see crypto.stackexchange.com/q/15485/46 - feel free to ask for clarification there :) – user46 Apr 9 '14 at 9:18

@Ninefingers answers the question quite well; I just want to add a few details.

Encrypt-then-MAC is the mode which is recommended by most researchers. Mostly, it makes it easier to prove the security of the encryption part (because thanks to the MAC, a decryption engine cannot be fed with invalid ciphertexts; this yields automatic protection against chosen ciphertext attacks) and also avoids any trouble to confidentiality from the MAC (since the MAC operates on the encrypted text, it cannot reveal anything about the plaintext, regardless of its quality). Note that the padding oracle attacks, which have been applied in the field to ASP.NET, are chosen ciphertext attacks.

Ferguson and Schneier, in their book Practical Cryptography, have argued the opposite: that MAC-then-encrypt (or MAC-and-encrypt) is the "natural" order and that encrypt-then-MAC is overly complex. The sore point of encrypt-then-MAC is that you have to be careful about what you MAC: you must not forget the initialization vector, or (in case the protocol allows algorithm flexibility) the unambiguous identifier for the encryption algorithm; otherwise, the attacker could change either, inducing a plaintext alteration which would be undetected by the MAC. To prove their point, Ferguson and Schneier describe an attack over an instance of IPsec in which the encrypt-then-MAC was not done properly.

So while encrypt-then-MAC is theoretically better, it is also somewhat harder to get right.

• It really depends on the priorities of your application, though :) Whenever authentication is the key point, use AtE, and whenever secrecy is paramount, use EtA :) I.e. whenever it's mostly about safety and security, go for AtE, and whenever it's mostly about secrecy and security, go for EtA :) – yeoman Oct 30 '16 at 20:31
• Plus, if you're going for AtE, please use a stream cypher because padding and AtE don't go together very well :) – yeoman Oct 30 '16 at 20:42
• And never ever even consider using the same key for A & E 😬 – yeoman Oct 30 '16 at 20:51
• "you must not forget the initialization vector, or ... the unambiguous identifier for the encryption algorithm" -- while implementing, it occurred to me that one has to be mindful as to how to do this: the combined binary string has to be unique (i.e. the mapping injective)! Plain concatenation of binary strings may not have this property if more than one component is of variable length. I opted for ASN-DER. – Raphael Jul 13 '17 at 15:05
• So to sum it all, the zeroday paranoids will do mac-encrypt-mac. Or even encrypt-mac-encrypt-mac. – Pacerier Oct 24 '17 at 8:37

Hugo Krawczyk has a paper titled The Order of Encryption and Authentication for Protecting Communications (or: How Secure Is SSL?). It identifies 3 types of combining authentication (MAC) with encryption:

1. Encrypt then Authenticate (EtA) used in IPsec;
2. Authenticate then Encrypt (AtE) used in SSL;
3. Encrypt and Authenticate (E&A) used in SSH.

It proves that EtA is the secure way to use, and both AtE and E&A are subject to attacks, unless the encryption method is either in CBC mode or it is a stream cipher.

The abstract says everything; I emphasized important parts by bolding them:

We study the question of how to generically compose symmetric encryption and authentication when building “secure channels” for the protection of communications over insecure networks. We show that any secure channels protocol designed to work with any combination of secure encryption (against chosen plaintext attacks) and secure MAC must use the encrypt-then-authenticate method. We demonstrate this by showing that the other common methods of composing encryption and authentication, including the authenticate-then-encrypt method used in SSL, are not generically secure. We show an example of an encryption function that provides (Shannon’s) perfect secrecy but when combined with any MAC function under the authenticate-then-encrypt method yields a totally insecure protocol (for example, finding passwords or credit card numbers transmitted under the protection of such protocol becomes an easy task for an active attacker). The same applies to the encrypt-and-authenticate method used in SSH.

On the positive side we show that the authenticate-then-encrypt method is secure if the encryption method in use is either CBC mode (with an underlying secure block cipher) or a stream cipher (that xor the data with a random or pseudorandom pad). Thus, while we show the generic security of SSL to be broken, the current practical implementations of the protocol that use the above modes of encryption are safe.

• CBC decrypt before authentication in an online prococol is secure? What about padding oracle attacks? Or do they explicitly specify that you need to verify the MAC in the last block before unpadding? – Maarten Bodewes Nov 29 '11 at 21:04
• note that OpenSSH also supports E-t-M modes now (can be selected by limiting the hmacs): stribika.github.io/2015/01/04/secure-secure-shell.html – eckes Jan 6 '15 at 17:00
• This list is not exhaustive though, there are cipher modes that provide authenticated encryption, i.e. with no need for a separate hash algorittm (e.g. Galois/Counter Mode). I came up with several own schemes but this is still early experimentation. One of them e.g. is called multi-pass CBC (which cyclically applies CBC several times between standard cipher rounds), which appears to resist not only attacks on same-key CBC-MAC but also padding oracle attacks, but is impractical for large messages. It will be a while before (and if) I publish. – Arne Vogel Jun 20 '19 at 14:56
• @ArneVogel: Sure there are other possibilities. Yet the OP is asking about the order of combing encryption and MAC. – M.S. Dousti Jun 21 '19 at 11:07

Although there are already many answers here, I wanted to strongly advocate AGAINST MAC-then-encrypt. I fully agree with Thomas' first half of the answer, but completely disagree with the second half. The ciphertext is the ENTIRE ciphertext (including IV etc.), and this is what must be MACed. This is granted.

However, if you MAC-then-encrypt in the straightforward way, then you are completely vulnerable to padding-oracle attacks. by the "straightforward way", what I mean is that you call the "decrypt" function, and afterwards the "mac verify". However, if you get an error in the decrypt function, then you return this straight away, as a padding error. You have now just got a full blown padding oracle attack and you are dead. You can now hack the API and give a single error message only, but the time it takes to return the error has to be the same, whether it's a MAC error or a padding error. If you think that this is easy, then look at the Lucky13 attack on SSL. It's really really really hard (and much harder than just MACing all of the ciphertext).

The argument by Schneier and Ferguson for MAC-then-encrypt has no formal basis at all. The definition of authenticated-encryption is met by encrypt-then-MAC and is NOT met by MAC-then-encrypt. Furthermore, most implementations of MAC-then-encrypt are actually completely vulnerable to padding oracle attacks and so are actually broken in practice. Don't do this!

Having said all of the above, my recommendation is to not use any of this. You should be using GCM or CCM today (GCM is much faster, so use it as long as you are sure that your IV won't repeat). A combined authenticated-encryption scheme, with a single API call, and now you won't get in trouble.

• You advocate against MAC-then-encrypt, and then recommend using CCM, which is exactly a MAC-then-encrypt scheme. Isn't it a contradiction? – Penghe Geng Sep 26 '16 at 17:08
• CCM is a mode of encryption with a stand-alone proof of security and this distinguishes it from MAC-then-encrypt. It should not have the pitfalls of MAC-then-encrypt. The only problem that can arise is a bad implementation. I am certainly willing to concede that there is more chance of a bad implementation in a mode like this, but then again everything can be badly implemented so I'm not sure it should be a factor. – Yehuda Lindell Sep 27 '16 at 0:08
• IV related question: If a mode that does not use IV (like CTR) is used, should "nonce" be used in MAC computation somehow or it will be computed only from plain text in this case? – Jolinar Aug 11 '18 at 11:53
• The counter or IV must be included in the MAC. It is part of the ciphertext. – Yehuda Lindell Aug 12 '18 at 3:31
• And if the IV/nonce is derived from a salt (and password using KDF), what should be the part of MAC? The salt, the derived IV, both, or it doesn't matter? Thanks – Jolinar Aug 12 '18 at 20:11

Moxie Marlinspike calls it in his article http://www.thoughtcrime.org/blog/the-cryptographic-doom-principle/ the doom principle:

if you have to perform any cryptographic operation before verifying the MAC on a message you’ve received, it will somehow inevitably lead to doom.

He also demonstrates two attacks which are possible because of trying to decrypt before checking the MAC.

To summarize: "Encrypt Then Authenticate" is the way to go.

• As-is, I have a hard time finding reason to upvote this answer because your answer is close to a link-only answer. Can you elaborate a bit on what you are quoting? For example: can you explain “why” it is a problem to be able to decrypt a message before checking authentication, and why Moxie says it will “inevitably lead to doom” if you MAC-then-encrypt? That would certainly make your answer more valuable… after all, the question clearly asks “What are the arguments for or against either?” I can't really see you're providing arguments. Instead, you merely point to and quote a site. – e-sushi Apr 3 '14 at 10:49
• @e-sushi Agreed - it remains that this is one of the best accessible treatment of the subject. – user2398029 Apr 8 '14 at 0:51
• It is worth noting that this principle rules out applying the MAC to the plaintext regardless of whether the MAC is later encrypted or not. The principle itself is intuitively sound because the sooner you can discard a message with an invalid MAC, the less code can be targeted with corrupted inputs. One just has to not fall into the trap of assuming that just because the message carries a valid MAC, there is no way it could possibly be used to exploit buffer overflows or other vulnerabilities. – kasperd Aug 12 '14 at 20:21

I think Encrypt-then-MAC does not deliver Plaintext integrity, but only ciphertext integrity. If the MAC over the ciphertext is OK but then we use the wrong key to decrypt (for whatever reason), then the recipient receives a plaintext that the sender did not send and did not vouch for. If this can happen, this is a violation of plaintext integrity.

So, Encrypt-then-MAC is only secure if you can somehow be sure that decryption won't use the wrong key, and that any other processing/decoding done to the ciphertext after checking the MAC is completely correct. This is a somewhat fragile aspect of Encrypt-then-MAC, and one reason why Ferguson and Schneier advocate against Encrypt-then-MAC.

• I edited the answer to more clearly express the point Josef was trying to make. Personally, I think the answer is fine (I upvoted it). – D.W. Apr 5 '14 at 1:08
• I'll respond below but this threat of using the wrong key to decrypt is really strange. If I verify the MAC using the wrong key then it will also be broken and rejected. Encrypt-then-MAC should certainly be used. – Yehuda Lindell Jul 1 '15 at 16:16
• @YehudaLindell, The safest for the paranoid is still mac-encrypt-mac – Pacerier Oct 24 '17 at 8:07

The really important thing is, not encrypt-and-mac. The other two, you can debate, but both are at least theoretically sound -- one might just practically be better than the other. Encrypt-and-MAC falls apart for a very simple reason, though: the MAC is not meant to keep the plaintext secret.

The MAC is based on the plaintext. Authentication is not designed to obscure the plaintext. A MAC, therefore, provides some information about the plaintext used to make it.

The not-quite-appropriate-but-easy-to-understand example is a checksum. If we have a nine digit number plaintext and a one digit checksum, and ship it with the first nine digits encrypted but the checksum not, the checksum is going to help me learn things about the first nine digits of plaintext. If I can somehow find out eight of the nine digits, I can use the checksum to find out what the last digit is. There might be a lot of other things I can do with that checksum that ruin the integrity of the first nine digits.

So, as a recap: do not use encrypt-and-mac. Otherwise, whatever, you're good.

• "the MAC is not meant to preserve the integrity of the plaintext" would be just as good a reason to avoid MAC-then-encrypt too. $\;$ – user991 Dec 4 '14 at 4:13
• No -- because the MAC and plaintext are both encrypted. Once you decrypt the ciphertext, you're not worried about the integrity anymore, you've decrypted it. – Daniel Dec 4 '14 at 4:15
• ... Yes we are, otherwise there would be no point to any of these constructions. $\;$ – user991 Dec 4 '14 at 4:53
• I suspect you meant "confidentiality". $\;$ – user991 Dec 6 '14 at 5:07
• @Pacerier -- if you're doing it right, yes. "Encrypt-and-mac" refers to the stupid strategy of encrypting the plaintext, mac'ing the plaintext, and then putting the plaintext mac at the end of the ciphertext. – Daniel Nov 3 '17 at 17:59

There is no property of a MAC that states that information about the input should not be leaked. As such, you should encrypt the message first, then apply a MAC. This way, even if the MAC leaks information, all that is leaked is ciphertext.

• Or MAC then Encrypt, so that the MAC can't leak information, because it can't be read by any attacker. – Daniel Dec 4 '14 at 4:09
• @Daniel, So how do you address the DOOM principle by Moxie? – Pacerier Oct 24 '17 at 8:11

Besides the security benefits of encrypt-then-MAC that many other answers have mentioned, there's a performance benefit. Checking the MAC first on the receiving end allows you to reject forged messages without doing the work to decrypt them. Bernstein mentions this in http://cr.yp.to/snuffle/design.pdf (in the section "Should the stream be independent of the plaintext?").

• That's such a tiny performance boost, given the vast, vast majority messages will be correct messages and will go through two steps anyway, that this benefit can be all but ignored, IMHO. – Penghe Geng Sep 26 '16 at 17:14
• @xiaobai I think the idea is that it makes it (slightly) harder for an attacker to DOS you in some (niche) situations. In a DOS attack, all of the packets flooding your server might be failing to authenticate, and the rate at which your server could drop them might matter. – Jack O'Connor Sep 28 '16 at 3:53
• Just note that "performance benefit" is not going to be any relevant if encrypt-mac itself was insecure. – Pacerier Oct 24 '17 at 8:41

If you look at the paper "Tweakable Block Ciphers" by Moses Liskov, Ronald L. Rivest, and David Wagner published in Advances in Cryptology - Crypto 2002, Proceedings, 2442, section 4.3 Tweakable Authenticated Encryption (TAE), the MAC is computed over the plaintext, appended to the plaintext, and encrypted along with the plaintext. They then supply a proof of their Theorem 3 "If E is a secure tweakable block cipher, the E used in TAE mode will be unforgeable and pseudorandom".

In order to provide message integrity, a hash or message authentication function (MAC) is used. Sometimes, encryption and integrity are used together as:

1. Encrypt-then-MAC: provides ciphertext integrity, but no plaintext integrity,
2. MAC-then-encrypt: provides plaintext integrity, but no ciphertext integrity, and
3. Encrypt-and-MAC: provides plaintext integrity, but no ciphertext integrity

Encrypt-then-MAC is the most secure mode, as any changes to the ciphertext can be filtered out before decryption using a valid MAC code, and this protects the messages against any modification attacks. However, a combination of encryption and MAC, such as Galois/Counter Mode (GCM): combines counter mode of encryption with Galois mode of authentication, or Counter with Cipher Block Chaining (CBC)-MAC (CCM): combines CBC-MAC with the counter mode of encryption, is preferred due to the security strength.

• Re "but no plaintext integrity", doesn't ciphertext integrity asserts plaintext integrity? – Pacerier Oct 24 '17 at 8:45

Reading all of this leads me thinking that the best solution would be:

## MAC-then-Encrypt-then-MAC

Bringing both guarranty on the plain text and cyphertext.

I fully agree both are important :

• MAC-then-Encrypt if your plain text is not structured and do not permit to confirm its integrity without a MAC
• Encrypt-then-MAC for the reasons provided in other answers, especially to avoid decrypting bad data
• Could you justify -1 please ? – lalebarde Feb 8 '19 at 17:00

In many applications, only part of the data (m) is encrypted, and some so-called Additional Authenticated Data (AAD, usually some header data including nonce) a is only authenticated but not encrypted.

Here is my argument: When AAD is used, Authentication-then-Encryption provides an additional layer of protection for AAD than Encryption-then-Authentication, thus one may argue it could be more secure in certain usages.

When AAD a is used, if we use Encryption-then-Authentication, we will get:

## E(m) + A(a + E(m))

for scheme, which means we encrypt m first, and then concatenate it with a, and then encrypt the result. Notice how a is only protected by one layer of cryptographic operation, the MAC operation A.

And if we use Authentication-then-Encryption, we will get

## E(m + A(a+m))

which means we first encrypt concatenated a and m, then concatenate the resulted MAC code with m, and then do the encryption. Notice a is effectively protected by two layers of cryptographic operations, both A and E.

Now suppose the authentication method is somehow broken and the encryption is not, which is not that far-fetched since some MAC algorithms (like HMAC-MD5) is indeed found weak, then a will be fully exposed to tampering when using Encryption-then-Authentication. The same cannot be said for Authentication-then-Encryption.

### Update on 2016-09-27:

I agree with some of the top comments that applying a cipher multiple times doesn't always lead to better security so I retracted that statement. But it actually is not relevant to my main point of AtE provides additional layer of security since we are not applying the same cipher to the same data twice in these A/E schemes.

• There is a good reason why we use 3DES rather than 2DES, don't you think? And if AES is broken, don't you think we'd loose confidentiality whichever encryption scheme we use (among about every cryptographic device having to be redesigned)? – Maarten Bodewes Sep 26 '16 at 20:35
• “If we agree applying a cypher multiple times is more secure than once” — cryptographers don't agree with this. At most, you can increase the strength of the keys, but that's only an issue if key size is an issue as in DES's 56 bits. AES uses a minimum of 128 bits, key size isn't an issue. (It might be if quantum computing delivers, but then we'd just switch to 256-bit keys.) Is there anything in your answer that doesn't depend on the invalid argument that multiple encryptions are a good thing? – Gilles 'SO- stop being evil' Sep 26 '16 at 20:52
• @MaartenBodewes That reason doesn't apply to algorithms with sufficiently large keys that make brute-force attacks infeasible and you just use double encryption to increase the effective number of rounds and in order to make it more resistant to cryptoanalysis. – CodesInChaos Sep 26 '16 at 20:54
• @CodesInChaos Yeah, my reason to make this answer invalid would only be correct if the reason of Gilles to make this answer incorrect would not apply. Unfortunately, two wrongs.... – Maarten Bodewes Sep 26 '16 at 21:59
• @MaartenBodewes A critical security system needs to consider the worst scenario and whether the system has a graceful downgrade rather than a total disaster. If AES is broken, yes we will lost confidentiality, but if we can still keep authentication that will be better than nothing. For a lot of applications, authentication is actually more important than confidentiality. – Penghe Geng Sep 27 '16 at 14:59