Hey! I'm David, a security consultant at Cryptography Services, the crypto team of NCC Group . This is my blog about cryptography and security and other related topics that I find interesting.

# Referencing eprint papers

## posted May 2016

Just realized that each ePrint paper has a BibTeX snippet to reference the paper in your own work. If you don't know what I'm talking about, I'm talking about that:

Go on any paper's page and click on the BibTeX Citation link. The snippet needs to be included in a .bib file and referenced from the your main .tex

@misc{cryptoeprint:2015:767,
author = {Daniel J. Bernstein and Tanja Lange and Ruben Niederhagen},
title = {Dual EC: A Standardized Back Door},
howpublished = {Cryptology ePrint Archive, Report 2015/767},
year = {2015},
note = {\url{http://eprint.iacr.org/}},
}

# How Gavin Andresen was duped into believing Wright is Satoshi

## posted May 2016

I won't be talking about how weird Wright is, how he was debunked a multitude of times, and how you shouldn't believe the press.

What I will be talking about, is how Gavin Andresen, a main bitcoin developer, could have been duped into thinking Wright was Satoshi:

I believe Craig Steven Wright is the person who invented Bitcoin.

First. How weird is it that instead of just signing something with Satoshi's public key and releasing it on the internet, Mr. Wright decides to demo a signature verification on closed door to TV channels, magazines and some bitcoin dev on a trip to London? From reddit, Gavin wrote:

Craig signed a message that I chose ("Gavin's favorite number is eleven. CSW" if I recall correctly) using the private key from block number 1. That signature was copied on to a clean usb stick I brought with me to London, and then validated on a brand-new laptop with a freshly downloaded copy of electrum. I was not allowed to keep the message or laptop (fear it would leak before Official Announcement).

That last sentence... is the rule number one in a magic trick or scam.

Now people are pointing out from the blogpost this intentional mistake in Wright's script to verify a signature:

Looks like the signature is also taken from an old transaction, so Wright is re-using a signature to prove he verified "something". Except he swapped the something.

Another way he might have done it, on his website he also has a oneliner:

>> base64 –decode signature > sig.asn1 & openssl dgst -verify sn-pub.pem -signature sig.asn1 sn7-message.txt

But the & sign is a single one instead of &&, making the two commands run at the same time instead of running the second command after the first one.

Someone else points at other tricks, like using doppelganger letters from the UTF-8 set of characters to trick someone in a demo.

myvar = "foo"
myvаr = "bar"  # This is a *different* variable.

print("first one:", myvar)
print("second one:", myvаr)

The amount of sleigh of hands that could have been done here is actually really interesting. We have cryptographic signatures so that we don't need to believe in human lies, but if the human is in between you and the verification of the signature, then good luck!

Also that python script makes me think of using this as a proof of concept backdoor.

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# The Noise Protocol Framework

## posted April 2016

WhatsApp just announced their integration of the Signal protocol (formerly known as the Axolotl protocol). An interesting aspect of it is the use of a TLS-like protocol called Noise Pipes. A protocol based on the Noise protocol framework, a one-man work led by Trevor Perrin with only a few implementations and a moderately long specificiations available here. I thought it would be interesting to understand how protocols are made from this framework, and to condense it in a 25 minutes video. Here it is.

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# The Juniper paper is out!

## posted April 2016

The Juniper paper is going to be a big deal

That's what I wrote at the end of Real World Crypto, 2 days after Hovav Shacham talked about the subject at the same conference.

If you have no idea what Juniper is or what happened here, go check the blogpost I wrote on the subject.

The paper is available on eprint. titled A Systematic Analysis of the Juniper Dual EC Incident, it contains some background on Dual EC, IKE and a timeline of event that should read like a nice story. This is the paper you're going to read next week! So go print it now =)

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# CVE-2016-3959

## posted April 2016

CVE-2016-3959 also called the golang infinite loop just triggered a new version of the language Go. The cherry on the cake is that it was discovered by me!

The issue was announced here on github, and in a bunch of different places. Here's a short Q/A to explain what's up:

Q: What's vulnerable?

A: Anything that uses the big.Exp function concurrently where the modulo parameter can be controlled by an attacker. For crypto this means mostly DSA and RSA which are used for example in TLS and SSH, as well as many other cryptographic applications, like recently in the Let's Encrypt client (hope they patched). ECDSA also use the big.Exp function but this elliptic curve version of DSA usually does not use custom curves so the attacker has usually no known way to make someone compute calculations over his curves parameters if they are non-standard.

Q: What's big.Exp?

A: It's the exponentiation function of Go. Declared in the big number library of Go: big.

func (z *Int) Exp(x, y, m *Int) *Int

Q: What's a big number library?

A: Programming languages have int types that can usually hold integers up to 64bits (For example, in C this type is called uint64_t). But crypto needs numbers that are much bigger than that, up to 4000 bits sometimes. So big number libraries are the libraries used to play with numbers of such sizes without getting a headache =)

Q: What was the problem with big.Exp?

A: It was a pretty simple one, the lack of a zero check for the modulus made the calculation turn into an infinite loop. Interestingly the developers of Go did not patch the vulnerability by adding the zero check inside of big.Exp but did it inside of the implementations of DSA, RSA and ECDSA. This means that other cryptographic functions or non-cryptographic functions that employ this big.Exp function, concurrently, with the third parameter controlled by the user, might still be subject to DoS attacks.

If you have any other questions feel free to ask! The comment section is here for that ;)

# Some Q/A on phone security

## posted March 2016

There is an excellent blogpost here on how would you go about getting into an encrypted phone.

I asked some questions to one of the co-author Adwait Nadkarni, I thought that it might be interesting to others:

But offline attacks can also be much harder, because they require either trying every single possible encryption key, or figuring out the user’s passcode and the device-specific key (the unique ID on Apple, and the hardware-bound key on newer versions of Android).

Q: I don't understand why you would have to guess that HBK, can't you just access it on the phone?

A: Thats a good question. To prevent the security from only being dependent on the user-supplied passcode, the HBK is supposed to be inaccessible from most software, similar to the iOS device-specific UID. That is, the HBK is supposed to be accessible only via the trusted executable environment (TEE), that is isolated on a different microprocessor. Untrusted software (even with compromise of the main kernel) is not supposed to be able to directly access the HBK.

That said, the reality is manufacturer-dependent. The TEE on different devices has been repeatedly compromised (Qualcomm TEE implementation compromised in 2014, HTC in 2015, etc.). Thus, there is threat of software compromise that may allow the attacker to retrieve or misuse the HBK.

Q: Is the secure enclave on the recent iPhones that TEE? Does that mean that most phones are vulnerable to offline brute force attacks? (since most phone don't have TEE (I'm not sure about that) and have a 4-6 digit PIN instead of an alphanumeric password)

A: The TEE is for Android; iOS uses secure enclave similarly. Most phones that do not use a device-specific key (i.e., old Android devices that run <Android 4.4, very old iOS devices) are vulnerable to offline brute-force attacks. Most phones (even old ones like our Nexus 4) do have TEE.

We built our own MDM application for our Android phone, and verified that the passcode can be reset without the user’s explicit consent; this also updated the phone’s encryption keys. We could then use the new passcode to unlock the phone from the lock screen and at boot time

Q: if you do that, the content on the phone would have to be decrypted with the real passcode and re-encrypted with your new passcode. I would imagine that the real passcode is not stored anywhere (there should be a password hash stored instead for verification only), so how does that technique works for the decryption phase? (don't know if the question is clear enough)

A: The phone is not directly encrypted with the passcode, but with a randomly generated DEK. The DEK is then encrypted with the KEK, which in turn is generated from the passcode and the HBK. Now, when the passcode is changed, the phone decrypts the DEK with the old KEK, then recreates the new KEK with the new passcode and HBK, and re-encrypts the DEK with the new KEK. Data is not touched when the passcode changes.

Q: so, specifically then, how does the phone uses the old KEK if it doesn't have the old passcode?

A: The old KEK is not created on the fly, but stored in the hardware-backed keystore (accessible only via the TEE). The TEE can retrieve it to decrypt the encrypted DEK.

Generally, operating system software is signed with a digital code that proves it is genuine, and which the phone requires before actually installing it.

this part made me wonder, what if we used lasers? Fault attacks are a big thing in the smart card industry, why is no one talking about it for cellphones? This prompted me to ask Frederico Menarini from Riscure:

Q: In iOS or Android if you want to update the phone, the update needs to be signed with Apple or Google or Samsung, etc... update key. But what you could do if you could mount a fault attack (lasers?) would be to target the point where the cellphone refuses the patch because of a false signature.

A: In principle, fault attacks are possible on phones – nothing prevents it and the scenario you described is valid. Laser attacks might be challenging though because certain chips use package-on-package or chip stacking, which means that you might not be able to directly affect the CPU using light.

In general attacking mobile phone chips will be complicated because they run at extremely high frequencies compared to smartcards (smartcards rarely run faster than 50 MHz) and because the feature size is much smaller (state of the art in smartcards is 90nm, which makes targeting the right area of the chip with a laser easier).

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# Demo of the Diffie-Hellman backdoor

## posted March 2016

Here's a little demo of my work in progress research =)

The top right screen is the client, the bottom right screen is the server. I modified two numbers in some Socat file (hopefully it will be one number soon) and the backdoor is there. It's a public value and both the server and the client can generate their own certificates and use them in the TLS connection. For simplicity I don't do that, but just know that it would change nothing.

To get a Man-in-the-middle position I took the simplest approach I could think of: the screen on the left is a proxy, the client connect to the server through the proxy.

You will see that the proxy on the left will start parsing the server and the client packets as soon as it sees a TLS handshake. It then collects the server and the client Randoms, the server and the client DH public keys, and the DH parameters of the server to check if the backdoor is there. You will see a red message displaying that indeed, the backdoor is present.

For simplicity again (this is a proof of concept) I only use TLS 1.2 with AES128-CBC as the symmetric cipher and SHA-256 as the hash function used in the PRF/MAC/etc...

In a few seconds the premaster key, then the master key, then the MAC and encryption keys are computed and the traffic is then decrypted live.

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# Pollard's p-1 factorization algorithm

## posted March 2016

Got my graphic tablet back, needed to do a small video to get back into it so I made something on Pollard's p-1 factorization algorithm:

You can find the records on factoring with p-1 on loria.fr, the biggest prime factor found was of 66 digits (~220bits) using B1=10^8 and B2=10^10. But people have been using bigger parameters like B1=10^10 and B2=10^15. It doesn't really make sense to continue using p-1 after that, and more efficient algorithms that still have a complexity tied to the size of the smallest factor exist. The Elliptic Curve Method (Or Lenzstra factorization method) is one of them, and is carrying the same ideas as p-1 in the elliptic curves.

In the video I also don't talk about B2. This is if you have a factorization of p-1 that is B1-powersmooth, except for a large single prime. You can just set a B2 which would be larger than this last factor and try every factor between B1 and B2. There are some optimizations that exist to do that faster instead of doing it naively but this is it.

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# To_print

## posted March 2016

I have this list of papers that is accumulating in a folder. After an idea of @gtank I decided to print the whole (~150 two-sided pages) and go to my local UPS store to bind it for ~8\$.

I'm not posting the pdf I printed here, but I made it with pdfjoin --paper letterpaper --rotateoversize false *, could have used pdfbook to make it smaller but after printing a few pages I felt that it would be too small for my weary eyes (now I sound like an old bag).

here's the list of the papers I printed. They all seem like you can print them without going to jail.

# How are TLS records encrypted?

## posted March 2016

Once we are done with the handshake, both parties are now holding the same set of keys. Right after the Server sends its ChangeCipherSpec message it starts encrypting. Right after the Client sends his own ChangeCipherSpec he starts encrypting his messages as well.

The encrypted records still start with the type of record, the TLS version and the length of the following bytes in clear. The rest is encrypted.

We won't talk about compression because there are a bunch of vulnerabilities that should make you think twice about using compression. So here it is, null! (more about that)

Let's follow the TLS 1.2 RFC here

struct {
ContentType type;
ProtocolVersion version;
uint16 length;
select (SecurityParameters.cipher_type) {
case stream: GenericStreamCipher;
case block:  GenericBlockCipher;
} fragment;
} TLSCiphertext;

So as I said, we start with the type, the version and the length.

Right after the CipherSpecChange both parties will send an encrypted handshake message (a MAC of the whole transcript to authenticate the handshake), but most of the messages after will be encrypted Application data messages containing the real communications we want to protect.

0x17 is the byte for application data, then we have the TLS version, for TLS 1.2 it is 0x0303 (don't bother), then we have the length of the fragment which is described below for the AES-CBC case.

struct {
opaque IV[SecurityParameters.record_iv_length];
block-ciphered struct {
opaque content[TLSCompressed.length];
opaque MAC[SecurityParameters.mac_length];
};
} GenericBlockCipher;

So in the case of AES-128, you would have an IV of 16 bytes followed by the encrypted data.

Yup, the MAC is not here because it is encrypted. TLS is a MAC-then-encrypt construction (...), you can do encrypt-then-MAC in practice but through an extension (cf. RFC 7366).

The rest is pretty straight forward, after decryption of the block-ciphered structure you remove the padding, check the MAC, use the content.

Here's how the mac is used:

   MAC(MAC_write_key, seq_num +
TLSCompressed.type +
TLSCompressed.version +
TLSCompressed.length +
TLSCompressed.fragment);

where "+" denotes concatenation.

That's it for today!

# Distinction between the TLS PRF for the Master Key and for the Keys

## posted March 2016

I just realized one more thing in TLS that doesn't make sense (besides the fact that different versions of TLS have different PRFs). Here's RFC 5246 (the RFC on TLS 1.2) on how to use the PRF transform your pre-master key into a master key:

Here's the same RFC on how to use the PRF to transform your master key into your 4 or 6 keys:

Noticed anything?

Took me some time, the first takes the server random appended to the client random, while the second takes the client random appended to the server random. I'm willing to bet this is not to circumvent any attack but rather to confuse the implementer...

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# TLS, Pre-Master Secrets and Master Secrets

## posted March 2016

Everything you want to know about TLS 1.2 is in RFC 5246. But as you may know, if you've read RFCs before, it is not easy to parse (plus they have some sort of double spaces non-sense).

Before we can encrypt/MAC everything with keys to secure our connection, we need to go over a key exchange called the Handshake to safely agree on a set of keys for both parties to use. The handshake can currently use 5 different algorithms to do the key exchange: RSA, Diffie-Hellman, Elliptic Curve Diffie-Hellman and the ephemeral versions of the last two algorithms.

This blogpost is about what happens between this key exchange and the encryption/authentication of data.

## The Pre-Master Secret

The pre-master key is the value you directly obtain from the key exchange (e.g. $g^{ab} \pmod{p}$ if using Diffie-Hellman). Its length varies depending on the algorithm and the parameters used during the key exchange. To make things simpler, we would want a fixed-length value to derive the keys for any cipher suite we would want to use. This is the reason behind a pre master secret. The fixed-length value we'll call master secret. Here the RFC tells us how to compute it from the pre-master secret after having removed the leading zeros bytes.

master_secret = PRF(pre_master_secret, "master secret",
ClientHello.random + ServerHello.random)
[0..47];

The two random values ClientHello.random and ServerHello.random, sometimes called "nonces", are randomly generated and sent during the ClientHello of each parties. This is to bound the soon-to-be master key to this session. PRF stands for Pseudo-random function, basically some concrete construction that emulates a random oracle: given an input will produce an output computationally indistinguishable from a truly random sequence. But let's move on, and we will see later what exactly is that PRF.

## The Master Secret

A master secret is always 48 bytes. So now that we have a fixed length value, we can derive 4 keys from it:

• client_write_MAC_key
• server_write_MAC_key
• client_write_key
• server_write_key

As you can probably guess, MAC keys are for the authentication and integrity with whatever MAC algorithm you chose in the cipher suite, write keys are for the symmetric encryption.

Interestingly, two keys are generated for every purpose: one key per side. This is mostly by respect of good practices. Always segregate the use of your keys.

The symmetric ciphers chosen in the handshake will dictate how long these keys we generate need to be. Note that AEAD ciphers that combine both authentication and encryption will not need MAC keys but will need two other keys instead: client_write_IV and server_write_IV. This is because their MAC keys are directly derived from the encryption keys.

The same PRF we used on the pre-master key will be used on the master-key over and over until enough bytes have been created for the keys. From the section 6.3 of the RFC:

key_block = PRF(SecurityParameters.master_secret,
"key expansion",
SecurityParameters.server_random +
SecurityParameters.client_random);

The key_block value is then cut into enough keys.

That's it! Here's a recap:

Diffie-Hellman -> pre-master key -> 48bytes master key -> 4 variable-length keys.

## The PRF

OK. Now that we got a nice global view of the process, let's dig deeper. The PRF used in TLS 1.2 is discussed here. It is quite different from the PRF used in TLS 1.1, see here.

Remember, for example how it was used to transform the pre-master key into a master key:

master_secret = PRF(pre_master_secret, "master secret",
ClientHello.random + ServerHello.random)
[0..47];

This is how the PRF function is used:

PRF(secret, label, seed) = P_<hash>(secret, label + seed)

If you want to follow along with code, here's the relevant golang code

P_hash(secret, seed) = HMAC_hash(secret, A(1) + seed) +
HMAC_hash(secret, A(2) + seed) +
HMAC_hash(secret, A(3) + seed) + ...

where + indicates concatenation, A() is defined as:

A(0) = seed
A(i) = HMAC_hash(secret, A(i-1))

This was a copy/paste from the RFC. To make it clearer: We use the label string ("master secret" in our example) concatenated with the two peers' random values as a seed.

We then MAC the seed with our pre-master secret as the key. We use the first output. Iterating the MAC gives us the subsequent values that we can append to our output.

$u_0 = label + serverHello.random + clientHello.random$

$u_i = HMAC(secret, u_{i-1})$

$output = u_1 , u_2 , \cdots$ This goes on and on until the output is long enough to cover the 48 bytes of the master key (or the 4 keys if we're applying to PRF on the master key).

If P_256 is being used, then SHA-256 is being used. This means the output of HMAC will be 256 bits (32 bytes). To get the 48 bytes of the master key, two iterations are enough, and the remaining bytes can be discarded.

# Discrete logarithms in Multiplicative prime groups

## posted March 2016

I'm doing some tests on how Pollard Rho performs. I implemented the thing in Sage here and it doesn't perform that well I found. Pollard Kangaroo is also bad, but that must come from my implementation (I didn't really go further here since I don't really need Kangaroo: I already know the order + the value I'm looking for is not in any particular interval)

old_rho is Pollard rho, rho_lambda is the mislabeled Pollard Kangaroo algorithm, trials is the simple enumeration.

I implemented the algorithm in Go, along some nice functions/variables that make Go's bignumber library a bit easier to tolerate. And guess what? What takes Sage 63 seconds to compute only take Go 5 seconds. The implementation is a copy/paste of what I did in Sage, no optimizations.

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# DROWN attack on OpenSSL

## posted March 2016

There is a new attack on OpenSSL. It's called DROWN.

Two problems:

1. in OpenSSL versions prior to January of this year, SSLv2 is by default not disabled. They thought that removing all the SSLv2 cipher suites from the default cipher string (back in 2010) would work but... nope. Even if not advertised in the serverHello, you can still do a handshake with whatever SSLv2 cipher you want. Another way of completely disabling SSLv2 exists, but it's recent and it is not the default option.

2. A padding oracle attack still exists in SSLv2. This is because of the export cipher suites. These weak ciphers and key lengths the USA government was forcing on OpenSSL so that people overseas could use it. So, these export cipher suites, nowadays they are bruteforce-able. It takes a few hours though, and a few hundred dollars, so no easy active MITM. It's a rather passive attack.

This is a cross-protocol attack. This means that you are a MITM, but you leave the client doing his thing on a TLS 1.2 or whatever SSLv3+ protocol. In the mean time though, you use the SSLv2 connection as an Oracle to recover the premaster-key (and thus the session key that is derived from it).

Three things:

1. The attack works on RSA handshakes. In the handshake (precisely in the clientKeyExchange) the client will encrypt his premaster-key with the server's RSA public key, this is what the attack decrypts. The server doesn't support RSA handshakes? You'll have to attack another server.

2. The server doesn't have to work with SSLv2. If another server (could even be a mail server) sharing the same RSA key and supporting SSLv2 exists, then you can use it as your oracle during the attack! Practical much?

3. To use the oracle, you need to first transform the RSA encrypted premaster-key into a valid SSLv2 RSA encrypted master-key. It is quite different, because of protocol differences, and you need to use quite a few tricks (trimmers!). It doesn't work all the time, around 1 out of 1,000 RSA encrypted premaster-key can be decrypted. This is often more than enough to steal the cookies and have consequences. If you're targeting a specific individual it can take time though, so to speed up these 1,000 handshakes just inject some javascript in a non-https webpage!

That's pretty much everything. I'm still going through the paper, trying to understand the math. There is a tool here to test your website. Another way of doing this (especially for internal servers) is to get an openssl version prior to january this year and do that on all of your subdomains/domains: openssl s_client -ssl2 -connect www.cryptologie.net:443

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