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.

# Dual EC or the NSA's Backdoor: Explanations

## posted August 2015

I've done a new video. It is an explanation following the paper Dual EC: A Standardized Backdoor by Daniel J. Bernstein, Tanja Lange and Ruben Niederhagen.

# Need helpz for my Master Thesis

## posted August 2015

I have two weeks left to turn in my Master thesis.

It is about a timing attack on OpenSSL that was found in this paper: Billy Bob Brumley and Nicola Tuveri - Remote Timing Attacks are Still Practical

I tried to replicate the results. But to make it interesting I explained in more details how to mount this attack. There are lattice involved. It should be pedagogical.

Well... it should be.

Can I ask for your help? If you have time to spare, read a tiny part of this whitepaper and tell me if something seems odd, wrong, or badly explained.

I'll credit you here, you will have my eternal love and I will buy you a beer at one point.

# Vegas - Part 3: Defcon 23

## posted August 2015

### Another world

I bought my Defcon badge through Blackhat to avoid having to move out of the Mandalay and miss some of the talks. Avoiding the long-and-early-in-the-morning lines of Defcon and still getting a "real" badge is also part of the benefits. So after lining up for 30 seconds at a small stand between two talks, I received a plastic bag with a program printed as a newspaper and several CDs containing music (I assume, but who owns a CD player nowadays?). The Defcon badge was an old and white record, apparently every other year the badge is non-electronic.

Defcon was taking place in Bally's and Paris this year. The talks were in Paris, the rest was in Bally's. If you wanted to mix them up you had to change casino over and over. The two are connected but it's still a pain.

I missed the first two days of Defcon. Well the first day isn't actually an official one as it takes place outside in a public park. The "toxic barbecue" is a gathering where people bring booze and meat. The second day, the official Defcon first day, is a single track of introductory talks that takes place in their Conference Center.

So I arrived in what I thought was something that already started, but all of blackhat and others that wanted to get the real deal were now rushing to the Defcon's talks, all at the same time. It was packed, the lines were not moving and the staff was screaming. I was starting to miss the organization of Blackhat.

After leaving my first talk, I figured I would never go to another talk again. But they finally moved the 101 track (talks that are more for begginers) and things got better.

And then I went to visit the other side of Defcon, and that's where everything made sense

### The Villages

My favorite part of Defcon was the Villages, small sized rooms (compared to the ones hosting the talks) where people of common interests gather and spend their whole Defcon together.

The crypto Village was great, apparently Diffie was there. Other renown cryptographers hung out there too and I met a bunch of people I had always wanted to meet :) (although most conversations were short, I guess others were more at ease in this kind of environment than me).

There were a bunch of posters everywhere on the walls. Here's my favorite one from Tony Arcieri:

You could also find byte descriptions of packets of certain protocols, they are all available here

Every hour, or 30 minutes, there was a talk. I left Defcon thinking that I should get more involved in this crypto village and that I should submit a talk for the next one.

There were maybe a dozen of other Villages. There was a lock picking one, but you had to buy your own gear so I passed (although I really wanted to do it).

After Defcon, sitting in the plane I read their "newspaper" and realized there was much more. There was a huge number of things that I didn't even know were going on. I could even have went and met some of them somewhere in the desert to shoot range.

I felt like I did nothing. I was a lurker and I took part in none of the cool things. Next time I will come prepared.

### The Parties

The parties were definitely better than the Blackhat ones. The Facebook student party was the best I got to do, few people, no loud music and a "bingo" game where you were handed a card with a bunch of "can do X" or "is X at facebook" and you had to find a facebook employee/intern that could sign it for you. If you got a full row plus a column signed you won. This was awesome as it gave you an excuse to go talk to them.

There was also a party in a suite of the hotel were I got to meet a lot of really cool people in the field as well. The funny thing is that everywhere I went, even at these parties, a huge amount of the people present were from my company (NCC Group) which made things super easy to meet people, we also were all wearing the company Tshirt.

### The Rest

There was a main room full of tables, people hacking, people playing, weird people handing me papers and tokens and telling me cryptic passphrase. Other weird people holding huge antennas and pointing them at everyone obviously looking for something/someone.

There was an OpenCTF space, and a CTF space as well with korean, french, american and chinese teams just sitting there on their computers and cracking stuff. I was not allowed to take a picture there :() Hacking contests are everywhere. The ambiance is nothing like Blackhat (Which is way more corporate). Between weird things happening on my wifi, the femtocell found in between the two casinos and the non-stop protocol downgrades on our phones, we felt like everyone was trying something on you.

A stand to cut your hair and make you a mohawk. A spaceX stand giving out posters.

A tesla hacking stand, someone on the floor looking at it. I heard they dismantled the whole car at one point.

and Finally... Hacker Jeopardy

This post makes no sense, but Defcon made no sense. It was awesome.

EDIT: Here's a video of a first timer

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# Lattices and Tikz

## posted August 2015

I'm writing a paper, which temporary (but maybe final) title is Timing and Lattice Attacks on a Remote ECDSA OpenSSL Server: How Practical Are They Really?

(and I already have a github repo for that)

I'm explaining a few things about Lattices, taking some of the old material I already wrote for my last paper Survey: Lattice Reduction Attacks on RSA. But this time I wanted to be more pedagogical, with more graphics and illustrated examples. For reasons that I ignore lattices are seldom well explained on the internet thing. Here's a little preview, I guess you can re-use the images however you want, just don't copyright them against me :|

What are Lattices?

The Shortest Vector Problem:

The Closest Vector Problem:

How do we solve (approximate) the SVP? LLL:

and Babai's first procedure that approximates a solution to the CVP:

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# Vegas - Part 2: Blackhat 2015

## Vendors

Blackhat is famously known for its vendor's room. A huge space where vendors knock themselves over to hand you their free goodies. There is also a "career fair" with a few tables where people are mostly interrested in hiring you contrarily to the other booths were people try to sell you something.

It was an excellent opportunity for me — coming from France and knowing close to 0 company names — to learn a lot about the field and who was a big actor there. I rapidly started recolting company names. Fireeye, Rapid7, Mandiant, Trustwave, Splunk... no I'm not paid to write that.

I also spent a few hours just recolting swag, just because I have an addictive personality. The number of stands giving away Tshirts was... impressive to say the least.

The RSA booth had an Oculus Rift demo, but it was disapointing and I wasted my time there staring at the emptiness of RSA's soul. I should have taken the clue seeing people taking off their headset making faces. I felt like with a better demo and controllers the execution would have been better, but after having tried the HTC Vive (see my blogpost), the competitor from valve and HTC, it's hard to be impressed by the Rift.

I saw people wining fitbit smartwatches, 50$amazon coupon (damn you Jason!) and bluetooth speakers... The whole thing is just entertainment if you're not trying to buy anything. There are raffles, games, and also after a certain hour... you get free beers (and even hard liquor at the Microsoft bar, but shhhh). And I didn't tell you about the cheese buffet, the baked-in-front-of-you cookies, the cupcakes everywhere, the... oh my! ## Arsenal I feel like I should mention Arsenal, although I didn't take part in it at all. From what I understood it's like briefings but for presenting a tool. Some people only swear by that but I felt like I would waste time trying to understand a tool I might have no use for. ## Networking and Parties The best thing I did while there was to attend the different parties. It's usualy short, like 2 hours, and you get free booze and sometimes free food. You get to meet a lot of cool people too. If I had to re-do it I would avoid these loud parties though, they were nice as I got to see what big clubs in Vegas look like. But the music is often too loud and the bars so crowded that you end up doing nothing and talking to no one. The trainer's party was the nicest I attended (but you need to be a trainer, speaker, etc...), Rapid7's was the most impressive. Protip: always take the card that is inside your badge with you, you might get bounced if you don't show up with it since they always want to scan your badge. read part 3 here, it's about Defcon 2 comments # Vegas - Part 1: Blackhat 2015 ## posted August 2015 inb4 people start complaining that this blogpost is not about crypto. It's not. ## Diving in That's it, I'm leaving Chicago for the arid desert of Nevada. Las Vegas, we meet again. First let me say that I love Vegas, and I think anyone should go see what it looks like at least once in their life. Imagine a bunch of billionaire wandering in the desert, high on cocain, lost in their train of thoughts, laughing their ass off and suddenly coming up with the idea of bringing dozens of architects in the same desert and throw loads of money at them with no directions what-so-ever. Just for the lulz. And that's how Vegas happened. But I'm not here to eyeball at buildings and visit their guts. This time I'm here to mingle with nerds, geeks and other SAPs (Socially Awkward Penguins). I'm here to learn about the latest security vulnerabilities, the craziest discoveries of the best of the best. I'm here to meet with my tribe. I'm here to attend BlackHat and Defcon, the two biggest hacker conventions. And I'm seldom going to see the natural lights of our sun for a good long week. But weird things started on the way, in the plane, when one of the hotess handed me a napkin. To me, only me. A white and clean napkin, nothing else. Did I have a booger? Nope. Was it something on my face then? Nein. The United Airline skeequing chairs, crying babies and eye-vessels blowing/nose congesting air conditionner were already killing me when we began to dive toward the unfamous LV. ## Training A couple of hours after I was in the Mandalay arpenting the corridors of its enormous conference center. Two huge floors filled by multiple rooms of different sizes. Not a living soul. I checked-in to get my badge and got a blackhat bag with a few goodies. The four first days of blackhat are reserved for trainings. I waited in the hallways, enjoying the complimentary coffee & cookies while sitting in these huge sofas that were decorating the place. At 6pm I met with my coworkers and we went to play Craps The next morning I woke up early, dressed and went to eat the blackhat breakfast in a huge room filled with empty tables, some of them had people sat across each other not saying a word. I ate, drank my coffee and went to the class room. I spent two days as a trainer helping Tom Ritter, Sean Devlin and Alex Balducci giving the course Beyond the BEAST: Deep dives into crypto vulnerabilities. A mix of general culture in crypto, reknown attacks as exercises, cool crypto stuff we are excited about and some hours spent in the mathematics of cryptography. Every break we would go in the hallway, get some of the free pastries and coffee and chat a bit. Then we would go back to the class and teach. It went pretty well and I thought the convention would continue like that. I had no idea of the storm that was going to happen. ## Briefings I woke up and headed to the Conference, passing by the swimming pool that I had still not visited and that I would not visit for the rest of my stay. Attending Blackhat and the Defcon was pretty much staying indoors for a week. It was working, drinking, getting free stuff and meeting people without producing any natural vitamins. The briefings are the talks. A bunch of people apply for Blackhat CFP (Call For Papers) and if they get accepted by a jury they are allowed to give a talk at the convention. People then have to choose between 8 talks happening at the same time (more or less), and then regroup in these gigantesc rooms to hear someone talking about something. This is not training time anymore, we don't receive complimentary breakfast and lunch, hallways are now crowded and you can even see camera crews. Thing that you will never see at Defcon. I started by going mostly to crypto talks or other subject I understood better. Crypto talks were rare. Not that it mattered since I was expecting this but I felt like the quality of most talks were meh and I rarely went out of a room with the feeling that I actually got something from it. Jeff Jarmoc told me that a good way of taking something out of these was to not look at the schedule and to wander and go sit at random talks. This is an excellent idea that I'll try to apply next time. Most of the time I felt like it could have been better explained, or I could have read about that/watched a video on youtube and understood it way better. Maybe it's just me and the format of attending a talk is not working in my case, but besides a few talks I left unimpressed most of the time. One talk stood out from the others, Remote Exploitation of an Unaltered Passenger Vehicle by Charlie Miller & Chris Valasek. First it was entertaining, second it was telling a story. That's what a good talk should do no? Be easy to follow, and by that I don't mean easy, but pedagogical. The "conversation" format where Charlie and Chris talked like they were just talking to one another retelling a story to their friends was just awesome. I left out, read that they were giving the same talk again at Defcon and planned to go see their talk one more time. That's how good it was. read part 2 here comment on this story # PBKDF2 Performance Matters ## posted August 2015 Joseph Birr-Pixton gave a talk last week at Passwords15 in Vegas. He talks about it in his blog and there is a video of his presentation. And it's really good! He says "my slides were 100% algebra before someone told me to put diagrams instead". And the diagrams are very well made, really comprehensible. I felt like I learned a bunch of stuff in a few minutes, which I rarely feel after watching a talk. So spare a few minutes will you! comment on this story # Homomorphic Encryption Vocabulary ## posted July 2015 As I'm doing some research on Homomorphic Encryption, and trying to watch everything from Gentry (lots of videos available and he has a soothing voice), and possibly read everything from him (which I didn't do so don't take my word). Here's a vocab list I did for reference: • HE: Homomorphic Encryption • leveled: no bootstrapping, only compute circuits up to a degree (public key grows with the depth of the circuit for f ) • LWE: Learning With Error (a problem hard to solve) • R-LWE: Ring-Learning With Error • Craig Gentry: the one who found the holy grail • holy grail: Fully Homomomorphic Encryption • FHE: another name for the holy grail • SHE/SWHE: somewhat homomorphic encryption • BGV: the first Leveled FHE (without bootstraping), from Brakerski, Gentry and Vaikuntanathan • GSW: a FHE scheme from Gentry, Sahai and Waters, that takes ideas from BGV and like BGV has its security based on LWE • NTRU: N-th degree truncated polynomial ring, the base of a lattice-based cryptosystem • modulus switching: (some messy operation that they got rid of in bra12) • bootstrapping: to make a bootstrappable somwehat homomorphic encryption scheme into a fully homomorphic encryption scheme (Gentry recommends not to use this, although it was the original way of building FHE) • IBE: Identity Based Encryption scheme (introduced by the famous Boneh paper) • IBFHE: Identity Based Fully Homomoprhic Encryption scheme (introduced by GSW) • SIMD: Single Instruction, Multiple Data ... more to come comment on this story # How to fairly compare two objects? ## posted July 2015 Alex asked me if I knew a way of comparing two sets of data: two players want to compare their guesses on some game, without giving away their guesses. You could think of Zero-Knowledge protocols, but this is usually a one-way proof. This is actually the Socialist Millionaire Problem and it is solved by doing a multi-party computation of a function (a comparison function in our case) on two inputs (the two guesses in our case). In cryptography, the socialist millionaire problem is one in which two millionaires want to determine if their wealth is equal without disclosing any information about their riches to each other. It is a variant of the Millionaire's Problem whereby two millionaires wish to compare their riches to determine who has the most wealth without disclosing any information about their riches to each other. But how to make it fair? What if one party stops the protocol at one point, for example when he knows if the guesses are the same or not, so that the other party doesn't learn anything. This seems like a difficult problem to solve, but an interesting problem that crypto should be able to solve. Alex found this paper: A fair and efficient solution to the socialist millionaires’ problem, where they explain what they call a "fair" protocol. And the solution is quite elegant! I haven't read the whole thing but the idea is basically to compare bit by bit (I guess under the surface they must use garbled circuits) so that if one party stops the protocol early, he only has one bit of advantage over the other one. Finally, the fairness of the fair version of our protocol is straightforward. Both Alice and Bob are unable to compute the result of the comparison before the beginning of step 4. Moreover, during the fourth step, Bob's advantage over Alice is at most one bit. So, if Bob decides to abort the protocol and tries to search the remaining bits by exhaustive research, Alice needs no more than twice as much time compared to Bob to compute the same result. comment on this story # Homomorphic Encryption : Part 1 ## posted July 2015 I'm reading stuff about HE (Homomorphic Encryption) and so why not share what I find? Hopefuly there will be more than one post on the subject, and they won't be too long, and they will make others learn something new ## So what is Homomorphic Encryption? Well let's start at the beginning shall we? It all began in 1977 when RSA was invented. If you recall, to encrypt with RSA you take your message/number $m$ and raise it to the power of the public exponent $e$ modulo a product of primes $N$ like so: $c = m^e \pmod{N}$ An incredible property of textbook RSA is the fact that the scheme is malleable. If you have a ciphertext $c$ but don't know what number $m$ it's decrypting to, you can modify that ciphertext $c$ so that it would decrypt to $3m$ or $9999m$ or more generally $x \cdot m$. Just take your number $x < N$ and encrypt it, then multiply that to your ciphertext like so: $x^e \cdot c \pmod{N}$ And notice that beneath the encryption, this is equal to $x^e \cdot m^e \pmod{N}$ That is the same as $(x \cdot m)^e \pmod{N}$ and will obviously decrypt as $x \cdot m$. Tell me if I'm going too slow =) This is called Homomorphic Encryption, which you might not want as a property when using RSA and that's why you should never use RSA without a padding system. The state of the art being OAEP. This made Rivest and his friends raise the question, a year later in 1978, can this property be extended so that any kind of circuit could be computed on encrypted data? (R. Rivest, L. Adleman, and M. Dertouzos. On data banks and privacy homomorphisms. In Foundations of Secure Computation) ## Fully Homomorphic Encryption The applications thought were mostly "data manipulation" where you would want someone to manage/operate on your data without seeing it. Think banks, search engines, the cloud. A bunch of other cryptosystem that provided homomorphic properties came to life after that. For example in 1999 the Paillier cryptosystem, which unlike RSA provides additive homomorphic encryption (RSA provides multiplicative homomorphic encryption). The open problem was still out there. Could you create a cryptosystem that would provide enough homomorphic properties, that combined could compute any kind of circuits. A Fully Homomorphic Cryptosystem. Any circuit can be simplified to these simple instructions: AND, OR and NOT, which would only need a cryptosystem to have addition, subtraction and multiplication to be able to emulate these instructions. Modulo 2 would be enough, look, if $x \in \mathbb{Z}_2$ (the set of 0 and 1) then: • $\text{AND}(x,y) = xy$ • $\text{OR}(x,y) = 1 - (1-x)(1-y)$ • $\text{NOT}(x) = 1 - x$ With these properties combined you could then compute any circuit on encrypted data (think of a function, like AES() or select all my data that starts with the letter A, etc...). So, just a recap so that we're on the same page. With a FHE Alice could send $c = E(m)$ the encryption of her message $m$ to Bob, and bob could compute the function $f$ on the encrypted data so that it would decrypt to a function $f$ on the plaintext: $D(f(c)) = f(m)$ Note that in reality, we can't really compute $f$ on the ciphertext directly, what we do is that typically a Homomorphic Encryption scheme is defined with a function called Eval (for Evaluate) which we would use like that: $D(\text{Eval}(f, c)) = f(m)$ In 2009, Dan Boneh's doctorate student Craig Gentry finished his thesis, unveilling the first FHE (Fully Homomorphic Encryption): In a presentation to my fellow Ph.D. admits four years ago, Dan highlighted fully homo- morphic encryption as an interesting open problem and guaranteed an immediate diploma to anyone who solved it. Perhaps I took him too literally. Craig Gentry, Fully homomorphic encryption using ideal lattices, 2009 His thesis of 200 pages was later resumed in a 10 pages article for STOC 2009: Fully Homomorphic Encryption Using Ideal Lattices. A bit later Gentry et al simplified that scheme using only hard problems on integers instead of lattices, this was explained as well in another article for CACM here: Computing Arbitrary Functions of Encrypted Data In the next post we'll see how that FHE works! 2 comments # What is GCM (Galois Counter Mode)? ## posted July 2015 In this video I'm explaining what is that Galois Counter Mode that provides Authenticated Encryption with Associated Data (AEAD). You must have heard it combined with AES, and maybe used in TLS, ... This is just a small explanation, you can get more on the NIST specs. follow me right now on twitter 2 comments # CVE TOMEK ## posted June 2015 My coworker Tomek found a vulnerability in Rack, a Ruby thingy that is used pretty much in every web framework (Rails, Ramaze, Sinatra...) to translate queries (POST and GET) into Ruby objects. Tomek: David you don't understand anything, go read this: https://www.omniref.com/ruby/gems/railties/4.2.0/symbols/Rails::Application#annotation=4084035&line=161 It all started when he read about how to_sym() used to work in Ruby versions prior to MRI 2.2. This function converts strings into symbols. A symbol is this thing: :symbol, that usually is tied to a value: :symbol => 'something' and that you must have seen written in a really nice way thanks to Ruby's lovely syntax sugar: symbol: 'something'. Developers use the to_sym() method a lot to transform the strings from GET/POST to symbols. Problem: the symbols created by to_sym() were stored in the memory and never freed. No garbage collection. That is a problem if you let user input infinitely use that to_sym() method. For example if you naively transformed the GET variables of a request to symbols through that function, then a malicious user could have queried that page with many ?stuff=something so that your code would have infinitely stocked symbols in memory until no memory was left. Tomek was looking for the fastest method to fill up a server's memory. To do this, he tested various forms of parameters to see what would be the most effective. This included many small symbol names, large symbol names, and nested parameters. The most efficient way ended up being a lot of concurrent requests with huge symbol names, the server would go down in less than 2 minutes. And it was through the nested parameter testing that he found CVE-2015-3225 ## CVE-2015-3225 https://groups.google.com/forum/#!topic/rubyonrails-security/gcUbICUmKMc Potential Denial of Service Vulnerability in Rack There is a potential denial of service vulnerability in Rack. This vulnerability has been assigned the CVE identifier CVE-2015-3225. Versions Affected: All. Not affected: None. Fixed Versions: 1.6.2, 1.5.4 Impact ------ Carefully crafted requests can cause a SystemStackError and potentially cause a denial of service attack. All users running an affected release should either upgrade or use one of the workarounds immediately.  In Ruby on Rails, one of the nice things you can do is use associative arrays (called hashes in Ruby) in your forms. For example, in your HTML <input type="text" name="form[name]" value="david"> would translates to Ruby as {"form"=>{"name"=>"david"}} And that is thanks to Rack! But there is a small problem here, Rack parses these nested hashes by recursively calling itself: def normalize_params(params, name, v = nil) ... if params_hash_type?(params[k].last) && !params[k].last.key?(child_key) normalize_params(params[k].last, child_key, v) else params[k] << normalize_params(params.class.new, child_key, v) Here, Ruby seems to push a bunch of info to the stack before calling the new function. A bit like an assembly prolog. The thing is, after a while the stack gets full and Ruby throws an exception. And then? Rack catch the exception? Tries again? We don't really know, but the program hangs there. So Tomek found out that when you would send a POST request with a deep enough hash you would cause the program to hang. This is bad because of DoS attacks. Also, the problem cannot happen in json because json has a nest limit, and doesn't happen in GET requests either for the same reason. ## What now? CVE and Patches are talked about here: http://www.openwall.com/lists/oss-security/2015/06/16/14 Another thread there: https://hackerone.com/reports/42797 He's still trying to find out what is happening exactly, and he just opened a blog. So who knows, he might write something about it soon. comment on this story # OWASP Chicago ## posted June 2015 This evening I was at Braintree's office in Chicago for the new edition of the Owasp meeting. The offices were amazing and huge! They had beer pong tables, ping pong tables, a mini-arcade and a bar! (all that right next to the workspace) Plenty of nice conference rooms Some had whiteboard tables! And in the largest building of Chicago! ## 1 Trojaned Gems - You can’t tell you’re using one! Brandon Myers, a security researcher at Trustwave, was the first one to talk. He found out that when you executed gem fetch or gem install, the ruby package manager, it would allow a Man In The Middle to do a DNS poisoning attack to redirect you to his servers. Even though everything happens over TLS! This is because gem doesn't check for the domain in the certificate of rubygems.org: it just checks that the server has a valid certificate and that's all. You would then download the gem on his server and... game over. He said that the same thing was happening when developers were pushing their gems to rubygems.org ... That's a shame, and way worse than the downgrade https attack of go. One way of mitigating the first MITM would be to just use curl or wget directly with https://www.rubygems.org and do whatever the gem fetch does to get the gems. Because curl or wget should have a correct implementation of TLS that dodge fake DNS responses (that's why DNSSEC is useless if you query a https webpage with a correctly signed certificate). To mitigate the second attack Brandon talked about signed gems, and that it was far from being efficient since none of the top gems are signed. Two other problem were that if a fix comes around, gem update --system is vulnerable to the attack (since gem is itself a gem) and not using the fully secure gem signing allows some dependencies of not being signed (and thus a MITM would be able to modify those). ## 2 Attacking and Defending DevOps Patrick Thomas and Alec Gleason followed by explaining how much they pwned their client with heartbleed, passwords in clear and github hooks. They then explained how you could get more information out of a pwned machine if there was git, vagrant, chef, docker and other non-crypto stuff installed on the machine. All of this was facilitated by Devops, a software development method that emphasizes communication, collaboration (information sharing and web service usage), integration, automation, and measurement of cooperation between software developers and other IT professionals. https://en.wikipedia.org/wiki/DevOps They said it was still a good thing but if done correctly. After that I went to Chisec meet some people of the security community! comment on this story # Let's Encrypt Overview ## posted June 2015 ## What is Let's Encrypt? Basically, it's a way to get a quick x509 certificate for your server without knowing much about what is a x509 certificate: You have a website. You want people to be able to log in on it from starbucks without the guy sitting at a near table reading the passwords in clear from the packets you're sending everyone around you. So you google a few random keywords like "secure website https" and you end up with a bunch of links and services (which may not be free) and you suddenly have to understand what are certificates, PKI, x509, public-key cryptography, RSA, FQDN, haaa.... Well, worry no more, Let's Encrypt was thought so that you wouldn't have to go through all that trouble and destroy your server on the way. Oh and yeah. It's for free. But is hasn't been released yet. ## How does it work? You can learn more reading their technical overview, or some of their videos... or read my tl;dr: 1. You download their program on your server that has the address www.example.com: sudo apt-get install lets-encrypt 1. You run it as sudo telling it you want to get a certificate for your domain lets-encrypt example.com And voila. Behing the curtains this is what happens: 1. lets-encrypt will generate a pair of RSA private key/public key and contact the CA with your public key. 2. The CA will register your public key 3. The program will then ask the CA to verify your domain. 4. The CA will answer with a set of challenges. These are some tasks you can complete to prove to the CA you own that domain. One of the common one is to upload a certain file at a certain address of that domain. 5. The program you installed will then do that for you and poll the CA for a confirmation 6. The CA will tell you "OK man, all is good". 7. The program will then generate another long term pair of private key/public key, generate a CSR (Certificate Signing Request) with the new public key and send that CSR to the CA. 8. The CA will extract the information, create a beautiful x509 certificate, sign it and send it back to you. 9. lets-encrypt will install the certificate on your server and set certain options (or not) to force https By the way, the certificate you will get will be a DV certificate, meaning that they only verified that you owned the domain, nothing more. If you want an EV certificate this is what you will have to go through (according to wikipedia): • Establish the legal identity as well as the operational and physical presence of website owner; • Establish that the applicant is the domain name owner or has exclusive control over the domain name; and • Confirm the identity and authority of the individuals acting for the website owner, and that documents pertaining to legal obligations are signed by an authorised officer. ## But how does it really work? So! The lets-encrypt program you run on your server is open sourced here: https://github.com/letsencrypt/lets-encrypt-preview. It is called lets-encrypt-preview I guess because it isn't done yet. It's written in Python and has to be run in sudo so that it can do most of the work for you. Note that it will install the certificates on your server only if you are using Apache or Nginx. Also, the address of the CA is hardcoded in the program so be sure to use the official lets-encrypt. The program installed on the CA is also open sourced! So that anyone can publicly review and audit the code. It's called Boulder and it's here: https://github.com/letsencrypt/boulder and written in Go. Lets-encrypt and Boulder both use the protocol ACME for Automated Certificate Management Environment specified here as a draft: https://letsencrypt.github.io/acme-spec/ ## ACME ACME is written like a RFC. It actually wants to become an RFC eventually! So if you've read RFCs before you should feel like home. The whole protocol is happening over TLS. As a result the exchanges are encrypted, you know that you are talking to the CA you want to talk to (eventhough you might not use DNSSEC) and replay attacks should be avoided. The whole thing is actually a RESTful API. The client, you, can do GET or POST queries to certains URI on the CA webserver. ## Registration The first thing you want to do is register. Registration is actually done by generating a new pair of RSA keys and sending them the public key (along with your info). ACME specifies that you should use JWS for the transport of data. Json Web Signature. It's basically Json with authentication (so that you can sign your messages). It actually uses a variant of JWS called Jose that doesn't use a normal base64 encoding but that's all you should know for now. If you really want to know more there is an RFC for it. So here what a request should look like with JWS (your information are sent unencrypted in the payload field (but don't worry, everything is encrypted anyway because the exchange happens over TLS)): POST /acme/new-registration HTTP/1.1 Host: example.com { "payload":"<payload contents>", "signatures":[ {"protected":"<integrity-protected header 1 contents>", "header":<non-integrity-protected header 1 contents>, "signature":"<signature 1 contents>"} } Boulder will check the signature with the public key you passed, verify the information you gave and eventually add you to its database. Once you are registered, you can perform several actions: • Update your infos • Get one domain authorized (well actually as many as you'd like) The server will authenticate you because you will now send your public key along AND you will sign your requests. This all runs on top of TLS by the way. I know I already said that. ## Boulder's guts Boulder is separated in multiple components, this makes the code clearer and ensure that every piece of code does what it is supposed to do and nothing more. One of the components is called the Web-Front-End (WFE) and is the only one accepting queries from the Client. It parses them, verifies them and passes them to the Registration Authority (RA) that combines the other authorities together to produce a response. The response is then passed back to the WFE and to the client over the ACME protocol. Are you following? TWe'll see what other authorities the RA has access to in the next queries the client can do. But just to talk about the previous query, the new registration query, the RA talks to the Storage Authority that deals with the database (Which is currently SQLlite) to register your new account. All the components can be run from a single machine (for the exception of the CA that runs on another library), but they can also be run seperately from different machines that will communicate on the same network via AMQP. ## New Authorization Now that you are registered, you have to validate a domain before you can request a certificate. You make a request to a certain URI. Well to be exact you make a POST request to /new-authz, and the response will be 201 if it works. It will also give you some information about where you can go next to do stuff (/authz) Here's the current list of API calls you can do and the relevant answers. The server will pass the info to the Policy Authority (PA) and ask it if it is willing to accept such a domain. If so, it will then answer with a list of challenges you can complete to prove you own the domain, along with combinations of accepted challenges to complete. For now they only have two challenges and you can complete either one: • SimpleHTTPS • DVSNI If you choose SimpleHTTPS the lets-encrypt client will generate a random value and upload something at the address formed by a random value the CA sent you and the random value you generated. If you choose DVSNI, the client will create a TLS certificate containing some of the info of the challenge and with the public key associated to his account. The client then needs to query the CA again and the CA's Validation Authority (VA) will either check that the file has been uploaded or will perform a handshake with the client's server and verify that specific fields of the certificates have been correctly filled. If everything works out the VA will tell the RA that will tell the WFE that will tell you... After that you are all good, you can now make a Certificate Signing Request :) ## New Certificate The agent will now generate a new pair of private key/public key. And create a CSR with it. So that your long term key used in your certificate is not the same as your let's encrypt account. a CSR example, containing the identifier and the public key After reception of it, the Web-Front-End of Boulder will pass it to the Registration Authority (RA) which will pass it to the Certificate Authority (CA) that will do all the work and will eventually sign it and send it back to the chain. 1: Client ---new-cert--> WFE 2: WFE ---NewCertificate--> RA 3: RA ---IssueCertificate--> CA 4: CA --> CFSSL 5: CA <-- CFSSL 6: RA <------return--------- CA 7: WFE <------return------- RA 8: Client <------------- WFE Oh and also. the CA is talking to a CFSSL server which is CloudFlare's PKI Toolkit, a nice go library that you can use for many things and that is used here to act as the CA. CFSSL has recently pushed code to be compatible with the use of HSM which is a hardware device that you HAVE to use to sign keys when you are a CA. After reception the lets-encrypt client will install the fresh certificate along with the chain to the root on your server and voila! You can now revoke a certificate in the same way, but interestingly you won't need to sign the request with your account key, but with the private key associated to your certificate's public key. So that even if you lose your agent's key you can still revoke the certificate. ## Other stuff There are a bunch of stuff that you will be able to do with the lets-encrypt client but that haven't been implemented yet: • Renew a certificate • Read the Terms of Service • Query OCSP requests (see if a certificate has been revoked) ... ## Moar This post is a simplification of the protocol. If you want to know more and don't want to dig in the ACME specs right now you can also take a look at Boulder's flow diagrams. If you've followed the news you should have seen that Let's Encrypt just generated its root certificate along with several other certificates: https://letsencrypt.org/2015/06/04/isrg-ca-certs.html This is because when you are a CA you are suppose to keep the root certificate offline. So you sign a (few) certificate(s) with that root, you lock that root and you use the signed certificate(s) to sign other certificates. This is all very serious because if something goes wrong with the root certificate, you can't revoke anything and well... the internet goes wrong as a result (until vendors start removing these from their list of trusted roots). So the keys for the certificate have to be generated during a "ceremony" where everything is filmed and everyone must authenticate oneself at least with two different documents, etc... Check Wikipedia's page on Key Ceremony it's "interesting". Also, I received a note from Seth David Schoen and I thought that was an interesting anecdote to share :) the name "Boulder" is a joke from the American children's cartoon Looney Tunes: https://en.wikipedia.org/wiki/Wile_E._Coyote_and_The_Road_Runner This is because the protocol that Boulder implements is called ACME, which was also the name of the company that made the products unsuccessfully used by the coyote to attempt to catch the roadrunner. https://en.wikipedia.org/wiki/Acme_Corporation Two of those products were anvils (the original name of the CA software) and boulders. 20 comments # Hacking Week 2015 : Crypto 4 Write-Up ## posted June 2015 The Hacking Week ended 2 weeks ago and EISTI got the victory. I'm the proud creator of the crypto challenge number 4, still available here, which was solved 12 times. I also wrote a Proof of Solvableness, reading it should teach you about a simple and elegant crypto attack on RSA: the Same Modulus Attack. (Note that I wrote that back in January) ## Let's start We are presentend with 4 files: • alice.pub • irc.log • mykey.pem • secret the irc.log reads like this: Session Start: Thu Feb 05 20:49:04 2015 Session Ident: #mastercsi [20:49] * Now talking in #mastercsi [20:49] * Topic is 'http://www.math.u-bordeaux1.fr/CSI/ |||| http://www.youtube.com/watch?v=zuDtACzKGRs "das boot, ouh, ja" ||| http://www.koreus.com/video/chat-saut-balcon.html ||| http://blog.cryptographyengineering.com/ ||| http://www.youtube.com/watch?v=K1LZ60eMpiw ||| petit chat http://www.youtube.com/watch?v=eu2kVcWKvRo ||| sun : t'as le droit de boire quand même va' [20:49] * Set by [email protected]:41d0:52:100::65d on Sat Nov 22 00:06:50 [20:49] <asdf> et donc j'ai chopé une vieille clé rsa qu'alice utilisait [20:49] <qwer> alice la alice? tu te fous de moi ? [20:49] <asdf> haha non [20:49] <asdf> mais le truc est corrompu, ça a l'air de marcher pour chiffrer mais la moitié de la clé a disparu [20:49] <qwer> attend j'ai sa clé publique qui traine quelque part, et même un fichier chiffré avec. me suis toujours demandé ce que c'était... [20:50] <asdf> je t'ai envoyé le truc, mais ça m'étonnerait que ça soit la même clé non ? [21:22] * Disconnected Session Close: Thu Feb 05 21:22:11 2015 so alice.pub seems to be alice public rsa key. secret seems to be the file encrypted under this key and mykey.pem should be the partial key which was found. Private-Key: (1024 bit) modulus: 00:c6:c8:35:29:a2:38:8f:14:63:65:c5:f5:fd:4b: 0d:88:89:61:b9:5d:e1:0f:fa:88:53:a3:c2:cb:ed: 75:0e:99:59:bd:0f:f8:72:c2:23:2f:6b:ad:32:62: 4f:35:6a:82:d0:62:75:5e:1e:4f:ed:ae:54:e8:ca: 24:71:fc:8d:13:ac:70:0e:e2:57:20:d4:d9:08:9f: d6:fb:d4:2f:12:e6:a4:1e:1c:1d:e8:1f:57:8c:32: 13:2a:d0:85:94:e8:51:84:1d:02:39:cd:41:0d:ef: 11:d1:c1:5e:e7:5b:92:f8:6a:04:f7:c6:c7:f3:6b: 90:46:b8:fb:2f:e2:95:65:b1 publicExponent: 3 (0x3) privateExponent: 00:84:85:78:c6:6c:25:b4:b8:42:43:d9:4e:a8:dc: b3:b0:5b:96:7b:93:eb:5f:fc:5a:e2:6d:2c:87:f3: a3:5f:10:e6:7e:0a:a5:a1:d6:c2:1f:9d:1e:21:96: df:78:f1:ac:8a:ec:4e:3e:be:df:f3:c9:8d:f0:86: c2:f6:a8:5e:0b:ef:c0:ca:19:c5:e2:49:55:49:fe: e5:2e:51:3e:7b:e9:f2:22:07:d2:4b:84:7f:bb:0c: b5:ba:b7:95:c6:90:05:3e:65:2d:11:53:9a:2d:96: 0f:ea:de:cb:9b:17:54:87:00:0f:78:12:ce:ac:f5: db:83:30:16:06:cc:35:7d:a3 prime1: 245 (0xf5) prime2: 207 (0xcf) exponent1: 163 (0xa3) exponent2: 138 (0x8a) coefficient: 189 (0xbd) It looks like prime1, prime2 and some other stuff are pretty short. I guess this is what he meant by "half the key" is messed up. By the way this is what a RSA PrivateKey should look like: > RSAPrivateKey ::= SEQUENCE { version Version, modulus INTEGER, -- n publicExponent INTEGER, -- e privateExponent INTEGER, -- d prime1 INTEGER, -- p prime2 INTEGER, -- q exponent1 INTEGER, -- d mod (p-1) exponent2 INTEGER, -- d mod (q-1) coefficient INTEGER, -- (inverse of q) mod p otherPrimeInfos OtherPrimeInfos OPTIONAL } So this is what exponent1, exponent2 and coefficient are. Just additional information so that computations are faster thanks to CRT. Let's ignore that for the moment. $ openssl rsa -pubin -in alice.pub -modulus -noout
$openssl rsa -in mykey.pem -modulus -noout Modulus=C6C83529A2388F146365C5F5FD4B0D888961B95DE10FFA8853A3C2CBED750E9959BD0FF872C2232F6BAD32624F356A82D062755E1E4FEDAE54E8CA2471FC8D13AC700EE25720D4D9089FD6FBD42F12E6A41E1C1DE81F578C32132AD08594E851841D0239CD410DEF11D1C15EE75B92F86A04F7C6C7F36B9046B8FB2FE29565B1 the partial key and alice public key seems to share the same modulus. this is vulnerable. If our public/private exponents are not messed up, this means we can factor the modulus and thus inverse Alice's public key. Let's retrieve all the info we have and put them in a file: openssl rsa -pubin -in alice.pub -modulus -noout | sed 's/Modulus=//' | xclip -selection c Here's the modulus. We know that our public key is 3, let's get the private key in the clipboard as well openssl asn1parse -in mykey.pem | grep 129 | tail -n1 | awk '{ print$7}' | sed 's/://' | xclip -selection c

here I parse mykey.pem with openssl. I select the lines I want with grep. It returns two results, the modulus and the private key. I select only the second line with tail. I select only the 7th column with awk. I remove the : with sed. And now I have a beautiful integer in my clipboard.

Okay so let's do a bit of Sage now:

# let's write the info we have

public = 3

# now let's factor the modulus
k = (private * public - 1)//2
carre = 1
g = 2
while carre == 1 or carre == modulus - 1:
g += 1
carre = power_mod(g, k, modulus)

p = gcd(carre - 1, modulus)
print(p)

This does not work. This should work.

Let's re-do the maths:

We know that our private and public keys cancel out. This is RSA:

private * public = 1 mod phi(N)

so we have private * public - 1 = 0 mod phi(N)

So for any g in our ring, we should have g^(private * public - 1) = 1 mod N

This is how RSA works.

Let's write it like that: private * public - 1 = k with k a multiple of phi(n). And we know that phi(n) = (p-1)(q-1) is even. So it could be written like this: k = 2^t * r with r an odd number.

Now if we take a random g mod N and we do g^(k/2) it should be the square root of a 1.

The Chinese Remainder Theorem tells us that there are 4 square roots mod N:

• 1 mod p
• -1 mod p
• 1 mod q
• -1 mod q

and two of them should be 1 mod N and -1 mod N. The 2 others should be different from 1 and -1 mod N. That's what I was trying to find in my code.

Once we have found this x mod N which is a square root of 1 mod N, we know that it is either x = 1 mod p or x = -1 mod p. If we are in the first case, we shoudl have x - 1 = 0 mod p which translates into x - 1 is a multiple of p. Doing gcd(x - 1, N) should give us p the first prime. If you don't understand it maybe check Dan Boneh's explanation (proof end of page 3) which should be clearer than mine.

With p it's easy to get q the other prime.

But it doesn't work...

Ah! I forgot that g^(k/2) could equal 1 all the time if k/2 were to be a multiple of phi(n). So let's code a loop that divides k by 2 and tries any g^k until it is giving us something else than 1. Then we know how many times we have to divide k by 2 so it's not a multiple of phi(n) anymore.

It turns out we just have to do it 3 times. And then it magically works. A bit more of Sage gives us the primes:

# p and q our primes
p = gcd(carre - 1, modulus)
q = modulus // p

# now that we have factored N let's find alice decryption key
public = 65537
phi = (p - 1) * (q - 1)
private = inverse_mod(public, phi)

Now that we have Alice's private key there are two ways to decrypt our secret:

• recreate a valid rsa key with those values and use openssl rsautl
• figure out how openssl rsautl works to do it ourselves

Let's do the first one. We'll modify our mykey.pem for this:

openssl rsa -in  mykey.pem -outform DER -out newkey.bin
xxd -p newkey.bin > newkey.hex

we get this:

3082012202010002818100c6c83529a2388f146365c5f5fd4b0d888961b9
62755e1e4fedae54e8ca2471fc8d13ac700ee25720d4d9089fd6fbd42f12
5b92f86a04f7c6c7f36b9046b8fb2fe29565b102010302818100848578c6
6c25b4b84243d94ea8dcb3b05b967b93eb5ffc5ae26d2c87f3a35f10e67e
0aa5a1d6c21f9d1e2196df78f1ac8aec4e3ebedff3c98df086c2f6a85e0b
efc0ca19c5e2495549fee52e513e7be9f22207d24b847fbb0cb5bab795c6
cc357da3020200f5020200cf020200a30202008a020200bd

This is a DER encoding. One particular encoding from the ASN.1 family. It is a TLV kind of encoding (Type Lenght Value).

For example in:

02 8181 00c6c83529a2388f146365c5f5fd4b0d888961b95de10ffa8853
ae54e8ca2471fc8d13ac700ee25720d4d9089fd6fbd42f12e6a41e1c1de8
c6c7f36b9046b8fb2fe29565b1

first is coded the type 02 (integer), then the length (81 repeated twice because the value block is bigger than 127bits, so we set the first byte to 81 (10000001, the first bit means it is a long way of defining the length, the 7 following bits are the number of byte it will take to define the length, in our case only one and it will be the next one) and the second byte to the actual size), then there is our modulo in hexadecimal. Note that the most significant bit of our value has to be zero if it is a positive integer, that's why we use 41 instead of 40 and lead the payload with 00.

So let's take the time and break this apart:

3082 // some header
0122 // the length of everything that follows (in byte)
0201 // integer of size 1
00
028181 // integer of size 0x81 (our modulus)
0201 // integer of size 1 (our public key)
03
028181 // integer of size 0x81 (our private key)
00848578c66c25b4b84243d94ea8dcb3b05b967b93eb5ffc5ae26d2c87f3a35f10e67e
0aa5a1d6c21f9d1e2196df78f1ac8aec4e3ebedff3c98df086c2f6a85e0b
efc0ca19c5e2495549fee52e513e7be9f22207d24b847fbb0cb5bab795c6
cc357da3
0202 // integer of size 2 (prime 1)
00f5
0202 // integer of size 2 (prime 2)
00cf
0202 // integer of size 2 (exponent 1)
00a3
0202 // integer of size 2 (exponent 2)
008a
0202 // integer of size 2 (coefficient)
00bd

Now let's remove everything which is after the modulus and let's refill the file with our own values. Let's go back in Sage to calculate them:

public = 65537
phi = (p - 1) * (q - 1)
private = inverse_mod(public, phi)
exponent1 = inverse_mod(private, p - 1)
exponent2 = inverse_mod(private, q - 1)
coefficient = inverse_mod(q, p)

After filling and modifying the header's length accordingly, we obtain a nice hexadecimal file that we can transform back to binary:

xxd -r -p new_key.hex | openssl asn1parse -inform DER

It works! So now let's decrypt with is shall we?

xxd -r -p new_key.hex | openssl rsa -inform DER -outform PEM -out newkey.pem
openssl rsautl -decrypt -in secret -inkey newkey.pem

We have our secret :)!