Hey! I'm David, the author of the Real-World Cryptography book. I'm a crypto engineer at O(1) Labs on the Mina cryptocurrency, previously I was the security lead for Diem (formerly Libra) at Novi (Facebook), and a security consultant for the Cryptography Services of NCC Group. This is my blog about cryptography and security and other related topics that I find interesting.

# Cryptography Services to audit Let's Encrypt posted April 2015

Like the audit of OpenSSL wasn't awesome enough, today we learned that we were going to audit Let's Encrypt this summer as well. Pretty exciting agenda for an internship!

https://letsencrypt.org/2015/04/14/ncc-group-audit.html

ISRG has engaged the NCC Group Crypto Services team to perform a security review of Let’s Encrypt’s certificate authority software, boulder, and the ACME protocol. NCC Group’s team was selected due to their strong reputation for cryptography expertise, which brought together Matasano Security, iSEC Partners, and Intrepidus Group.

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# ASN.1 vs DER vs PEM vs x509 vs PKCS#7 vs .... posted April 2015

I was really confused about all those acronyms when I started digging into OpenSSL and RFCs. So here's a no bullshit quick intro to them.

# PKCS#7

Or Public-Key Crypto Standard number 7. It's just a guideline, set of rules, on how to send messages, sign messages, etc... There are a bunch of PKCS that tells you exactly how to do stuff using crypto. PKCS#7 is the one who tells you how to sign and encrypt messages using certificates. If you ever see "pkcs#7 padding", it just refers to the padding explained in pkcs#7.

# X509

In a lot of things in the world (I'm being very vague), we use certificates. For example each person can have a certificate, and each person's certificate can be signed by the government certificate. So if you want to verify that this person is really the person he pretends to be, you can check his certificate and check if the government signature on his certificate is valid.

TLS use x509 certificates to authenticate servers. If you go on https://www.facebook.com, you will first check their certificate, see who signed it, checked the signer's certificate, and on and on until you end up with a certificate you can trust. And then! And only then, you will encrypt your session.

So x509 certificates are just objects with the name of the server, the name of who signed his certificate, the signature, etc...

Example from wikipedia:

    Certificate
Version
Serial Number
Algorithm ID
Issuer
Validity
Not Before
Not After
Subject
Subject Public Key Info
Public Key Algorithm
Subject Public Key
Issuer Unique Identifier (optional)
Subject Unique Identifier (optional)
Extensions (optional)
...
Certificate Signature Algorithm
Certificate Signature

# ASN.1

So, how should we write our certificate in a computer format? There are a billion ways of formating a document and if we don't agree on one then we will never be able to ask a computer to parse a x509 certificate.

That's what ASN.1 is for, it tells you exactly how you should write your object/certificate

# DER

ASN.1 defines the abstract syntax of information but does not restrict the way the information is encoded. Various ASN.1 encoding rules provide the transfer syntax (a concrete representation) of the data values whose abstract syntax is described in ASN.1.

Now to encode our ASN.1 object we can use a bunch of different encodings specified in ASN.1, the most common one being used in TLS is DER

DER is a TLV kind of encoding, meaning you first write the Tag (for example, "serial number"), and then the Length of the following value, and then the Value (in our example, the serial number).

DER is also more than that:

DER is intended for situations when a unique encoding is needed, such as in cryptography, and ensures that a data structure that needs to be digitally signed produces a unique serialized representation.

So there is only one way to write a DER document, you can't re-order the elements.

And a made up example for an ASN.1 object:

OPERATION ::= CLASS
{
&operationCode INTEGER UNIQUE,

&InvocationParsType,

&ResponseParsAndResultType,

&ExceptionList ERROR OPTIONAL
}

And its DER encoding:

0110 0111 0010 110...

# Base64

Base64 is just a way of writing binary data in a string, so you can pass it to someone on facebook messenger for exemple

From the openssl Wiki:

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
0000000000111111111122222222223333333333444444444455555555556666
0123456789012345678901234567890123456789012345678901234567890123

And if you see any equal sign =, it's for padding.

So if the first 6 bits of your file is '01' in base 10, then you will write that as B in plaintext. See an example if you still have no idea about what I'm talking about.

# PEM

A pem file is just two comments (that are very important) and the data in base64 in the middle. For example the pem file of an encrypted private key:

-----BEGIN ENCRYPTED PRIVATE KEY-----
MIIFDjBABgkqhkiG9w0BBQ0wMzAbBgkqhkiG9w0BBQwwDgQIS2qgprFqPxECAggA
MBQGCCqGSIb3DQMHBAgD1kGN4ZslJgSCBMi1xk9jhlPxP3FyaMIUq8QmckXCs3Sa
9g73NQbtqZwI+9X5OhpSg/2ALxlCCjbqvzgSu8gfFZ4yo+Xd8VucZDmDSpzZGDod
X0R+meOaudPTBxoSgCCM51poFgaqt4l6VlTN4FRpj+c/WZeoMM/BVXO+nayuIMyH
H0ga/iLNvWYexG7FHLRiq5hTj0g9mUPEbeTXuPtOkTEb/0ckVE2iZH9l7g5edmUZ
GEs=
-----END ENCRYPTED PRIVATE KEY-----

And yes the number of - are important

# Video: How the RSA attacks using lattices work posted April 2015

This is my second video, after the first explaining how DPA works. I'm still trying to figure out how to do that but I think it is already better than the first one. Here I explain how Coppersmith used LLL, an algorithm to reduce lattices basis, to attack RSA. I also explain how his attack was simplified by Howgrave-Graham, and the following Boneh and Durfee attack simplified by Herrmann and May as well.

The repo is here, you can check the survey here as well.

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# I'm officialy an intern at Cryptography Services posted April 2015

I haven't been posting for a while, and this is because I was busy looking for a place in Chicago. I finally found it! And I just accomplished my first day at Cryptography Services, or rather at Matasano since I'm in their office, or rather at NCC Group since everything must be complicated :D

I arrived and received a bag of swags along with a brand new macbook pro! That's awesome except for the fact that I spent way too much time trying to understand how to properly use it. A few things I've discovered:

• you can pipe to pbcopy and use pbpaste to play with the clipboard
• open . in the console opens the current directory in Finder (on windows with cygwin I use explorer .)
• in the terminal preference: check "use option as meta key" to have all the unix shortcuts in the terminal (alt+b, ctrl+a, etc...)
• get homebrew to install all the things

I don't know what I'll be blogging about next, because I can't really disclose the work I'll be doing there. But so far the people have been really nice and welcoming, the projects seem to be amazingly interesting (and yeah, I will be working on OpenSSL!! (the audit is public so that I can say :D)). The city is also amazing and I've been really impressed by the food. Every place, every dish and every bite has been a delight :)

# Talk: RSA and LLL attacks posted March 2015

I posted previously about my researches on RSA attacks using lattice's basis reductions techniques, I gave a talk today that went really well and you can check the slides on the github repo

Also on SlideShare

I wanted to record myself so I could have put that on youtube along with the slides but... I completely forgot once I got on stage. But this is OK as I got corrected on some points, it will make the new recording better :) I will try to make it as soon as possible and upload it on youtube.

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# End to End encryption for Yahoo mail users (plugin) posted March 2015

Yahoo has released a plugin that allows end to end encryption for yahoo mail users. It's seems to be part of the new "yahoo" redesign:

we’ve heard you loud and clear: We’re building the best products to ensure a more secure user experience and overall digital ecosystem.

It's open sourced and they also setup a bug bounty program (from 50$to 15,000$)

While at this stage we’re rolling out the source code for feedback from the wider security industry

More on their tumblr (this sounds weird).

Glancing over the code it looks like it's cumbersome to use:

The extension requires a keyserver implementing this API to fetch keys for other users.

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# Survey on RSA Attacks using Lattice reduction techniques (LLL) posted March 2015

And here's the survey of what I talked about previously: https://github.com/mimoo/RSA-and-LLL-attacks/raw/master/survey_final.pdf

It's my first survey ever and I had much fun writing it! I don't really know if I can call it a survey, it reads like a vulgarization/explanation of the papers from Coppersmith, Howgrave-Graham, Boneh and Durfee, Herrmann and May. There is a short table of the running times at the end of each sections. There is also the code of the implementations I coded at the end of the survey.

If you spot a typo or something weird, wrong, or badly explained. Please tell me!

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# Implementation of Boneh and Durfee attack on RSA's low private exponents posted March 2015

I've Implemented a Coppersmith-type attack (using LLL reductions of lattice basis). It was done by Boneh and Durfee and later simplified by Herrmann and May. The program can be found on my github.

The attack allows us to break RSA and the private exponent d. Here's why RSA works (where e is the public exponent, phi is euler's totient function, N is the public modulus):

$ed = 1 \pmod{\varphi(N)}$ $\implies ed = k \cdot \varphi(N) + 1 \text{ over } \mathbb{Z}$ $\implies k \cdot \varphi(N) + 1 = 0 \pmod{e}$ $\implies k \cdot (N + 1 - p - q) + 1 = 0 \pmod{e}$ $\implies 2k \cdot (\frac{N + 1}{2} + \frac{-p -q}{2}) + 1 = 0 \pmod{e}$

The last equation gives us a bivariate polynomial $f(x,y) = 1 + x \cdot (A + y)$. Finding the roots of this polynomial will allow us to easily compute the private exponent d.

The attack works if the private exponent d is too small compared to the modulus: $d < N^{0.292}$.

To use it:

• look at the tests in boneh_durfee.sage and make your own with your own values for the public exponent e and the public modulus N.
• guess how small the private exponent d is and modify delta so you have d < N^delta
• tweak m and t until you find something. You can use Herrmann and May optimized t = tau * m with tau = 1-2*delta. Keep in mind that the bigger they are, the better it is, but the longer it will take. Also we must have 1 <= t <= m.
• you can also decrease X as it might be too high compared to the root of x you are trying to find. This is a last recourse tweak though.

Here is the tweakable part in the code:

# Tweak values here !
delta = 0.26 # so that d < N^delta
m = 3        # x-shifts
t = 1        # y-shifts # we must have 1 <= t <= m