Hey! I'm David, cofounder of zkSecurity and the author of the Real-World Cryptography book. I was previously a crypto architect at O(1) Labs (working on the Mina cryptocurrency), before that 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.

# 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

# Apple rejects Signal 2 from the appstore posted March 2015

EDIT: the tweet has been deleted, no news about what happened

There was a lot of talks about Signal 2, a messaging app that was doing end-to-end encryption on iOS.

It seems like Apple is not going to allow that:

WTF Apple?! They are rejecting Signal 2.0.1 because we are doing privacy-friendly bloom filter contact intersection.

@Frederic Jacobs

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A Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set. False positive matches are possible, but false negatives are not, thus a Bloom filter has a 100% recall rate. In other words, a query returns either "possibly in set" or "definitely not in set". Elements can be added to the set, but not removed (though this can be addressed with a "counting" filter). The more elements that are added to the set, the larger the probability of false positives.

Bloom Filter on Wikipedia

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# Hacking Week CTF starting April the 3rd posted March 2015

One of my professor is organizing a CTF, it's in french (sorry), it will start next month and should last for a week, and... there might be a challenge I've made for them =). I don't know if it has been accepted but here you go: HackingWeek 2015 if you are interested and you can speak french

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# Starfighter posted March 2015

Thomas Ptacek had left Matasano, 2 years after selling to NCC, and I spotted him talking about a new "hiring" kind of company on hackernews... Well today they announced what is going to be a new kind of hiring process. After the revolution of education with Coursera and other MOOC (Massive Open Online Courses), now comes the revolution of hiring. It's called Starfighter and it will be live soon.

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# Pretty diagrams with Tikz in LaTeX posted March 2015

Because studying Cryptography is also about using LaTeX, it's nice to spend a bit of time understanding how to make pretty documents. Because, you know, it's nicer to read.

Here's an awesome quick introduction of Tikz that allows to make beautiful diagram with great precision in a short time:

And I'm bookmarking one more that seems go way further.

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# GPS tracking device in real life! posted March 2015

I've only seen that in movies. Not that it couldn't exist, it's just "fun" to see that happen in real life as well.

The story is here. It's about someone's car which got "bugged". It was discovered while X was at the Circumvention Tech Festival in Valencia, Spain.

more pictures there

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