david wong

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.

Talk: RSA and LLL attacks

posted March 2015

lll

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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How Enigma Works

posted March 2015

I've watched The Imitation Game recently, a movie about Turing, and I was really disappointed at how they don't explain anything at all. I was also disappointed at how much time they spend drinking or doing something else than doing real work, or how they ended the movie before a potentially interesting second part of Turing's life (Imagine if they showed the persecution, it would have been kind of a Life is beautiful. So anyway, I ran into this explanation of Enigma:

more

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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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Citizen Four

posted March 2015

I just watched the documentary about Snowden. It was pretty stressing to see the events unfold from his point of view. You can download on Cryptome

The part where Ladar Levison, the owner of Lavabit, talks out is pretty intense.

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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
2 comments

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

--

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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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.

bug

more pictures there

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Funny matasano job post

posted March 2015

I stumbled on this funny job post from jeff jarmoc:

This thread will, no doubt, be dominated by posts with laundry lists of requirements. Many employers will introduce themselves by describing what they want from you. At Matasano, we're a little different. We like to start by telling you about us. This month, I want to try to do that by drawing analogy to Mission Impossible.
What made the original show so great is exactly what was lost in the 'Tom Cruise takes on the world' reboot. The original 1960's and 70's Mission Impossible was defined primarily by a team working together against all odds to achieve their objective. It acknowledged that what they were doing was improbable, and more so for a solo James Bond or Tom Cruise character. As a team though, each character an expert in their particular focus area, the incredible became credible -- the impossible, possible.

the rest is here: https://news.ycombinator.com/item?id=9127813

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