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.

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# The story behind Schneier's law posted March 2015

...what I think of as Schneier's Law: "any person can invent a security system so clever that she or he can't think of how to break it."

It's pretty old but 4 years ago Schneier wrote a bit about the story behind it: check it out here.

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# Invisibility glasses posted March 2015

AVG will reveal its new product: Invisibility glasses at pepcom barcelona.

It seems to be some kind of glasses you wear so that cameras and facial recognition softwares won't recognize you, it works by displaying lights that are only visible to cameras and not human eyes

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# Keep in touch with crypto posted February 2015

I have collected a list of 60 blogs about cryptography and security. If you feel like one is missing or one shouldn't be here please tell me! The list is here

Here's the list if you hate RSS:

# The ghetto way of extracting the private key of superfish posted February 2015

A realy entertaining piece by Errata Security where Robert Graham ghetto reverse the current controversial superfish of Lenovo.

The goal is to set the right break point before it actually infects your machine -- reversers have been known to infect themselves this way.

his ghetto way of reversing is first to infect himself with the "virus" and then using procdump to dump the process memory. Then dumping all the strings that the memory contains with the tool strings and voila. You have have the private certificate in the clear.

But the private certificate is protected by a passphrase. But apparently not, it was just protected by a password contained in the memory in clear as well...

I advise you to read the article, it comes with screenshots and nice commands that use text processing tools:

grep "^[a-z]*\$" super.txt | sort | uniq > super.dict

spoiler alert, the password to protect the certificate is komodia the name of the company who created this mitm adware.

Note that if they would have used an RSA whitebox this would not have happened... so quickly.

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# Big Numbers posted February 2015

An amazing story by Scott Aaronson on Big Numbers.

Keywords: exponential growth, NP-complete problems, Ackermann sequence, Turing Machine, Halting Problem, Busy Beaver,

some quotes :)

In an old joke, two noblemen vie to name the bigger number. The first, after ruminating for hours, triumphantly announces "Eighty-three!" The second, mightily impressed, replies "You win."

Consider, for example, the oft-repeated legend of the Grand Vizier in Persia who invented chess. The King, so the legend goes, was delighted with the new game, and invited the Vizier to name his own reward. The Vizier replied that, being a modest man, he desired only one grain of wheat on the first square of a chessboard, two grains on the second, four on the third, and so on, with twice as many grains on each square as on the last. The innumerate King agreed, not realizing that the total number of grains on all 64 squares would be 264-1, or 18.6 quintillion—equivalent to the world’s present wheat production for 150 years.

Rado called this maximum the Nth "Busy Beaver" number. (Ah yes, the early 1960’s were a more innocent age.)

To solve the Halting Problem for super machines, we’d need an even more powerful machine: a ‘super duper machine.’ And to solve the Halting Problem for super duper machines, we’d need a ‘super duper pooper machine.’

If we could run at 280,000,000 meters per second, there’d be no need for a special theory of relativity: it’d be obvious to everyone that the faster we go, the heavier and squatter we get, and the faster time elapses in the rest of the world. If we could live for 70,000,000 years, there’d be no theory of evolution, and certainly no creationism: we could watch speciation and adaptation with our eyes, instead of painstakingly reconstructing events from fossils and DNA. If we could bake bread at 20,000,000 degrees Kelvin, nuclear fusion would be not the esoteric domain of physicists but ordinary household knowledge.

But do people fear big numbers? Certainly they do. I’ve met people who don’t know the difference between a million and a billion, and don’t care. We play a lottery with ‘six ways to win!,’ overlooking the twenty million ways to lose. We yawn at six billion tons of carbon dioxide released into the atmosphere each year, and speak of ‘sustainable development’ in the jaws of exponential growth.

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# Using crypto to replace database access. posted February 2015

A pretty fresh article on how you could use crypto to replace a lot of complicated schemes you might use on your website like password reset or mail confirmation:

tl;dr: instead of creating a table for tokens, you could create the password reset url like this:

and at the place of the token you would put the output of a MAC. Checking the MAC again after receiving the url would confirm that YOU created that url and it has not been modified. Remember, MAC provides integrity and authentication. The author also provides a way to only render this usable once: use the original hashed password as a nonce.

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# Babun, Cmder and Tmux posted February 2015

I've used Cmder for a while on Windows. Which is a pretty terminal that brings a lot of tools and shortcuts from the linux world. I also have Chocolatey as packet manager. And all in all it works pretty great except Cmder is pretty slow.

I've ran into Babun yesterday, that seems to be kind of the same thing, but with zsh, oh-my-zsh and another packet manager: pact. The first thing I did was downloading tmux and learning how to use it. It works pretty well and I think I have found a replacement for Cmder =)

Here is a video of what is tmux:

# Implementation of Coppersmith attack (RSA attack using lattice reductions) posted February 2015

I've implemented the work of Coppersmith (to be correct the reformulation of his attack by Howgrave-Graham) in Sage.

You can see the code here on github.

I won't go too much into the details because this is for a later post, but you can use such an attack on several relaxed RSA models (meaning you have partial information, you are not totally in the dark).

I've used it in two examples in the above code:

## Stereotyped messages

For example if you know the most significant bits of the message. You can find the rest of the message with this method.

The usual RSA model is this one: you have a ciphertext c a modulus N and a public exponent e. Find m such that m^e = c mod N.

Now, this is the relaxed model we can solve: you have c = (m + x)^e, you know a part of the message, m, but you don't know x. For example the message is always something like "the password today is: [password]". Coppersmith says that if you are looking for N^1/e of the message it is then a small root and you should be able to find it pretty quickly.

let our polynomial be f(x) = (m + x)^e - c which has a root we want to find modulo N. Here's how to do it with my implementation:

dd = f.degree()
beta = 1
epsilon = beta / 7
mm = ceil(beta**2 / (dd * epsilon))
tt = floor(dd * mm * ((1/beta) - 1))
XX = ceil(N**((beta**2/dd) - epsilon))
roots = coppersmith_howgrave_univariate(f, N, beta, mm, tt, XX)

You can play with the values until it finds the root. The default values should be a good start. If you want to tweak:

• beta is always 1 in this case.
• XX is your upper bound on the root. The bigger is the unknown, the bigger XX should be. And the bigger it is... the more time it takes.

## Factoring with high bits known

Another case is factoring N knowing high bits of q.

The Factorization problem normally is: give N = pq, find q. In our relaxed model we know an approximation q' of q.

Here's how to do it with my implementation:

let f(x) = x - q' which has a root modulo q.
This is because x - q' = x - ( q + diff ) = x - diff mod q with the difference being diff = | q - q' |.

beta = 0.5
dd = f.degree()
epsilon = beta / 7
mm = ceil(beta**2 / (dd * epsilon))
tt = floor(dd * mm * ((1/beta) - 1))
XX = ceil(N**((beta**2/dd) - epsilon)) + 1000000000000000000000000000000000
roots = coppersmith_howgrave_univariate(f, N, beta, mm, tt, XX)

What is important here if you want to find a solution:

• we should have q >= N^beta
• as usual XX is the upper bound of the root, so the difference should be: |diff| < XX
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