Some Thoughts On Secure Random Numbers

October 30th, 2016

Many protocols and cryptographic primitives such as DSA rely on secure random numbers. For example, the Signal messenger and it’s quite intricate protocol was recently analyzed and a paper about the analyses published[1]. The authors wrote that they “do not consider faulty/malicious random number generators” in their threat model, but also state that if “[…] generated randomness is compromised or bad, Signal offers no protection”. Secure random numbers are the most common weakness. A compromised random number generator used widely even allows for bulk data collection and decryption[2].

In my mind this problem is relatively easy to avoid. For one, protocols can be modified to  not to leak raw output of the random number generator, which makes practical attacks on the rng much harder. For example, instead of sending a nonce consisting of raw rng output, which would give an eavesdropper information to determine the state of the rng, one could use the sha512 of the rng output. To ensure that this is correctly implemented the protocol participants can exchange the raw rng output later once secure communication has been established and ensure that indeed the nonce that was used was sha512(rng) and not raw rng output itself. For primitives that require random numbers for operation (e.g., signing) one can use the secure hash of the message and private-key for a unique, deterministic and secure random number (this is used by ed25519, IIRC). My point is that most of these problems seem avoidable and systems can be hardened to not completely fail even if the random number generator has been compromised.

The other point is that random numbers should be generated by the OS and incorporate as many different sources as possible. Linux, OpenBSD and other operating systems offer APIs that return secure random numbers collected from various sources of entropy in the system. The latest generation of x86 chips even has RNG instructions that generate secure random numbers (caveats: [3,4]). I think the more entropy from difference sources the better (caveat: [5]), and personally I think systems like HAVEGED can be helpful as an additional source of entropy. One counter argument that I heard was that nobody knows how good this cpu entropy really is, and that entropy extracted from hard-disk latency (and similar). However, for other sources of entropy we don’t know that either. The most sensible paper showing entropy extraction from disk drive latency[6] shows that technically only for certain drives, and I’m willing to wager that all of these results will look quite differently for modern SSD drives. As far as I know quantifying the goodness of entropy sources on computers is an open research problem. I think adding entropy from cpu sources like HAVEGED does is helpful, especially in situations like device startup and other situations where there’s not a lot of entropy available from other sources.


[1] Katriel Cohn-Gordon, Cas Cremers, Benjamin Dowling, Luke Garratt, and Douglas Stebila, “A Formal Security Analysis of the Signal Messaging Protocol”,

[2] Daniel J. Bernstein, Tanja Lange, Ruben Niederhagen. “Dual EC: a standardized back door.” Pages 256–281 in The new codebreakers: essays dedicated to David Kahn on the occasion of his 85th birthday, edited by Peter Y. A. Ryan, David Naccache, Jean-Jacques Quisquater. Lecture Notes in Computer Science 9100, Springer, 2015. ISBN 978-3-662-49300-7.


[4] Becker, CHES’13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems,Pages 197-214, DOI 10.1007/978-3-642-40349-1_12,


[6] D. Davis, R. Ihaka, and P. Fenstermacher, “Cryptographic Randomness from Air Turbulience in Disk Drives,” Advances in Cryptology — CRYPTO ’94 Proceedings, Springer-Verlag, 1994, pp. 114–120.

Machine Learning Newsticker

April 2nd, 2016

Shameless plug: I’ve fixed my scripts and my Machine Learning Newsticker (that reaches back to February 2005) is back in business. RSS Link Expect periodic updates on ML and AI related news items.


Chromebook Reboot Loop

December 2nd, 2014

My Chromebook (a Samsung XE500C21) ended up stuck in a reboot loop. Various keyboard shortcuts I found online didn’t work and I ended up having to wipe the disk and restore from a recovery image. Fortunately all data was in Google Drive anyways. I had to perform a Chromebook hard reset to get to the recovery screen. I wrote down the model number and then followed the recovery instructions for using a USB stick: Chromebook Recovery Image . I used the Linux based method. The tool found a suitable boot image, wrote it onto the designated USB stick. I did another hard reset and then inserted the USB stick with the image. The image installed itself without further intervention and after a reboot everything was fixed. All my settings, Chrome extensions etc. were synced to the machine after the first login. The only thing not synced was the wallpaper. Oh well…



Random Number Generation on low entropy computer systems

October 13th, 2014

Lately, I got interested in random number generation. Generating random numbers securely so they are suitable for cryptographic use is hard.

Linux introduced /dev/random, a block device to a random number generator in the kernel. The generator keeps an estimate of the number of bits of noise in the entropy pool. From this entropy pool, random numbers are created by using a secure hash function on the data in the pool . When read, the /dev/random device will only return random bytes within the estimated number of bits of noise in the entropy pool. The Operating System adds entropy from all sorts of sources, such as disk latency. However, if you are running Linux on an embedded device (or “internet of things”) or in a cloud instance, there may not be a “real” disk drive, and whatever latency is measured may not contain good enough entropy. Another important source of entropy is the clock-cycle timer (rdtsc) that is called at various instances to measure the time between interrupts and other frequently and somewhat randomly occurring events. The rdtsc instruction is often virtualized in cloud-machines which could make it harder to get good entropy.  Anyways… the problem of getting random numbers in low-entropy situations is important enough that Intel added an on-chip random number generator to their new processors (rdrand), but many cloud instances emulate older CPUs and embedded system don’t necessarily run with x86 chips that have rdrand.

So far, so good. For now, I don’t have an embedded system to experiment with, but a similar problem is with servers in the cloud. Can the rdtsc instruction still be used to get entropy in a virtual machine? I found this, played around a bit with the program listed and also learned about the existence of haveged (I’ll get back to that). I started a micro-instance (1 CPU, 512Mb RAM) in a popular cloud service and found that, yes indeed, the rdtsc instruction seems to be virtualized. The average tick count between millions of two consecutive rdtsc instructions is far too small to account for whatever else is going on on the machine (unless, of course, I somehow got a 512MB machine all by myself – which is unlikely). On the other hand, the output of the least significant bit of the difference of two consecutive rdtsc calls looked pretty random, but didn’t pass randomness tests. Adding von-Neumann whitening on the LSB obtained from two rdtsc calls is actually sufficiently random to pass FIPS 140-2 randomness tests (I used the implementation in rngtest) and only fails about 1 in 1000 (comparison: a test-run with entropy from /dev/random failed 1:10000). So in theory, this should be okay to use as an entropy source, but maybe it should still be combined with other sources of entropy.

Coming back to other already existing solutions. It turns out there’s an entropy gathering demon called haveged that can add entropy to the pool to remedy low-entropy conditions that can occur in servers, but possibly also on embedded devices and in cloud instance. The method exploits the modifications of the internal volatile hardware states as a source of uncertainty. Modern superscalar processors feature various hardware mechanisms which aim to improve performance: caches, branch predictors, TLBs and much more. The state of these components is also volatile and cannot be directly monitored in software. On the other hand, every invocation of the operating system modifies thousands of these binary volatile states. The general idea of extracting entropy from rdtsc still works, however the only thing that still makes me wonder a bit is that the full timer (not just the LSB) is used and that the whitening method is rather complex.

I learned a lot, but there’s still more to explore. Cloud machines probably have more going on than embedded systems, so I’m still not convinced that this will work on embedded devices. I’ll try to wrap my head around the whitening function in haveged. It’s still being developed and maybe ARM support will be added some day. Then the demon could be used on smart phones to improve the security of the random number generation.



Strengths and Weaknesses of various Clustering Algorithms

April 27th, 2014

Clustering is one of the most fascinating areas in the data mining field for me. For example, it can be shown that under some simple and fairly straightforward it is impossible to find a clustering function (Kleinberg’s impossibility theorem for clustering).That means that some trade-offs and relaxations have to be made in all the existing clustering algorithms. Every clustering algorithm will have a weakness and fail to cluster some data sets in a sensible manner.

The Fundamental Clustering Problem Suite (Ultsch, 2005) contains several synthetic data sets and a variety of clustering problems that algorithms should be able to solve. The data set contains the data and ground-truth labels as well as labels for k-Means, Single-Linkage, Wards-Linkage and a Self-Organizing map. I decided to play around with it a bit, converted the SOM activation matrix to labels using k-Means, added Spectral Clustering and Self-Tuning Spectral Clustering, and an EM Gaussian Mixture model. I was particularly curious how well Spectral Clustering would do. Determining the true number of clusters from the underlying data is an entirely different problem. Hence in all cases the number of clusters was specified unless otherwise noted. The regular Spectral Clustering used the Ng-Jordan-Weiss algorithm with a kernel sigma of 0.04 after linear scaling of the inputs. The Self-Tuning Spectral Clustering used k=15 nearest neighbors. I also used Random Forest’s “clustering”, an extension of the classification algorithm that will generate a distance matrix from the classification tree ensemble. The distance matrix was then used in single linkage to obtain cluster labels. Random Forest is a special case as it derives a distance matrix out of classification using gini – a metric built for classification, not clustering.


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Detecting Click Fraud in Online Advertising

March 2nd, 2014

JMLR has an interesting paper summarizing the results from a contest to build the best model for ClickFraud detection. The second place entry described some nice feature engineering that I found interesting. The first place did feature selection and then used gbm, a really good ensemble algorithm.


Big Data, Predictive Policing and the Tyranny/Anarchy Trade-Off

August 17th, 2013

Bloomberg had an interesting article today about a talk on the implications and privacy trade-offs of predictive policing and profiling. Jim Adler’s “felon classifier” is also described in his blog.

Basically, he built a classifier predicting from some innocuous (but possibly correlated variables) the likelihood of somebody having a felony offense. The classifier isn’t meant to be used in practice (from eye-balling the Precision/Recall curve in the talk slides, I estimate an AUC of about 0.6-ish; not too great), but it was built to start a discussion. It turns out that courts have upheld the use of profiling in some cases as “reasonable suspicion,” a legal standard for the police to stop somebody and investigate. This could lead to “predictive policing” being taken even further in the future. Due to the model outputting a score Jim also discusses the trade-off of where the prediction of such a model may be actionable – he calls it the Tyranny/Anarchy Trade-Off (a catchy name 🙂

Having done statistical work in criminal justice before, I think predictive analysis can be helpful in many areas of policing and criminal justice in general (e.g., parole supervision). On the other hand, I find profiling and supporting a “reasonable suspicion” from statistical models unconvincing. I think the courts will have to figure out a minimum reliability standard for such predictors, and hopefully they’ll set the threshold far higher than what the ‘felony classifier’ is producing. There’s just too many ways using a statistical model for “reasonable suspicion” to go wrong. Even if variables of protected classes (gender, ethnicity, etc.) are not used directly, there may be correlated variables (hair-color, income, geographic area) as discussed in the talk Jim gave. Even more problematic in my mind would be variables that do not or hardly ever change, as they would lead to the same people being hassled over and over again. Also the training data from which these models are built is biased since everybody in it by definition has been arrested before. It’s beyond me how one can correct for this sample bias in a reliable way. Frankly, I don’t think policing by profiling (statistical or otherwise) can be done well, and hopefully courts will recognize that eventually.


Removing AVG Secure Search from Chrome

May 11th, 2013

I use AVG as my anti-virus and today it installed the whole safe-search toolbar thing in the background while I was playing a video game. I’m pretty sure I didn’t consent to that, but whatever… Undoing the damage to my settings took quite a bit of work and I had trouble removing it from Chrome. First I followed all the steps outlined here, but pressing the home button in Chrome would still bring up the  “” website no matter what settings I changed.

Uninstalling the AVG toolbar component finally solved the Chrome start-page problem for me.

Man, what I piece of work. I’m not alone thinking that AVG did something bad for the user here.

On Statistical Significance Testing

March 26th, 2013

I found a good read about the fallacies of statistical significance testing. See also here.

Frequentist vs. Bayesian Inference

November 19th, 2012

I found a good article discussing the difference between the Frequentist and Bayesian approach to Inference.