A Brief Survey of Physical Attacks on Cryptographic Hardware

Previously, the topic of side-channel attacks (SCA) was covered on this blog. These attacks are very popular, for they can be mounted using very cheap equipment and do not necessarily require high level of expertise. Hence, SCA are widely accessible and present a common danger. As a result, they are well researched, and various countermeasures have been developed. Still, they are just a small part of the stack of physical attacks. Figure 1. crudely depicts the this colorful “stack”. The one thing all physical attacks have in common is that it is assumed that the attacker must gain physical access to the target device, and attain it for a certain amount of time. In the remainder of this post, a brief survey of these attacks will be given. More detailed descriptions will be provided in a series of posts that will follow. 

Figure 1: Stack of Physical Attacks

Invasiveness

The first segregation is based on the “invasiveness”. Invasive attacks entail breach of target’s packaging, or its surrounding enclosure. This is often a very delicate process which often requires expensive equipment and a high level of expertise. Since the breach is destructive by nature, it can be easily detected by subsequent users — if the chip itself was not destroyed in the process that is. The goal of this breach is to gain access to internal state of a chip. Commonly attackers target on-chip busses or storage elements, which may contain sensitive intermediaries of cryptographic computations or keys themselves. Aforementioned enclosures are a privilege of expensive devices, often called Hardware Security Modules (HSMs). HSMs may cost tens of thousands of Euros, and are envisioned to provide secure computational environments at high speeds. Apart from restricting access to the chip using sturdy build and “tamper-proof” latches and locks, enclosures are frequently equipped with seals and coatings that are supposed to witness any foul play that may have taken place. Additionally, tamper detection measures may be built in, envisioned to void all sensitive information at the first glimpse of attacker’s activities. Hence, invading these juggernauts is commonly more expensive and time consuming. Unfortunately, market-share of HSMs compared to bare smart-cards and RFIDs is neighboring negligible, especially with the rise of the IoT.

On the contrary, non-invasive adversaries do not cause any structural damage to packaging nor enclosures. They interact with the target device using its existing interfaces, and mediums that require no mechanical interaction with the device. They are virtually free, but may require significant expertise of attackers.

Activeness

The second segregation is based on the “activeness” of the attacker. Active attacks entail induction of computational (logical) or structural changes in the target chip. When we talk about computational changes, a very common example are Fault Injection (FI) attacks. There are two phases to FI attacks: fault injection during the execution of the targeted algorithm, and the analysis based on the observations of faulty outputs. A common method for altering device’s execution is called clock glitching. Namely, by introducing a premature edge on the clock signal, attacker violates devices’s critical path. As a result, incorrect values are captured in device’s registers. Alternatively, faults can be induced by shooting a laser beam with enough power to change the state of the device, while allowing it to remain operational. Here, any data or control register fall under “state of the device”. For example, round counter, commonly used in implementations of block ciphers, is a very favored target for such faults. Active attacks may require higher level of technical skill, and a more sophisticated setup.

On the contrary, passive adversaries may only observe device’s execution, while interacting through its predefined interfaces. Well-known SCA fall under this category. These attacks are well researched, and can be mounted using very cheap equipment. Developed techniques (e.g., Mutual Information Analysis) are extremely powerful, and once incorporated in the attackers setup can be reproduced quite trivially. Consequently, although they entail only limited exposure of the device, they pose a serious threat for they are very accessible even to attackers with modest capabilities.

The Reality

Activeness and invasiveness are two orthogonal properties, resulting in a total of four possibilities (although I find that the existence of “invasive and passive attacks” calls for a philosophical debate). Unfortunately, situation is much more complex than that in practice. Firstly, attackers are likely to use combined attacks. For example, FI + SCA may be a very powerful combination. Additionally, the distinction mentioned above is not as binary. Rather, along each of the two orthogonal axes there are many shades. For example, faults can be injected in some chips by applying laser beams to their packaging (non-invasive), while others may be shielded from such beams (hence they have to be attacked invasively).

Consequently, there exists a myriad of possible attack variations. Moreover, even if we lock on a certain extreme — let us say passive, non-invasive, CPA — quality of the measurement setup plays a very significant role. A 500 Euro oscilloscope can hardly match its 30000 Euro counterpart. In hindsight, there are no upper bounds to the power of a skilled invasive attacker performing a battery of active and passive attacks, apart from the temporal and financial constraints.

Taking all above into account, choosing a set of countermeasures is a difficult task (let alone implementing them properly). Bare in mind that these countermeasures are not for free. They may significantly increase the price of devices, reducing the profit margins severely. Therefore, there are no silver bullets in protection against physical attacks. In other words, in practice security engineers work to demotivate attackers with high probability. They try to stop “the attacker of interest”, rather then stopping all attacks. To achieve this, first step is identifying potential attackers. This process is often called profiling, and in a nutshell I would describe it as follows. Please note that this is a gross simplification of the problem, meant to depict the general idea. No distinction is made between fixed (price of the setup) and recurring (every time the attack is mounted) costs, nor between temporal and financial costs. Lastly, please note that the value of assets is heavily simplified as well, for the sake of avoiding a philosophical discussion yet again.

Manufacturer’s Dilemma

Assume that a device D, which costs d to manufacture, protects assets worth x , and features a
countermeasure C that costs c to deploy. We may consider D to be secure against an attacker A, who can mount a successful attack at a cost a (which includes A’s investment in
development of expertise), as long as

x ≤a+μA,

μA being the attackers profit margin. In other words, if the cost a is high enough attacker can not obtain desired amount of profit for given assets. On the other hand a manufacturer M that produces D wants to sell for a price m such that

m ≥ d + c + μM,

μ M being M’s profit margin. In other words, price of deploying countermeasures c directly cuts into manufacturer’s profits. Looking at these inequalities, it seems that there is no dilemma at all. Nevertheless, cost of attack depends on the selection of a countermeasure, i.e.,

a =f(c).

Assuming that an increase in c leads to the increase in a , by applying some high school math (readers are welcome to play with it), we see that the selection of C must be performed based on the value of assets it protects. A more detailed discussion on this topic will be given in one of the following posts.
In conclusion, physical attacks are a great threat. As IoT progresses, and the amount of ubiquitous devices increases their potential impact may only grow. Deploying devices that protect assets against physical attacks is a complex problem, which demands bespoke solutions, tailored to individual use cases. 

Algorithm and Key Size Document

The ECRYPT Algorithm and Key Size document is probably the most high impact output from our ECRYPT projects. It is referenced and used throughout the world, to guide the uses of cryptography in practice. The current version of the document can be found here

Algorithms, Key Size and Protocols Report (2016)

We are requesting input for the next edition of this document. To do this we have created a Slack channel where people can debate inputs.

We encourage everyone to get involved by sending us your email so we can add you. Once added you can add other people to the channel as you see fit. Please email Nigel Smart or Saartje Verheyen to be added if you do not know someone who is already involved.

We ask you to add comments to the slack channel of corrections and new text to add (including where you think it should go). After you have presented some input, other people can then comment on your text, and add further corrections. 

At the end of September we will freeze the discussion and start the process of incorporating all the suggestions into the final document. 

If you have contributed to the Slack discussion in a positive manner we will include you as an author on the final document as a contributor. That way you get to claim you have contributed to a high impact document (carrot); if you do not contribute however then you cannot complain if we say something you disagree with (stick). 

Of course in the end it is a community effort, and in case of disagreement the editors will need to take one side or another.

Boomerang Attacks

In cryptography, a boomerang attack is a method of cryptanalysis that is based on differential cryptanalysis.

Boomerang attacks were first introduced by Wagner and allow an adversary to concatenate two high probability differential trails to attack a cipher. This is especially useful if there is a lack of long differentials with sufficient probabilities. The adversary can therefore decompose the encryption function $F$ in two subciphers $f$ and $g$ such that $F = f \circ g$. Then the adversary can search for high probability trails $\Delta \rightarrow \Delta^*$ with probability $p$ for  $f$ and  $\nabla \rightarrow \nabla^*$ with probability $q$ for $g$. The differential trails can then be combined in a chosen plaintext/adaptive chosen ciphertext attack to mount a boomerang distinguisher and then a key recovery attack based on this distinguisher to recover the secret key.

A boomerang distinguisher

The basic attack works as follows:

1. The adversary chooses a random plaintext $X_1$ and calculates $X_2 = X_1 \oplus \Delta$.
2. The adversary requests the ciphertexts for $X_1$ and $X_2$ from an encryption oracle which are $Y_1 = F(X_1)$ and $Y_2 = F(X_2)$
3. Calculate ciphertexts $Y_3 = Y_1 \oplus \nabla$ and $Y_4 = Y_2 \oplus \nabla$.
4. Request the decryptions of $Y_3$ and $Y_4$ to obtain $X_3 = F^{-1}(Y_3)$ and $X_4 = F^{-1}(Y_4)$.
5. If the difference between $X_3$ and $X_4$ is the same as between $X_1$ and $X_2$, namely $\Delta$ we obtain a correct quartett $(X_1, X_2, X_3, X_4)$.

Calculating a correct quartet requires an attacker to consider both plaintext pairs $(X_1, X_2)$ and $(X_3, X_4)$ and results in a total probability of (pq)^2.
For an attack to succeed, for the probability of the boomerang distinguisher it must hold that $(pq) > 2^{n/2}$. For N plaintext pairs, an adversary expects about $N\cdot(pq)^2$ correct quartets in an attack, while there are only $N\cdot2^{-n}$ (where n is the blocksize) correct quartets for an ideal primitive.

Yet Another "Ni Hao (Hello)"

Hello, everyone. I am Junwei Wang from China. It’s pleasant to be an ECRYPT-NET fellow and to receive funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie actions (MSCA).

I received my bachelor degree and master degree from Shandong University in 2012 and the University of Luxembourg in 2015, respectively. My master thesis is about the practical implementation of countermeasures resistant again high-order differential power analysis (DPA). Presently, I am doing my Ph.D. student at CryptoExperts under the supervisor of Jean-Sébastien CORON, Sihem MESNAGER, Pascal PAILLIER, and Matthieu RIVAIN.  My research interest is white-box cryptography.

The advent of content-protected applications and mobile payment systems in recent years motivates the exploration of a solution to protect sensitive information from being extracted under the white-box context in which the attacker has the power of control the whole process of the execution of software. Though some theoretical evidence reveals the fact that no generic obfuscator can be constructed to shield algorithms to be attacked, and all existed practical schemes has been broken, it is still interesting to investigate new schemes which can withstand all the existing attacks, and to propose and analyse a new attacking method which is more generic than the existing ones. I hope somebody has similar interest with me, then we can deeply explore this area together.

By the way, I am looking forward to meeting with you in Paris during EUROCRYPT.

What does privacy mean to you? A 5-day challenge

I recently came across The Privacy Paradox project, a call by WNYC Studios to take part in a five-day-long challenge on defining what does privacy mean to yourself.

Amongst its best features, the process can be started anytime, by anyone, just by registering with an e-mail account. From that moment and during the five following days, you will receive a daily e-mail explaining you the topic addressed by that day's podcast, most of them finishing with an easy demand to the listener to reflect on the matter.

With the audio's length ranging from 11 to 15 minutes, and the topics from cryptography --with Bruce Schneier starring on the first episode-- to psychology, there is something on it for everyone, and at a very accessible level. I personally found the format very nice and entertaining, and it is maybe something to learn about when we talk about privacy with people not so interested in the topic.

Finally, the people behind the project also gathered a nice list with things you can do to face the current privacy situation.

https://project.wnyc.org/privacy-paradox/

Robust encryption for symmetric primitives

Robustness for encryption schemes has been introduced in the context of public-key encryption in the work of Abdalla, Bellare and Neven. In a nutshell, it states that a ciphertext cannot be decrypted under two different keys. Later, their work has been extended, by taking into account the cases where the keys are adversarially generated.
The work of Farshim, Orlandi and Roşie studies the robustness in the context of symmetric primitives under the incorrect usage of keys. Roughly speaking, a  key-robust scheme does not output ciphertexts/tags that are valid with respect to distinct keys. Key-robustness is a notion that is often tacitly expected/assumed in protocol design --- as is the case with anonymous auction, oblivious transfer, or public-key encryption.

To motivate the new notion, "consider the following protocol, for constructing a ${3 \choose 2}$-OT protocol using only ${3 \choose 1}$-OTs: the sender picks $3$ random keys $k_1,k_2,k_3$ and inputs the message $x_1=(k_2,k_3),x_2=(k_1,k_3)$ and $x_3=(k_1,k_2)$ to the OT. At the same time, the sender sends encryptions of his messages under these keys, i.e., sends $c_i=E(k_i,m_i)$ for $i=1..3$. Now the receiver inputs the index of the message he does not want to learn to the ${3 \choose 1}$-OT and learns all keys except $k_i$. Intuitively the fact that the messages are sent only once (encrypted) should guarantee that the sender's choice of messages is uniquely defined. However, consider the following attack: the corrupt sender inputs $x^*_1=(k_2, k^*)$ (instead of $x_1$) such that $D(k^*,c_3)=m^*_3$ with $m^*_3\neq m_3$ and $m^*_3\neq \bot$. This means that the receiver will see two different versions of $m_3$ depending on whether the receiver asked for the pair $(2,3)$ or $(1,3)$. (This attack is an example of input-dependence and is a clear breach of security since it cannot be simulated in the ideal world)."
In terms of the results, the new work considers "both notions where the adversary has control over the keys and notions where the keys are generated honestly. The strongest notion that is formulated is called complete robustness and allows an adversary to generate the keys used in the system. The work shows that whether the adversary is in control of the keys or not makes a significant difference, by giving separations between the notions. While previous work in the public-key setting also had to deal with adversarially generated keys that were also invalid, this is not an issue in the setting, since in the symmetric world keys are often bit-strings of some pre-specified length and can be easily checked for validity. By focusing on correctly formed keys it can can shown equivalence between  complete robustness and a syntactically simpler notion, which we call full robustness." Then, it is shown that full robustness composes well: any fully robust symmetric encryption when combined with a fully robust MAC results in a fully robust AE scheme. Analogous composition results also hold for MAC-then-Encrypt and Encrypt-and-MAC.

One of the most interesting question is if "feasibility results for robustness in the public-key setting can be translated to the symmetric setting. This turns out not to be the case. The main reason for this is that in the asymmetric setting the public key can be used as a mechanism to commit to its associated secret key. In the symmetric case, on the other hand, there is no such public information. It might be tempting to think that one can just commit to the secret key and append it to the ciphertext. Unfortunately this approach cannot be proven secure due to a circular key-dependency between the encryption and the commitment components. To give a provably secure construction, with the authors constructing appropriate commitments that can be used in this setting. This requires  a right-injective PRG, that can be in turn based on one-way permutations. This result relies on the one-time security of the MAC and its collision-resistance, which once again is based on right-injective PRGs."

Three everyday git scenarios

You may remember Ralph's post on git basics from a little over a year ago. In this post, I'll share three things I've learned are possible (and practically painless) to do with git that go beyond the basic add, merge, push, and pull. Everything in this post is done from the command line.

Scenario 1

You're working on a project with others. These hardworking colleagues of yours just pushed a bunch of commits and you want to see exactly what they changed since your last commit.

What to do

Use git diff. Besides using it to show unstaged changes, you can also use git diff to show changes between any two commits. Suppose that after your last commit, your colleagues made 4 commits. To see the changes, use git diff HEAD~4 HEAD or git diff HEAD^^^^ HEAD. If you don't want to count how many commits there were, you can look up the abbreviated commit IDs (SHA-1 hashes in hex) using git log --oneline. Then, you could use something like git diff 54180a8 129ec44.

There's a lot more to git diff: you can use it to compare specific files, you can show differences at the word level rather than at the line level, etc. If you want to learn more about it, see its page on the git website. If you're working on LaTeX files, git-latexdiff is convenient: given any two commits, it will produce a PDF file showing the changes, with removed text striked through and in red, and added text underlined and in blue.

Scenario 2

You were in the zone, hacking away at multiple issues and successfully completing all of them. Well done, you! Wait—each issue should have its own commit...

What to do

Use interactive staging: use git add -p or git add --patch to add the file or files. Git will look at each file you want to add and split the changes into hunks. For each hunk, it will show you the diff and ask you what to do with it:

Stage this hunk [y,n,q,a,d,/,s,e,?]?

Here is the full list of options. They're pretty easy to remember, especially if you're a vi user who is used to navigating with HJKL.

y - stage this hunk
n - do not stage this hunk
q - do not stage this hunk or any of the remaining ones
a - stage this hunk and all later hunks in the file
d - do not stage this hunk or any of the later hunks in the file
g - select a hunk to go to
/ - search for a hunk matching the given regex
j - leave this hunk undecided, see next undecided hunk
J - leave this hunk undecided, see next hunk
k - leave this hunk undecided, see previous undecided hunk
K - leave this hunk undecided, see previous hunk
s - split the current hunk into smaller hunks
e - manually edit the current hunk
? - print help

git add -p is a powerful command that helps you keep your commits reasonably sized. It does require some care, though, since each individual commit should be consistent.

Scenario 3

You have to stop working, but you haven't finished fixing the issue you're working on.

What to do

You should do something because you don't want to have a dirty working directory.

Option 1: commit now, then use git commit --amend (introduced in Ralph's post) once you've finished what you were working on. git commit --amend is useful for a bunch of other things, like adding files you forgot to stage to a commit and fixing typos in a commit message.

Commits are local, so what should you do if you're worried about hardware failure? If you're working on a personal project, it may be acceptable to push this commit and later push the amended commit. You'll need the -f (--force) flag for the latter push. If you're working on a project with others, however, it would be bad practice to amend a commit that you've already pushed. Instead, you could create a temporary personal branch, commit your changes to this branch, and push it to the remote repository. Then, you could push the amended commit to this branch without worrying about rewriting anyone else's history and merge it with the main branch when you've finished fixing the issue.

Option 2: shelve your changes with git stash, which will sweep away both staged and unstaged changes, leaving you with a clean working directory. You can stash changes more than once. To see all stashes, use git stash list. To re-apply the most recent stash you made, use git stash pop. By default, git stash excludes new files (that haven't yet been staged) and ignored files. git stash is also useful when you want to see upstream changes made by someone else, but aren't ready to commit your work.

There's much more you can do with stashes: apply one stash to multiple branches, delete stashes you no longer need, stash parts of a file, etc. Stashes are always local; they can never be pushed to a remote repository. Atlassian has a good, detailed tutorial on git stash.

Some books you may (or may not) find useful.