Entries Tagged "cryptography"

Page 24 of 55

Massive MIMO Cryptosystem

New paper: “Physical-Layer Cryptography Through Massive MIMO.”

Abstract: We propose the new technique of physical-layer cryptography based on using a massive MIMO channel as a key between the sender and desired receiver, which need not be secret. The goal is for low-complexity encoding and decoding by the desired transmitter-receiver pair, whereas decoding by an eavesdropper is hard in terms of prohibitive complexity. The decoding complexity is analyzed by mapping the massive MIMO system to a lattice. We show that the eavesdropper’s decoder for the MIMO system with M-PAM modulation is equivalent to solving standard lattice problems that are conjectured to be of exponential complexity for both classical and quantum computers. Hence, under the widely-held conjecture that standard lattice problems are hard to solve in the worst-case, the proposed encryption scheme has a more robust notion of security than that of the most common encryption methods used today such as RSA and Diffie-Hellman. Additionally, we show that this scheme could be used to securely communicate without a pre-shared secret and little computational overhead. Thus, the massive MIMO system provides for low-complexity encryption commensurate with the most sophisticated forms of application-layer encryption by exploiting the physical layer properties of the radio channel.

MIMO stands for “multiple-input multiple-output.” I had to look that up.

In general, I’m not optimistic about the security of these sorts of systems. Whenever non-cryptographers come up with cryptographic algorithms based on some novel problem that’s hard in their area of research, invariably there are pretty easy cryptographic attacks.

So consider this a good research exercise for all budding cryptanalysts out there.

Posted on October 15, 2013 at 6:27 AM • View Comments

Insecurities in the Linux /dev/random

New paper: “Security Analysis of Pseudo-Random Number Generators with Input: /dev/random is not Robust, by Yevgeniy Dodis, David Pointcheval, Sylvain Ruhault, Damien Vergnaud, and Daniel Wichs.

Abstract: A pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. A formal security model for PRNGs with input was proposed in 2005 by Barak and Halevi (BH). This model involves an internal state that is refreshed with a (potentially biased) external random source, and a cryptographic function that outputs random numbers from the continually internal state. In this work we extend the BH model to also include a new security property capturing how it should accumulate the entropy of the input data into the internal state after state compromise. This property states that a good PRNG should be able to eventually recover from compromise even if the entropy is injected into the system at a very slow pace, and expresses the real-life expected behavior of existing PRNG designs. Unfortunately, we show that neither the model nor the specific PRNG construction proposed by Barak and Halevi meet this new property, despite meeting a weaker robustness notion introduced by BH. From a practical side, we also give a precise assessment of the security of the two Linux PRNGs, /dev/random and /dev/urandom. In particular, we show several attacks proving that these PRNGs are not robust according to our definition, and do not accumulate entropy properly. These attacks are due to the vulnerabilities of the entropy estimator and the internal mixing function of the Linux PRNGs. These attacks against the Linux PRNG show that it does not satisfy the “robustness” notion of security, but it remains unclear if these attacks lead to actual exploitable vulnerabilities in practice. Finally, we propose a simple and very efficient PRNG construction that is provably robust in our new and stronger adversarial model. We present benchmarks between this construction and the Linux PRNG that show that this construction is on average more efficient when recovering from a compromised internal state and when generating cryptographic keys. We therefore recommend to use this construction whenever a PRNG with input is used for cryptography.

Posted on October 14, 2013 at 1:06 PM • View Comments

Will Keccak = SHA-3?

Last year, NIST selected Keccak as the winner of the SHA-3 hash function competition. Yes, I would have rather my own Skein had won, but it was a good choice.

But last August, John Kelsey announced some changes to Keccak in a talk (slides 44-48 are relevant). Basically, the security levels were reduced and some internal changes to the algorithm were made, all in the name of software performance.

Normally, this wouldn’t be a big deal. But in light of the Snowden documents that reveal that the NSA has attempted to intentionally weaken cryptographic standards, this is a huge deal. There is too much mistrust in the air. NIST risks publishing an algorithm that no one will trust and no one (except those forced) will use.

At this point, they simply have to standardize on Keccak as submitted and as selected.

CDT has a great post about this.

Also this Slashdot thread.

EDITED TO ADD (10/5): It’s worth reading the response from the Keccak team on this issue.

I misspoke when I wrote that NIST made “internal changes” to the algorithm. That was sloppy of me. The Keccak permutation remains unchanged. What NIST proposed was reducing the hash function’s capacity in the name of performance. One of Keccak’s nice features is that it’s highly tunable.

I do not believe that the NIST changes were suggested by the NSA. Nor do I believe that the changes make the algorithm easier to break by the NSA. I believe NIST made the changes in good faith, and the result is a better security/performance trade-off. My problem with the changes isn’t cryptographic, it’s perceptual. There is so little trust in the NSA right now, and that mistrust is reflecting on NIST. I worry that the changed algorithm won’t be accepted by an understandably skeptical security community, and that no one will use SHA-3 as a result.

This is a lousy outcome. NIST has done a great job with cryptographic competitions: both a decade ago with AES and now with SHA-3. This is just another effect of the NSA’s actions draining the trust out of the Internet.

Posted on October 1, 2013 at 10:50 AM • View Comments

How to Remain Secure Against the NSA

Now that we have enough details about how the NSA eavesdrops on the Internet, including today’s disclosures of the NSA’s deliberate weakening of cryptographic systems, we can finally start to figure out how to protect ourselves.

For the past two weeks, I have been working with the Guardian on NSA stories, and have read hundreds of top-secret NSA documents provided by whistleblower Edward Snowden. I wasn’t part of today’s story—it was in process well before I showed up—but everything I read confirms what the Guardian is reporting.

At this point, I feel I can provide some advice for keeping secure against such an adversary.

The primary way the NSA eavesdrops on Internet communications is in the network. That’s where their capabilities best scale. They have invested in enormous programs to automatically collect and analyze network traffic. Anything that requires them to attack individual endpoint computers is significantly more costly and risky for them, and they will do those things carefully and sparingly.

Leveraging its secret agreements with telecommunications companies—all the US and UK ones, and many other “partners” around the world—the NSA gets access to the communications trunks that move Internet traffic. In cases where it doesn’t have that sort of friendly access, it does its best to surreptitiously monitor communications channels: tapping undersea cables, intercepting satellite communications, and so on.

That’s an enormous amount of data, and the NSA has equivalently enormous capabilities to quickly sift through it all, looking for interesting traffic. “Interesting” can be defined in many ways: by the source, the destination, the content, the individuals involved, and so on. This data is funneled into the vast NSA system for future analysis.

The NSA collects much more metadata about Internet traffic: who is talking to whom, when, how much, and by what mode of communication. Metadata is a lot easier to store and analyze than content. It can be extremely personal to the individual, and is enormously valuable intelligence.

The Systems Intelligence Directorate is in charge of data collection, and the resources it devotes to this is staggering. I read status report after status report about these programs, discussing capabilities, operational details, planned upgrades, and so on. Each individual problem—recovering electronic signals from fiber, keeping up with the terabyte streams as they go by, filtering out the interesting stuff—has its own group dedicated to solving it. Its reach is global.

The NSA also attacks network devices directly: routers, switches, firewalls, etc. Most of these devices have surveillance capabilities already built in; the trick is to surreptitiously turn them on. This is an especially fruitful avenue of attack; routers are updated less frequently, tend not to have security software installed on them, and are generally ignored as a vulnerability.

The NSA also devotes considerable resources to attacking endpoint computers. This kind of thing is done by its TAO—Tailored Access Operations—group. TAO has a menu of exploits it can serve up against your computer—whether you’re running Windows, Mac OS, Linux, iOS, or something else—and a variety of tricks to get them on to your computer. Your anti-virus software won’t detect them, and you’d have trouble finding them even if you knew where to look. These are hacker tools designed by hackers with an essentially unlimited budget. What I took away from reading the Snowden documents was that if the NSA wants in to your computer, it’s in. Period.

The NSA deals with any encrypted data it encounters more by subverting the underlying cryptography than by leveraging any secret mathematical breakthroughs. First, there’s a lot of bad cryptography out there. If it finds an Internet connection protected by MS-CHAP, for example, that’s easy to break and recover the key. It exploits poorly chosen user passwords, using the same dictionary attacks hackers use in the unclassified world.

As was revealed today, the NSA also works with security product vendors to ensure that commercial encryption products are broken in secret ways that only it knows about. We know this has happened historically: CryptoAG and Lotus Notes are the most public examples, and there is evidence of a back door in Windows. A few people have told me some recent stories about their experiences, and I plan to write about them soon. Basically, the NSA asks companies to subtly change their products in undetectable ways: making the random number generator less random, leaking the key somehow, adding a common exponent to a public-key exchange protocol, and so on. If the back door is discovered, it’s explained away as a mistake. And as we now know, the NSA has enjoyed enormous success from this program.

TAO also hacks into computers to recover long-term keys. So if you’re running a VPN that uses a complex shared secret to protect your data and the NSA decides it cares, it might try to steal that secret. This kind of thing is only done against high-value targets.

How do you communicate securely against such an adversary? Snowden said it in an online Q&A soon after he made his first document public: “Encryption works. Properly implemented strong crypto systems are one of the few things that you can rely on.”

I believe this is true, despite today’s revelations and tantalizing hints of “groundbreaking cryptanalytic capabilities” made by James Clapper, the director of national intelligence in another top-secret document. Those capabilities involve deliberately weakening the cryptography.

Snowden’s follow-on sentence is equally important: “Unfortunately, endpoint security is so terrifically weak that NSA can frequently find ways around it.”

Endpoint means the software you’re using, the computer you’re using it on, and the local network you’re using it in. If the NSA can modify the encryption algorithm or drop a Trojan on your computer, all the cryptography in the world doesn’t matter at all. If you want to remain secure against the NSA, you need to do your best to ensure that the encryption can operate unimpeded.

With all this in mind, I have five pieces of advice:

  1. Hide in the network. Implement hidden services. Use Tor to anonymize yourself. Yes, the NSA targets Tor users, but it’s work for them. The less obvious you are, the safer you are.
  2. Encrypt your communications. Use TLS. Use IPsec. Again, while it’s true that the NSA targets encrypted connections—and it may have explicit exploits against these protocols—you’re much better protected than if you communicate in the clear.
  3. Assume that while your computer can be compromised, it would take work and risk on the part of the NSA—so it probably isn’t. If you have something really important, use an air gap. Since I started working with the Snowden documents, I bought a new computer that has never been connected to the Internet. If I want to transfer a file, I encrypt the file on the secure computer and walk it over to my Internet computer, using a USB stick. To decrypt something, I reverse the process. This might not be bulletproof, but it’s pretty good.
  4. Be suspicious of commercial encryption software, especially from large vendors. My guess is that most encryption products from large US companies have NSA-friendly back doors, and many foreign ones probably do as well. It’s prudent to assume that foreign products also have foreign-installed backdoors. Closed-source software is easier for the NSA to backdoor than open-source software. Systems relying on master secrets are vulnerable to the NSA, through either legal or more clandestine means.
  5. Try to use public-domain encryption that has to be compatible with other implementations. For example, it’s harder for the NSA to backdoor TLS than BitLocker, because any vendor’s TLS has to be compatible with every other vendor’s TLS, while BitLocker only has to be compatible with itself, giving the NSA a lot more freedom to make changes. And because BitLocker is proprietary, it’s far less likely those changes will be discovered. Prefer symmetric cryptography over public-key cryptography. Prefer conventional discrete-log-based systems over elliptic-curve systems; the latter have constants that the NSA influences when they can.

Since I started working with Snowden’s documents, I have been using GPG, Silent Circle, Tails, OTR, TrueCrypt, BleachBit, and a few other things I’m not going to write about. There’s an undocumented encryption feature in my Password Safe program from the command line; I’ve been using that as well.

I understand that most of this is impossible for the typical Internet user. Even I don’t use all these tools for most everything I am working on. And I’m still primarily on Windows, unfortunately. Linux would be safer.

The NSA has turned the fabric of the Internet into a vast surveillance platform, but they are not magical. They’re limited by the same economic realities as the rest of us, and our best defense is to make surveillance of us as expensive as possible.

Trust the math. Encryption is your friend. Use it well, and do your best to ensure that nothing can compromise it. That’s how you can remain secure even in the face of the NSA.

This essay previously appeared in the Guardian.

EDITED TO ADD: Reddit thread.

Someone somewhere commented that the NSA’s “groundbreaking cryptanalytic capabilities” could include a practical attack on RC4. I don’t know one way or the other, but that’s a good speculation.

Posted on September 15, 2013 at 8:11 AM • View Comments

Ed Felten on the NSA Disclosures

Ed Felten has an excellent essay on the damage caused by the NSA secretly breaking the security of Internet systems:

In security, the worst case—the thing you most want to avoid—is thinking you are secure when you’re not. And that’s exactly what the NSA seems to be trying to perpetuate.

Suppose you’re driving a car that has no brakes. If you know you have no brakes, then you can drive very slowly, or just get out and walk. What is deadly is thinking you have the ability to stop, until you stomp on the brake pedal and nothing happens. It’s the same way with security: if you know your communications aren’t secure, you can be careful about what you say; but if you think mistakenly that you’re safe, you’re sure to get in trouble.

So the problem is not (only) that we’re unsafe. It’s that “the N.S.A. wants to keep it that way.” The NSA wants to make sure we remain vulnerable.

Posted on September 12, 2013 at 6:05 AM • View Comments

The NSA's Cryptographic Capabilities

The latest Snowden document is the US intelligence “black budget.” There’s a lot of information in the few pages the Washington Post decided to publish, including an introduction by Director of National Intelligence James Clapper. In it, he drops a tantalizing hint: “Also, we are investing in groundbreaking cryptanalytic capabilities to defeat adversarial cryptography and exploit internet traffic.”

Honestly, I’m skeptical. Whatever the NSA has up its top-secret sleeves, the mathematics of cryptography will still be the most secure part of any encryption system. I worry a lot more about poorly designed cryptographic products, software bugs, bad passwords, companies that collaborate with the NSA to leak all or part of the keys, and insecure computers and networks. Those are where the real vulnerabilities are, and where the NSA spends the bulk of its efforts.

This isn’t the first time we’ve heard this rumor. In a WIRED article last year, longtime NSA-watcher James Bamford wrote:

According to another top official also involved with the program, the NSA made an enormous breakthrough several years ago in its ability to cryptanalyze, or break, unfathomably complex encryption systems employed by not only governments around the world but also many average computer users in the US.

We have no further information from Clapper, Snowden, or this other source of Bamford’s. But we can speculate.

Perhaps the NSA has some new mathematics that breaks one or more of the popular encryption algorithms: AES, Twofish, Serpent, triple-DES, Serpent. It wouldn’t be the first time this happened. Back in the 1970s, the NSA knew of a cryptanalytic technique called “differential cryptanalysis” that was unknown in the academic world. That technique broke a variety of other academic and commercial algorithms that we all thought secure. We learned better in the early 1990s, and now design algorithms to be resistant to that technique.

It’s very probable that the NSA has newer techniques that remain undiscovered in academia. Even so, such techniques are unlikely to result in a practical attack that can break actual encrypted plaintext.

The naive way to break an encryption algorithm is to brute-force the key. The complexity of that attack is 2n, where n is the key length. All cryptanalytic attacks can be viewed as shortcuts to that method. And since the efficacy of a brute-force attack is a direct function of key length, these attacks effectively shorten the key. So if, for example, the best attack against DES has a complexity of 239, that effectively shortens DES’s 56-bit key by 17 bits.

That’s a really good attack, by the way.

Right now the upper practical limit on brute force is somewhere under 80 bits. However, using that as a guide gives us some indication as to how good an attack has to be to break any of the modern algorithms. These days, encryption algorithms have, at a minimum, 128-bit keys. That means any NSA cryptanalytic breakthrough has to reduce the effective key length by at least 48 bits in order to be practical.

There’s more, though. That DES attack requires an impractical 70 terabytes of known plaintext encrypted with the key we’re trying to break. Other mathematical attacks require similar amounts of data. In order to be effective in decrypting actual operational traffic, the NSA needs an attack that can be executed with the known plaintext in a common MS-Word header: much, much less.

So while the NSA certainly has symmetric cryptanalysis capabilities that we in the academic world do not, converting that into practical attacks on the sorts of data it is likely to encounter seems so impossible as to be fanciful.

More likely is that the NSA has some mathematical breakthrough that affects one or more public-key algorithms. There are a lot of mathematical tricks involved in public-key cryptanalysis, and absolutely no theory that provides any limits on how powerful those tricks can be.

Breakthroughs in factoring have occurred regularly over the past several decades, allowing us to break ever-larger public keys. Much of the public-key cryptography we use today involves elliptic curves, something that is even more ripe for mathematical breakthroughs. It is not unreasonable to assume that the NSA has some techniques in this area that we in the academic world do not. Certainly the fact that the NSA is pushing elliptic-curve cryptography is some indication that it can break them more easily.

If we think that’s the case, the fix is easy: increase the key lengths.

Assuming the hypothetical NSA breakthroughs don’t totally break public-cryptography—and that’s a very reasonable assumption—it’s pretty easy to stay a few steps ahead of the NSA by using ever-longer keys. We’re already trying to phase out 1024-bit RSA keys in favor of 2048-bit keys. Perhaps we need to jump even further ahead and consider 3072-bit keys. And maybe we should be even more paranoid about elliptic curves and use key lengths above 500 bits.

One last blue-sky possibility: a quantum computer. Quantum computers are still toys in the academic world, but have the theoretical ability to quickly break common public-key algorithms—regardless of key length—and to effectively halve the key length of any symmetric algorithm. I think it extraordinarily unlikely that the NSA has built a quantum computer capable of performing the magnitude of calculation necessary to do this, but it’s possible. The defense is easy, if annoying: stick with symmetric cryptography based on shared secrets, and use 256-bit keys.

There’s a saying inside the NSA: “Cryptanalysis always gets better. It never gets worse.” It’s naive to assume that, in 2013, we have discovered all the mathematical breakthroughs in cryptography that can ever be discovered. There’s a lot more out there, and there will be for centuries.

And the NSA is in a privileged position: It can make use of everything discovered and openly published by the academic world, as well as everything discovered by it in secret.

The NSA has a lot of people thinking about this problem full-time. According to the black budget summary, 35,000 people and $11 billion annually are part of the Department of Defense-wide Consolidated Cryptologic Program. Of that, 4 percent—or $440 million—goes to “Research and Technology.”

That’s an enormous amount of money; probably more than everyone else on the planet spends on cryptography research put together. I’m sure that results in a lot of interesting—and occasionally groundbreaking—cryptanalytic research results, maybe some of it even practical.

Still, I trust the mathematics.

This essay originally appeared on Wired.com.

EDITED TO ADD: That was written before I could talk about this.

EDITED TO ADD: The Economist expresses a similar sentiment.

Posted on September 6, 2013 at 6:30 AM • View Comments

The NSA Is Breaking Most Encryption on the Internet

The new Snowden revelations are explosive. Basically, the NSA is able to decrypt most of the Internet. They’re doing it primarily by cheating, not by mathematics.

It’s joint reporting between the Guardian, the New York Times, and ProPublica.

I have been working with Glenn Greenwald on the Snowden documents, and I have seen a lot of them. These are my two essays on today’s revelations.

Remember this: The math is good, but math has no agency. Code has agency, and the code has been subverted.

EDITED TO ADD (9/6): Someone somewhere commented that the NSA’s “groundbreaking cryptanalytic capabilities” could include a practical attack on RC4. I don’t know one way or the other, but that’s a good speculation.

EDITED TO ADD (9/6): Relevant Slashdot and Reddit threads.

EDITED TO ADD (9/13): An opposing view to my call to action.

Posted on September 5, 2013 at 2:46 PM • View Comments

1 … 22 23 24 25 26 … 55

Sidebar photo of Bruce Schneier by Joe MacInnis.