Decoding the Voynich Manuscript
The Voynich Manuscript has been partially decoded. This seems not to be a hoax. And the manuscript seems not to be a hoax, either.
Here’s the paper.
Entries Tagged "cryptanalysis"
Page 11 of 22
New Results in Software Obfuscation
Amit Sahai and others have some new results in software obfuscation. The papers are here. An over-the top Wired.com story on the research is here. And Matthew Green has a great blog post explaining what’s real and what’s hype.
NSA/GCHQ Accused of Hacking Belgian Cryptographer
There has been a lot of news about Belgian cryptographer Jean-Jacques Quisquater having his computer hacked, and whether the NSA or GCHQ is to blame. There have been a lot of assumptions and hyperbole, mostly related to the GCHQ attack against the Belgian telecom operator Belgacom.
I’m skeptical. Not about the attack, but about the NSA’s or GCHQ’s involvement. I don’t think there’s a lot of operational value in most academic cryptographic research, and Quisquater wasn’t involved in practical cryptanalysis of operational ciphers. I wouldn’t put it past a less-clued nation-state to spy on academic cryptographers, but it’s likelier this is a more conventional criminal attack. But who knows? Weirder things have happened.
Catalog of Snowden Revelations
This looks to be very good.
Add that to these three indexes of NSA source material, and these two summaries.
This excellent parody website has a good collection of all the leaks, too.
EDITED TO ADD (2/5): Another catalog site.
Acoustic Cryptanalysis
This is neat:
Here, we describe a new acoustic cryptanalysis key extraction attack, applicable to GnuPG’s current implementation of RSA. The attack can extract full 4096-bit RSA decryption keys from laptop computers (of various models), within an hour, using the sound generated by the computer during the decryption of some chosen ciphertexts. We experimentally demonstrate that such attacks can be carried out, using either a plain mobile phone placed next to the computer, or a more sensitive microphone placed 4 meters away.
Beyond acoustics, we demonstrate that a similar low-bandwidth attack can be performed by measuring the electric potential of a computer chassis. A suitably-equipped attacker need merely touch the target computer with his bare hand, or get the required leakage information from the ground wires at the remote end of VGA, USB or Ethernet cables.
Defending Against Crypto Backdoors
We already know the NSA wants to eavesdrop on the Internet. It has secret agreements with telcos to get direct access to bulk Internet traffic. It has massive systems like TUMULT, TURMOIL, and TURBULENCE to sift through it all. And it can identify ciphertext—encrypted information—and figure out which programs could have created it.
But what the NSA wants is to be able to read that encrypted information in as close to real-time as possible. It wants backdoors, just like the cybercriminals and less benevolent governments do.
And we have to figure out how to make it harder for them, or anyone else, to insert those backdoors.
How the NSA Gets Its Backdoors
The FBI tried to get backdoor access embedded in an AT&T secure telephone system in the mid-1990s. The Clipper Chip included something called a LEAF: a Law Enforcement Access Field. It was the key used to encrypt the phone conversation, itself encrypted in a special key known to the FBI, and it was transmitted along with the phone conversation. An FBI eavesdropper could intercept the LEAF and decrypt it, then use the data to eavesdrop on the phone call.
But the Clipper Chip faced severe backlash, and became defunct a few years after being announced.
Having lost that public battle, the NSA decided to get its backdoors through subterfuge: by asking nicely, pressuring, threatening, bribing, or mandating through secret order. The general name for this program is BULLRUN.
Defending against these attacks is difficult. We know from subliminal channel and kleptography research that it’s pretty much impossible to guarantee that a complex piece of software isn’t leaking secret information. We know from Ken Thompson’s famous talk on “trusting trust” (first delivered in the ACM Turing Award Lectures) that you can never be totally sure if there’s a security flaw in your software.
Since BULLRUN became public last month, the security community has been examining security flaws discovered over the past several years, looking for signs of deliberate tampering. The Debian random number flaw was probably not deliberate, but the 2003 Linux security vulnerability probably was. The DUAL_EC_DRBG random number generator may or may not have been a backdoor. The SSL 2.0 flaw was probably an honest mistake. The GSM A5/1 encryption algorithm was almost certainly deliberately weakened. All the common RSA moduli out there in the wild: we don’t know. Microsoft’s _NSAKEY looks like a smoking gun, but honestly, we don’t know.
How the NSA Designs Backdoors
While a separate program that sends our data to some IP address somewhere is certainly how any hacker—from the lowliest script kiddie up to the NSA—spies on our computers, it’s too labor-intensive to work in the general case.
For government eavesdroppers like the NSA, subtlety is critical. In particular, three characteristics are important:
- Low discoverability. The less the backdoor affects the normal operations of the program, the better. Ideally, it shouldn’t affect functionality at all. The smaller the backdoor is, the better. Ideally, it should just look like normal functional code. As a blatant example, an email encryption backdoor that appends a plaintext copy to the encrypted copy is much less desirable than a backdoor that reuses most of the key bits in a public IV (initialization vector).
- High deniability. If discovered, the backdoor should look like a mistake. It could be a single opcode change. Or maybe a “mistyped” constant. Or “accidentally” reusing a single-use key multiple times. This is the main reason I am skeptical about _NSAKEY as a deliberate backdoor, and why so many people don’t believe the DUAL_EC_DRBG backdoor is real: they’re both too obvious.
- Minimal conspiracy. The more people who know about the backdoor, the more likely the secret is to get out. So any good backdoor should be known to very few people. That’s why the recently described potential vulnerability in Intel’s random number generator worries me so much; one person could make this change during mask generation, and no one else would know.
These characteristics imply several things:
- A closed-source system is safer to subvert, because an open-source system comes with a greater risk of that subversion being discovered. On the other hand, a big open-source system with a lot of developers and sloppy version control is easier to subvert.
- If a software system only has to interoperate with itself, then it is easier to subvert. For example, a closed VPN encryption system only has to interoperate with other instances of that same proprietary system. This is easier to subvert than an industry-wide VPN standard that has to interoperate with equipment from other vendors.
- A commercial software system is easier to subvert, because the profit motive provides a strong incentive for the company to go along with the NSA’s requests.
- Protocols developed by large open standards bodies are harder to influence, because a lot of eyes are paying attention. Systems designed by closed standards bodies are easier to influence, especially if the people involved in the standards don’t really understand security.
- Systems that send seemingly random information in the clear are easier to subvert. One of the most effective ways of subverting a system is by leaking key information—recall the LEAF—and modifying random nonces or header information is the easiest way to do that.
Design Strategies for Defending against Backdoors
With these principles in mind, we can list design strategies. None of them is foolproof, but they are all useful. I’m sure there’s more; this list isn’t meant to be exhaustive, nor the final word on the topic. It’s simply a starting place for discussion. But it won’t work unless customers start demanding software with this sort of transparency.
- Vendors should make their encryption code public, including the protocol specifications. This will allow others to examine the code for vulnerabilities. It’s true we won’t know for sure if the code we’re seeing is the code that’s actually used in the application, but surreptitious substitution is hard to do, forces the company to outright lie, and increases the number of people required for the conspiracy to work.
- The community should create independent compatible versions of encryption systems, to verify they are operating properly. I envision companies paying for these independent versions, and universities accepting this sort of work as good practice for their students. And yes, I know this can be very hard in practice.
- There should be no master secrets. These are just too vulnerable.
- All random number generators should conform to published and accepted standards. Breaking the random number generator is the easiest difficult-to-detect method of subverting an encryption system. A corollary: we need better published and accepted RNG standards.
- Encryption protocols should be designed so as not to leak any random information. Nonces should be considered part of the key or public predictable counters if possible. Again, the goal is to make it harder to subtly leak key bits in this information.
This is a hard problem. We don’t have any technical controls that protect users from the authors of their software.
And the current state of software makes the problem even harder: Modern apps chatter endlessly on the Internet, providing noise and cover for covert communications. Feature bloat provides a greater “attack surface” for anyone wanting to install a backdoor.
In general, what we need is assurance: methodologies for ensuring that a piece of software does what it’s supposed to do and nothing more. Unfortunately, we’re terrible at this. Even worse, there’s not a lot of practical research in this area—and it’s hurting us badly right now.
Yes, we need legal prohibitions against the NSA trying to subvert authors and deliberately weaken cryptography. But this isn’t just about the NSA, and legal controls won’t protect against those who don’t follow the law and ignore international agreements. We need to make their job harder by increasing their risk of discovery. Against a risk-averse adversary, it might be good enough.
This essay previously appeared on Wired.com.
EDITED TO ADD: I am looking for other examples of known or plausible instances of intentional vulnerabilities for a paper I am writing on this topic. If you can think of an example, please post a description and reference in the comments below. Please explain why you think the vulnerability could be intentional. Thank you.
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.
Breaking Taiwan's Digital ID
There’s a serious random-number generation flaw in the cryptographic systems used to protect the Taiwanese digital ID. Article and paper.
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.
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.
Sidebar photo of Bruce Schneier by Joe MacInnis.