More on the Five Eyes Statement on Encryption and Backdoors

Earlier this month, I wrote about a statement by the Five Eyes countries about encryption and back doors. (Short summary: they like them.) One of the weird things about the statement is that it was clearly written from a law-enforcement perspective, though we normally think of the Five Eyes as a consortium of intelligence agencies. Susan Landau examines the details…

Earlier this month, I wrote about a statement by the Five Eyes countries about encryption and back doors. (Short summary: they like them.) One of the weird things about the statement is that it was clearly written from a law-enforcement perspective, though we normally think of the Five Eyes as a consortium of intelligence agencies.

Susan Landau examines the details of the statement, explains what's going on, and why the statement is a lot less than what it might seem.

from https://www.schneier.com/blog/

Evidence for the Security of PKCS #1 Digital Signatures

This is interesting research: "On the Security of the PKCS#1 v1.5 Signature Scheme": Abstract: The RSA PKCS#1 v1.5 signature algorithm is the most widely used digital signature scheme in practice. Its two main strengths are its extreme simplicity, which makes it very easy to implement, and that verification of signatures is significantly faster than for DSA or ECDSA. Despite the…

This is interesting research: "On the Security of the PKCS#1 v1.5 Signature Scheme":

Abstract: The RSA PKCS#1 v1.5 signature algorithm is the most widely used digital signature scheme in practice. Its two main strengths are its extreme simplicity, which makes it very easy to implement, and that verification of signatures is significantly faster than for DSA or ECDSA. Despite the huge practical importance of RSA PKCS#1 v1.5 signatures, providing formal evidence for their security based on plausible cryptographic hardness assumptions has turned out to be very difficult. Therefore the most recent version of PKCS#1 (RFC 8017) even recommends a replacement the more complex and less efficient scheme RSA-PSS, as it is provably secure and therefore considered more robust. The main obstacle is that RSA PKCS#1 v1.5 signatures use a deterministic padding scheme, which makes standard proof techniques not applicable.

We introduce a new technique that enables the first security proof for RSA-PKCS#1 v1.5 signatures. We prove full existential unforgeability against adaptive chosen-message attacks (EUF-CMA) under the standard RSA assumption. Furthermore, we give a tight proof under the Phi-Hiding assumption. These proofs are in the random oracle model and the parameters deviate slightly from the standard use, because we require a larger output length of the hash function. However, we also show how RSA-PKCS#1 v1.5 signatures can be instantiated in practice such that our security proofs apply.

In order to draw a more complete picture of the precise security of RSA PKCS#1 v1.5 signatures, we also give security proofs in the standard model, but with respect to weaker attacker models (key-only attacks) and based on known complexity assumptions. The main conclusion of our work is that from a provable security perspective RSA PKCS#1 v1.5 can be safely used, if the output length of the hash function is chosen appropriately.

I don't think the protocol is "provably secure," meaning that it cannot have any vulnerabilities. What this paper demonstrates is that there are no vulnerabilities under the model of the proof. And, more importantly, that PKCS #1 v1.5 is as secure as any of its successors like RSA-PSS and RSA Full-Domain.

from https://www.schneier.com/blog/

New Findings About Prime Number Distribution Almost Certainly Irrelevant to Cryptography

Lots of people are e-mailing me about this new result on the distribution of prime numbers. While interesting, it has nothing to do with cryptography. Cryptographers aren’t interested in how to find prime numbers, or even in the distribution of prime numbers. Public-key cryptography algorithms like RSA get their security from the difficulty of factoring large composite numbers that are…

Lots of people are e-mailing me about this new result on the distribution of prime numbers. While interesting, it has nothing to do with cryptography. Cryptographers aren't interested in how to find prime numbers, or even in the distribution of prime numbers. Public-key cryptography algorithms like RSA get their security from the difficulty of factoring large composite numbers that are the product of two prime numbers. That's completely different.

from https://www.schneier.com/blog/

Quantum Computing and Cryptography

Quantum computing is a new way of computing — one that could allow humankind to perform computations that are simply impossible using today’s computing technologies. It allows for very fast searching, something that would break some of the encryption algorithms we use today. And it allows us to easily factor large numbers, something that would break the RSA cryptosystem for…

Quantum computing is a new way of computing -- one that could allow humankind to perform computations that are simply impossible using today's computing technologies. It allows for very fast searching, something that would break some of the encryption algorithms we use today. And it allows us to easily factor large numbers, something that would break the RSA cryptosystem for any key length.

This is why cryptographers are hard at work designing and analyzing "quantum-resistant" public-key algorithms. Currently, quantum computing is too nascent for cryptographers to be sure of what is secure and what isn't. But even assuming aliens have developed the technology to its full potential, quantum computing doesn't spell the end of the world for cryptography. Symmetric cryptography is easy to make quantum-resistant, and we're working on quantum-resistant public-key algorithms. If public-key cryptography ends up being a temporary anomaly based on our mathematical knowledge and computational ability, we'll still survive. And if some inconceivable alien technology can break all of cryptography, we still can have secrecy based on information theory -- albeit with significant loss of capability.

At its core, cryptography relies on the mathematical quirk that some things are easier to do than to undo. Just as it's easier to smash a plate than to glue all the pieces back together, it's much easier to multiply two prime numbers together to obtain one large number than it is to factor that large number back into two prime numbers. Asymmetries of this kind -- one-way functions and trap-door one-way functions -- underlie all of cryptography.

To encrypt a message, we combine it with a key to form ciphertext. Without the key, reversing the process is more difficult. Not just a little more difficult, but astronomically more difficult. Modern encryption algorithms are so fast that they can secure your entire hard drive without any noticeable slowdown, but that encryption can't be broken before the heat death of the universe.

With symmetric cryptography -- the kind used to encrypt messages, files, and drives -- that imbalance is exponential, and is amplified as the keys get larger. Adding one bit of key increases the complexity of encryption by less than a percent (I'm hand-waving here) but doubles the cost to break. So a 256-bit key might seem only twice as complex as a 128-bit key, but (with our current knowledge of mathematics) it's 340,282,366,920,938,463,463,374,607,431,768,211,456 times harder to break.

Public-key encryption (used primarily for key exchange) and digital signatures are more complicated. Because they rely on hard mathematical problems like factoring, there are more potential tricks to reverse them. So you'll see key lengths of 2,048 bits for RSA, and 384 bits for algorithms based on elliptic curves. Here again, though, the costs to reverse the algorithms with these key lengths are beyond the current reach of humankind.

This one-wayness is based on our mathematical knowledge. When you hear about a cryptographer "breaking" an algorithm, what happened is that they've found a new trick that makes reversing easier. Cryptographers discover new tricks all the time, which is why we tend to use key lengths that are longer than strictly necessary. This is true for both symmetric and public-key algorithms; we're trying to future-proof them.

Quantum computers promise to upend a lot of this. Because of the way they work, they excel at the sorts of computations necessary to reverse these one-way functions. For symmetric cryptography, this isn't too bad. Grover's algorithm shows that a quantum computer speeds up these attacks to effectively halve the key length. This would mean that a 256-bit key is as strong against a quantum computer as a 128-bit key is against a conventional computer; both are secure for the foreseeable future.

For public-key cryptography, the results are more dire. Shor's algorithm can easily break all of the commonly used public-key algorithms based on both factoring and the discrete logarithm problem. Doubling the key length increases the difficulty to break by a factor of eight. That's not enough of a sustainable edge.

There are a lot of caveats to those two paragraphs, the biggest of which is that quantum computers capable of doing anything like this don't currently exist, and no one knows when -- or even if ­- we'll be able to build one. We also don't know what sorts of practical difficulties will arise when we try to implement Grover's or Shor's algorithms for anything but toy key sizes. (Error correction on a quantum computer could easily be an unsurmountable problem.) On the other hand, we don't know what other techniques will be discovered once people start working with actual quantum computers. My bet is that we will overcome the engineering challenges, and that there will be many advances and new techniques­but they're going to take time to discover and invent. Just as it took decades for us to get supercomputers in our pockets, it will take decades to work through all the engineering problems necessary to build large-enough quantum computers.

In the short term, cryptographers are putting considerable effort into designing and analyzing quantum-resistant algorithms, and those are likely to remain secure for decades. This is a necessarily slow process, as both good cryptanalysis transitioning standards take time. Luckily, we have time. Practical quantum computing seems to always remain "ten years in the future," which means no one has any idea.

After that, though, there is always the possibility that those algorithms will fall to aliens with better quantum techniques. I am less worried about symmetric cryptography, where Grover's algorithm is basically an upper limit on quantum improvements, than I am about public-key algorithms based on number theory, which feel more fragile. It's possible that quantum computers will someday break all of them, even those that today are quantum resistant.

If that happens, we will face a world without strong public-key cryptography. That would be a huge blow to security and would break a lot of stuff we currently do, but we could adapt. In the 1980s, Kerberos was an all-symmetric authentication and encryption system. More recently, the GSM cellular standard does both authentication and key distribution -- at scale -- with only symmetric cryptography. Yes, those systems have centralized points of trust and failure, but it's possible to design other systems that use both secret splitting and secret sharing to minimize that risk. (Imagine that a pair of communicants get a piece of their session key from each of five different key servers.) The ubiquity of communications also makes things easier today. We can use out-of-band protocols where, for example, your phone helps you create a key for your computer. We can use in-person registration for added security, maybe at the store where you buy your smartphone or initialize your Internet service. Advances in hardware may also help to secure keys in this world. I'm not trying to design anything here, only to point out that there are many design possibilities. We know that cryptography is all about trust, and we have a lot more techniques to manage trust than we did in the early years of the Internet. Some important properties like forward secrecy will be blunted and far more complex, but as long as symmetric cryptography still works, we'll still have security.

It's a weird future. Maybe the whole idea of number theory­-based encryption, which is what our modern public-key systems are, is a temporary detour based on our incomplete model of computing. Now that our model has expanded to include quantum computing, we might end up back to where we were in the late 1970s and early 1980s: symmetric cryptography, code-based cryptography, Merkle hash signatures. That would be both amusing and ironic.

Yes, I know that quantum key distribution is a potential replacement for public-key cryptography. But come on -- does anyone expect a system that requires specialized communications hardware and cables to be useful for anything but niche applications? The future is mobile, always-on, embedded computing devices. Any security for those will necessarily be software only.

There's one more future scenario to consider, one that doesn't require a quantum computer. While there are several mathematical theories that underpin the one-wayness we use in cryptography, proving the validity of those theories is in fact one of the great open problems in computer science. Just as it is possible for a smart cryptographer to find a new trick that makes it easier to break a particular algorithm, we might imagine aliens with sufficient mathematical theory to break all encryption algorithms. To us, today, this is ridiculous. Public- key cryptography is all number theory, and potentially vulnerable to more mathematically inclined aliens. Symmetric cryptography is so much nonlinear muddle, so easy to make more complex, and so easy to increase key length, that this future is unimaginable. Consider an AES variant with a 512-bit block and key size, and 128 rounds. Unless mathematics is fundamentally different than our current understanding, that'll be secure until computers are made of something other than matter and occupy something other than space.

But if the unimaginable happens, that would leave us with cryptography based solely on information theory: one-time pads and their variants. This would be a huge blow to security. One-time pads might be theoretically secure, but in practical terms they are unusable for anything other than specialized niche applications. Today, only crackpots try to build general-use systems based on one-time pads -- and cryptographers laugh at them, because they replace algorithm design problems (easy) with key management and physical security problems (much, much harder). In our alien-ridden science-fiction future, we might have nothing else.

Against these godlike aliens, cryptography will be the only technology we can be sure of. Our nukes might refuse to detonate and our fighter jets might fall out of the sky, but we will still be able to communicate securely using one-time pads. There's an optimism in that.

This essay originally appeared in IEEE Security and Privacy.

from https://www.schneier.com/blog/

GCHQ on Quantum Key Distribution

The UK’s GCHQ delivers a brutally blunt assessment of quantum key distribution: QKD protocols address only the problem of agreeing keys for encrypting data. Ubiquitous on-demand modern services (such as verifying identities and data integrity, establishing network sessions, providing access control, and automatic software updates) rely more on authentication and integrity mechanisms — such as digital signatures — than on…

The UK's GCHQ delivers a brutally blunt assessment of quantum key distribution:

QKD protocols address only the problem of agreeing keys for encrypting data. Ubiquitous on-demand modern services (such as verifying identities and data integrity, establishing network sessions, providing access control, and automatic software updates) rely more on authentication and integrity mechanisms -- such as digital signatures -- than on encryption.

QKD technology cannot replace the flexible authentication mechanisms provided by contemporary public key signatures. QKD also seems unsuitable for some of the grand future challenges such as securing the Internet of Things (IoT), big data, social media, or cloud applications.

I agree with them. It's a clever idea, but basically useless in practice. I don't even think it's anything more than a niche solution in a world where quantum computers have broken our traditional public-key algorithms.

Read the whole thing. It's short.

from https://www.schneier.com/blog/

Major Bluetooth Vulnerability

Bluetooth has a serious security vulnerability: In some implementations, the elliptic curve parameters are not all validated by the cryptographic algorithm implementation, which may allow a remote attacker within wireless range to inject an invalid public key to determine the session key with high probability. Such an attacker can then passively intercept and decrypt all device messages, and/or forge and…

Bluetooth has a serious security vulnerability:

In some implementations, the elliptic curve parameters are not all validated by the cryptographic algorithm implementation, which may allow a remote attacker within wireless range to inject an invalid public key to determine the session key with high probability. Such an attacker can then passively intercept and decrypt all device messages, and/or forge and inject malicious messages.

Paper. Website. Three news articles.

This is serious. Update your software now, and try not to think about all of the Bluetooth applications that can't be updated.

from https://www.schneier.com/blog/

Defeating the iPhone Restricted Mode

Recently, Apple introduced restricted mode to protect iPhones from attacks by companies like Cellebrite and Greyshift, which allow attackers to recover information from a phone without the password or fingerprint. Elcomsoft just announced that it can easily bypass it. There is an important lesson in this: security is hard. Apple Computer has one of the best security teams on the…

Recently, Apple introduced restricted mode to protect iPhones from attacks by companies like Cellebrite and Greyshift, which allow attackers to recover information from a phone without the password or fingerprint. Elcomsoft just announced that it can easily bypass it.

There is an important lesson in this: security is hard. Apple Computer has one of the best security teams on the planet. This feature was not tossed out in a day; it was designed and implemented with a lot of thought and care. If this team could make a mistake like this, imagine how bad a security feature is when implemented by a team without this kind of expertise.

This is the reason actual cryptographers and security engineers are very skeptical when a random company announces that their product is "secure." We know that they don't have the requisite security expertise to design and implement security properly. We know they didn't take the time and care. We know that their engineers think they understand security, and designed to a level that they couldn't break.

Getting security right is hard for the best teams on the world. It's impossible for average teams.

from https://www.schneier.com/blog/

Details on a New PGP Vulnerability

A new PGP vulnerability was announced today. Basically, the vulnerability makes use of the fact that modern e-mail programs allow for embedded HTML objects. Essentially, if an attacker can intercept and modify a message in transit, he can insert code that sends the plaintext in a URL to a remote website. Very clever. The EFAIL attacks exploit vulnerabilities in the…

A new PGP vulnerability was announced today. Basically, the vulnerability makes use of the fact that modern e-mail programs allow for embedded HTML objects. Essentially, if an attacker can intercept and modify a message in transit, he can insert code that sends the plaintext in a URL to a remote website. Very clever.

The EFAIL attacks exploit vulnerabilities in the OpenPGP and S/MIME standards to reveal the plaintext of encrypted emails. In a nutshell, EFAIL abuses active content of HTML emails, for example externally loaded images or styles, to exfiltrate plaintext through requested URLs. To create these exfiltration channels, the attacker first needs access to the encrypted emails, for example, by eavesdropping on network traffic, compromising email accounts, email servers, backup systems or client computers. The emails could even have been collected years ago.

The attacker changes an encrypted email in a particular way and sends this changed encrypted email to the victim. The victim's email client decrypts the email and loads any external content, thus exfiltrating the plaintext to the attacker.

A few initial comments:

1. Being able to intercept and modify e-mails in transit is the sort of thing the NSA can do, but is hard for the average hacker. That being said, there are circumstances where someone can modify e-mails. I don't mean to minimize the seriousness of this attack, but that is a consideration.

2. The vulnerability isn't with PGP or S/MIME itself, but in the way they interact with modern e-mail programs. You can see this in the two suggested short-term mitigations: "No decryption in the e-mail client," and "disable HTML rendering."

3. I've been getting some weird press calls from reporters wanting to know if this demonstrates that e-mail encryption is impossible. No, this just demonstrates that programmers are human and vulnerabilities are inevitable. PGP almost certainly has fewer bugs than your average piece of software, but it's not bug free.

3. Why is anyone using encrypted e-mail anymore, anyway? Reliably and easily encrypting e-mail is an insurmountably hard problem for reasons having nothing to do with today's announcement. If you need to communicate securely, use Signal. If having Signal on your phone will arouse suspicion, use WhatsApp.

I'll post other commentaries and analyses as I find them.

from https://www.schneier.com/blog/

Critical PGP Vulnerability

EFF is reporting that a critical vulnerability has been discovered in PGP and S/MIME. No details have been published yet, but one of the researchers wrote: We’ll publish critical vulnerabilities in PGP/GPG and S/MIME email encryption on 2018-05-15 07:00 UTC. They might reveal the plaintext of encrypted emails, including encrypted emails sent in the past. There are currently no reliable…

EFF is reporting that a critical vulnerability has been discovered in PGP and S/MIME. No details have been published yet, but one of the researchers wrote:

We'll publish critical vulnerabilities in PGP/GPG and S/MIME email encryption on 2018-05-15 07:00 UTC. They might reveal the plaintext of encrypted emails, including encrypted emails sent in the past. There are currently no reliable fixes for the vulnerability. If you use PGP/GPG or S/MIME for very sensitive communication, you should disable it in your email client for now.

This sounds like a protocol vulnerability, but we'll learn more tomorrow.

News articles.

from https://www.schneier.com/blog/