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February 27, 2012

SSL optimization and security talk

Filed under: Crypto,Network,Protocols,Security — Nate Lawson @ 6:12 am

I gave a talk at Cal Poly on recently proposed changes to SSL. I covered False Start and Snap Start, both designed by Google engineer Adam Langley. Snap Start has been withdrawn, but there are some interesting design tradeoffs in these proposals that merit attention.

False Start provides a minor improvement over stock SSL, which takes two round trips in the initial handshake before application data can be sent. It saves one round trip on the initial handshake at the cost of sending data before checking for someone modifying the server’s handshake messages. It doesn’t provide any benefit on subsequent connections since the stock SSL resume protocol only takes one round trip also.

The False Start designers were aware of this risk, so they suggested the client whitelist ciphersuites for use with False Start. The assumption is that an attacker could get the client to provide ciphertext but wouldn’t be able to decrypt it if the encryption was secure. This is true most of the time, but is not sufficient.

The BEAST attack is a good example where ciphersuite whitelists are not enough. If a client used False Start as described in the standard, it couldn’t detect an attacker spoofing the server version in a downgrade attack. Thus, even if both the client and server supported TLS 1.1, which is secure against BEAST, False Start would have made the client insecure. Stock SSL would detect the version downgrade attack before sending any data and thus be safe.

The False Start standard (or at least implementations) could be modified to only allow False Start if the TLS version is 1.1 or higher. But this wouldn’t prevent downgrade attacks against TLS 1.1 or newer versions. You can’t both be proactively secure against the next protocol attack and use False Start. This may be a reasonable tradeoff, but it does make me a bit uncomfortable.

Snap Start removes both round trips for subsequent connections to the same server. This is one better than stock SSL session resumption. Additionally, it allows rekeying whereas session resumption uses the same shared key. The security cost is that Snap Start removes the server’s random contribution.

SSL is designed to fail safe. For example, neither party solely determines the nonce. Instead, the nonce is derived from both client and server randomness. This way, poor PRNG seeding by one of the participants doesn’t affect the final output.

Snap Start lets the client determine the entire nonce, and the server is expected to check it against a cache to prevent replay. There are measures to limit the size of the cache, but a cache can’t tell you how good the entropy is. Therefore, the nonce may be unique but still predictable. Is this a problem? Probably not, but I haven’t analyzed how a predictable nonce affects all the various operating modes of SSL (e.g., ECDH, client cert auth, SRP auth, etc.)

The key insight between both of these proposed changes to SSL is that latency is an important issue to SSL adoption, even with session resumption being built in from the beginning. Also, Google is willing to shift the responsibility for SSL security towards the client in order to save on latency. This makes sense when you own a client and your security deployment model is to ship frequent client updates. It’s less clear that this tradeoff is worth it for SSL applications besides HTTP or other security models.

I appreciate the work people like Adam have been doing to improve SSL performance and security. Obviously, unprotected HTTP is worse than some reductions in SSL security. However, careful study is needed for the many users of these kinds of protocol changes before their full impact is known. I remain cautious about adopting them.

January 31, 2012

Why stream ciphers shouldn’t be used for hashing

Filed under: Crypto,Protocols,Security — Nate Lawson @ 10:48 am

I recently saw a blog post that discussed using RC4 as an ad-hoc hash in order to show why CBC mode is better than ECB. While the author’s example is merely an attempt to create a graphic, it reminded me to explain why a stream cipher shouldn’t be used as as a cryptographic hash.

A stream cipher like RC4 only has one input (the key) and one output, a variable-length keystream. During initialization, the key is expanded and stored in an internal buffer. When the user wants to encrypt or decrypt (both are the same operation), the buffer is updated in some way and keystream bits are output. It’s up to the caller to take that keystream data and XOR it with the plaintext to get the ciphertext (or vice versa). Very simple, right? You just initialize the stream cipher’s state with a key and then turn the crank whenever you want keystream bits.

A cryptographic hash algorithm like SHA-1 also has one input (the data) and one output, the digest. A variable-length stream of input data is crunched in blocks, giving a final output digest that should be difficult to invert, among other properties.

At first glance, it seems that a stream cipher can be used as a cryptographic hash by setting the data to hash as the key, turning the crank, and using some of the keystream as the digest. The reasoning goes, “since it should be difficult to recover the original stream cipher key merely by seeing some of the keystream, the output is usable as a hash”. While this may sound reasonable, it is often wrong, leading to various security problems.

There are numerous, vital design distinctions between stream ciphers and hashes. First, a stream cipher is designed to output an extremely long keystream sequence while a hash digest is a relatively small, fixed-length output. There are design differences that arise from expanding a key vs. compressing input. Also, resistance against a chosen input attack is a requirement for a cryptographic hash, while it may not have been considered for a stream cipher. What could an attacker gain if they can choose the input keys? By definition, they already know the secret key in this case.

The RC4 weakness that led to WEP being broken was a related-key attack. Even though an attacker could not choose WEP keys, the RC4 key was the concatenation of a counter and the secret key. Thus, subsequent outputs of the keystream are derived from closely related input keys.

But to use RC4 for hashing, it would have to be resistant not only to related key attacks, but to a chosen key attack. In this case, the attacker can target weaknesses in your key schedule algorithm by maliciously choosing many keys versus merely knowing that some relation exists between unknown keys that the attacker can’t choose. While chosen-IV attacks are part of the consideration for stream ciphers, I haven’t heard of full chosen-key resistance being an important design criteria. (Please correct me if I’m out of date on this, especially with eStream).

In contrast, resistance to a chosen-input attack is the very definition of a cryptographic hash algorithm. This resistance comes at a performance cost. Turning a hash algorithm into a stream cipher can be done (say, an HMAC using a key and counter), but it’s slower than stream ciphers that were designed as such. Stream cipher designs are optimized for performance and are usually not focused on preventing chosen-key attacks. An interesting corrolary is that analyzing a stream cipher’s key scheduling algorithm as a hash function (e.g., collision resistance) is often a good way to understand its possible weaknesses.

To summarize, don’t use cryptographic primitives for non-standard purposes. There are often built-in assumptions based on the original intended application that could compromise your modified design.

September 20, 2011

Recovering a private key with only a fraction of the bits

Filed under: Crypto,Security — Nate Lawson @ 10:43 am

Ever since my first post on breaking DSA, I’ve been meaning to write a clear description of how to recover a private key if you only have a fraction of the bits. For example, power analysis attacks may allow you to derive a few bits of the random k value on each measurement. It turns out you can combine multiple measurements to get a single k value and then recover the DSA private key. Of course, all this also applies to ECDSA.

Since I haven’t had time to put together a good summary article, here are some references for learning this on your own. The first paper in this area was Boneh and Venkatesan (1996). They described the basic Hidden Number Problem.

The next important paper was by Howgrave-Graham and Smart (1999) [1]. They used Babai’s algorithm[2] and LLL lattice reduction to solve for DSA private nonces. This was improved by Nguyen and Shparlinski (2000) [3] to solve for just the k values.

This attack applies any time the DSA nonce isn’t fully random and used only one time. It applies if a few of the bits are constant, if the RNG is biased towards certain values, or if you can recover part of the values by side channel attacks. These references should allow you to implement this attack yourself. It has been repeatedly used in private work, but I haven’t seen much public discussion about applying this to real-world systems.

[1] Howgrave-Grahm and Smart. “Lattice attacks on Digital Signature Schemes.” HP internal publication, 1999.
[2] Laszlo Babai. “On Lovász lattice reduction and the nearest lattice point problem.” Combinatorica 6. No online reference found.
[3] Nguyen and Shparlinski. “The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces.” Journal of Cryptology, volume 15, pp. 151-176, 2000.

Addendum: I found the following references to improve this list.

September 13, 2011

The Magic Inside Bunnie’s New NeTV

Filed under: Crypto,Embedded,Hardware,Security — Nate Lawson @ 11:19 pm

A year ago, what was probably the most important Pastebin posting ever was released by an anonymous hacker. The HDCP master key gave the ability for anyone to derive the keys protecting the link between DVD players and TVs. There was no possibility of revocation. The only remaining question was, “who would be the first to deploy this key in an HDCP stripper?”

Last week, the HDCP master key was silently deployed, but surprisingly, not in a stripper or other circumvention device. Instead, it’s enabling a useful new system called the Chumby NeTV. It was created by Bunnie Huang, who is known for inventing the Chumby and hacking the Xbox. He’s driving down the cost of TV-connected hardware with a very innovative approach.

The NeTV displays Internet apps on your TV. You can see Twitter feeds, view photos, and browse the web via an on-screen display. It overlays this information on your video source. You can control it from your iPhone or Android phone. It’s simple to install since you merely plug it inline with your cable box or DVD player’s HDMI connection to the TV. And in true Bunnie fashion, the hardware and software is all open source.

When I first heard of this last week, I didn’t think much of it. It’s a neat concept, but I don’t have an HDTV. Then, a friend contacted me.

“Have you figured out how the NeTV works? There’s a lot of speculation, but I think I’ve figured it out,” he said. I told him I hadn’t thought much about it, then downloaded the source code to the FPGA to take a look.

I was surprised to find an entire HDCP implementation, but it didn’t quite make sense. There was no decryption block or device keys. I emailed Bunnie, asking how it could do alpha blending without decrypting the video. He wrote back from a plane in Tokyo with a cryptic message, “No decryption involved, just chroma key.”

This was the hint I needed. I went back and watched the demo video. The overlay was not transparent as I had first thought. It was opaque. To do alpha blending, you have to have plaintext video in order to mask off the appropriate bits and combine them. But to apply an opaque overlay, you could just overwrite the appropriate video locations with your substituted data. It would require careful timing, but no decryption.

Chroma key (aka “blue/green screen”) uses color for in-band signaling. Typically, an actor performs in front of a green screen. A computer (or a filter, in the old days) substitutes data from another feed wherever there is green. This is the foundation of most special effects in movies. Most importantly, it is simple and can be performed quickly with a minimum of logic.

The NeTV generates its output signal by combining the input video source and the generated overlay with this same technique. The overlay is mostly filled with pixels of an unusual color (Bunnie called it “magic pink”). The FPGA monitors the input signal position (vertical/horizontal sync, which aren’t encrypted) to know where it is within each frame of video. When it is within the pink region of the overlay, it just passes through the encrypted input video. Otherwise, it displays the overlay. The HDCP implementation is needed to encrypt the overlay, otherwise this part of the screen will be scrambled when the TV tries to decrypt it. But, indeed, there is no decryption of the input content.

This is impressive work, on par with the demoscene. The NeTV synchronizes with every frame of video, no jitter, choosing which pixel stream to output (and possibly encrypt) on-the-fly. But there’s more.

To generate the keystream, the NeTV has to synchronize with the HDCP key exchange between video source and TV. It replicates each step of the process so that it derives the correct stream key. To keep any timing issues with the main CPU from delaying the key exchange, it resets the link after deriving the shared key to be sure everything is aligned again. Since the transport key only depends on the two endpoint device keys, the same shared key is always used.

This is extremely impressive from a technical standpoint, but it’s also interesting from a content protection standpoint. The NeTV has no device keys of its own; it derives the ones in use by your video source and TV as needed. It never decrypts video, only encrypts its on-screen display to match. It can’t easily be turned into an HDCP stripper since that would require a lot of rework of the internals. (The Revue, with its HDMI transceiver chip and Atom processor could probably be turned into an HDCP stripper with a similar level of effort.)

Bunnie has done it again with a cheap device that applies his extensive creativity to not just solve a problem, but do it in style. Whatever the outcome of his maverick engineering is in the marketplace, the internals are a thing of beauty.

June 28, 2011

Intermediate cryptography resources

Filed under: Crypto,Security — Nate Lawson @ 12:26 pm

People often ask me for a good introduction to intermediate cryptography. It’s often easy to find basic and dangerous introductions (“public key encryption is like a mailbox”), but the next level isn’t as available.

There’s no single source for this, but you can find good coverage of the main practical topics online. Here are some resources to get you started learning beyond cryptography basics.

Cryptography: an Introduction (Nigel Smart)

I can’t say enough good things about this book. It is a great way to learn about attacks on public key schemes (see part 4) and has good general coverage as well, including elliptic-curve.

Lecture Notes on Cryptography (Bellare and Goldwasser)

Good for understanding how to model block cipher constructions with PRFs and PRPs. When someone says “that construction is not IND-CPA-secure”, this will tell you what that means. Try chapters 5, 6, and 9. Also, see the class notes page for slides and individual chapters of this series.

Tom’s math and crypto libraries (Tom St. Denis)

It’s impossible to understand practical cryptography without looking at implementations. Tom’s libraries are relatively clear and readable and cover the gamut from low-level integer manipulation all the way up to protocols. There are no external dependencies and they are public domain. For extra credit, implement one of the ciphers yourself before looking at his code, then compare to see how you did.

He also includes a large PDF documenting the library, and it’s available as a book as well.

NIST FIPS, SP and RSA PKCS standards

The NIST standards are pretty clear. The RSA ones are a bit more difficult to read. In any case, it’s very helpful to read through these and ask “why?” for each requirement they make. There’s always a reason for every “shall” or “must”. But are there some “shoulds” that should be “shalls”?

Once you’ve moved beyond these resources, the best next level is to read survey papers (like Boneh’s coverage of RSA) in the specific area you’re interested in. If you have your own favorite resources for intermediate cryptography, let me know in the comments below.

May 17, 2011

State space explosion in program analysis and crypto

Filed under: Crypto,Reverse engineering,Security,Software protection — Nate Lawson @ 5:16 am

While analyzing some software the other day, I was struck by the duality of cryptanalyzing block ciphers and program analysis techniques. Both present a complex problem and similar tools can be applied to each.

The three main program analysis techniques are dynamic analysis (e.g., execution traces or debugging), symbolic execution, and abstract interpretation. Each has its place but also has unique disadvantages.

Dynamic analysis tests one set of paths through a program with some variance in inputs (and thus program state). Fuzzing is an attempt to increase the path coverage and number of states for each path via random inputs. Smart fuzzing directs the choice of these inputs by discovering constraints via an SMT solver. While dynamic analysis is fast and doesn’t give any false positives (a crash is a crash), it is extremely limited in coverage, both of code paths and program states.

Symbolic execution covers all possible inputs and code paths but has really poor performance. Since it models the exact behavior of the program for each state and code path, it does not lead to false positives or false negatives. The downside is that it is much too slow to handle more than a few simple functions.

Abstract interpretation has characteristics in common with both. It deploys three-valued logic (0, 1, and “unknown”) to predict a program’s behavior. While not fast, it is fast enough to be performed on the whole program (like dynamic analysis) and gives better coverage of inputs without the nondeterminism of fuzzing. Unlike symbolic execution, it is an under-approximation of behavior and thus leaves many questions unanswered. However, unlike fuzzing, you know exactly which states are indeterminate and can iterate on those areas.

One big problem with the two static techniques is state space explosion. Every time a conditional branch is encountered, the number of possible states doubles. Thinking cryptographically, this is analagous to adding one bit to a cipher’s key or a 1-bit S-box.

All modern block ciphers are based on the substitution and permutation primitives. Permutation is a linear operation and is easy to represent with a polynomial. Substitution (e.g., an S-box) is non-linear and increases the degree of the polynomial drastically, usually squaring it.

Algebraic cryptanalysis is a means of solving for a key by treating a cipher as a system of overdetermined equaations. What algorithms like XL do is convert a set of polynomials into linear equations, which are solvable by means such as Gaussian elimination. XL replaces each polynomial term with a single new variable, and then tries to reduce the equations in terms of the new variables. While it hasn’t broken AES yet, algebraic cryptanalysis will need to be accounted for as new ciphers are designed.

The duality between program analysis and cryptanalysis is interesting to me. Would it be useful to represent unknown conditional branches as bits of a key and the entire program as a cipher, then attempt to reduce with XLS? What about converting cipher operations on bits of an unknown key to conditional branches (or jump tables for bytewise operations) and reducing using abstract interpretation?

While this musing doesn’t have practical applications, it’s still fun to find parallels between distinct areas of your work.

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