Better-performing “25519” elliptic-curve cryptography

https://www.amazon.science/blog/better-performing-25519-elliptic-curve-cryptography

by lemaudit • 2 years ago

218 89 2 years ago

nanolith• 2 years ago

The formal methods nerd in me is happy to see HOL Light being used to formally verify this implementation. I'm curious to see how closely their abstract machine models follow specific machine implementations. OOO, speculation, and deep pipelining have non-trivial impacts on potential side channels, and these vary quite a bit by stepping and architecture.

holowoodman• 2 years ago

Even worse: Each new CPU generation will need a new machine model and a reevaluation. Because OOO, speculation and all the timing behaviour are non-functional properties that frequently change due to new optimizations, different internal structuring, etc.

saghm7• 2 years ago

My (probably naive) understanding is that 25519 already provided better performance than other algorithms used for similar purposes (e.g. RSA) when tuned for a roughly similar level of security; anecdotally, generating 2048-bit or larger RSA keys for me tends to be a lot slower than ed25519. At times I've run into places that require me to use RSA keys though (ironically, I seem to remember first experiencing this with AWS years back, although I honestly can't recall if this is still the case or not).

If this further improvement becomes widely used, it would be interesting to see if it's enough to tip the scales towards ed25519 being more of the de facto "default" ssh key algorithm. My experience is that a decent number of people still use RSA keys most of the time, but I don't feel like I have nearly enough of a sample size to conclude anything significant from that.

stouset2• 2 years ago

anecdotally, generating 2048-bit or larger RSA keys for me tends to be a lot slower than ed25519

That’s not really anecdotal. Generating an ed25519 key is barely more than generating a random 256-bit value. Generating an RSA key is significantly more work.

saghm7• 2 years ago

I did say my understanding was probably naive; I didn't know the details to be able to assert anything beyond my own observation!

toast03• 2 years ago

My (probably naive) understanding is that 25519 already provided better performance than other algorithms used for similar purposes (e.g. RSA) when tuned for a roughly similar level of security; anecdotally, generating 2048-bit or larger RSA keys for me tends to be a lot slower than ed25519.

My also naive (an possibly out of date) understanding is key generation is much faster in with ecc, and that signing is faster too, but verifying is faster for rsa. So switching from a RSA to an ECC server certificate saves bytes on the wire, because keys are smaller, and saves server cpu because signing is faster, but may increase client cpu because verification is slower. The byte savings may make up for the increase in cpu though.

saghm7• 2 years ago

My also naive (an possibly out of date) understanding is key generation is much faster in with ecc, and that signing is faster too, but verifying is faster for rsa. So switching from a RSA to an ECC server certificate saves bytes on the wire, because keys are smaller, and saves server cpu because signing is faster, but may increase client cpu because verification is slower. The byte savings may make up for the increase in cpu though.

Interesting! I wonder if this new algorithm is intended to help with that. I'm super curious if the smaller payload does indeed make a difference (with the current algorithm) like you mention; I know that with databases and filesystems, compression is commonly used to shift the balance from I/O to CPU due to disk writes being slow (with reduced storage size being a side benefit but not usually the main motivation), but I also know that cryptographic verification being too slow can be an anti-feature if it makes brute forcing feasible, so the amount of CPU work needed might be pretty high still.

scrapheap• 2 years ago

My experience is that a decent number of people still use RSA keys most of the time, but I don't feel like I have nearly enough of a sample size to conclude anything significant from that.

I wouldn't be surprised if a lot of people still use RSA for SSH keys for one or more of the following reasons:

1. A lot of tutorials about generating SSH Keys were written before ed25519, so if they follow an old tutorial they'll probably be generating an RSA key.

2. Older versions of OpenSSH, that you'd find on CentOS 7 and below, would default to RSA if you didn't specify a key type when running ssh-keygen.

3. There are some systems out there that don't support ed25519, though they are becoming rarer. If you have to deal with those systems then you're forced to use RSA (at least for that system).

4. Some of us have been using SSH keys from way before OpenSSH add support for ed25519 keys in 2014, so any long lived SSH keys won't be ed25519 keys (wow, ed25519 has now been about in OpenSSH for over 10 years).

miki123211• 2 years ago

5. a lot of people (especially older people I suspect) think "RSA" when they hear "public key cryptography".

I'm in my twenties and still have that reaction. I know elliptic curves exist, I even sort-of-kind-of have an awareness of how they work, but if I was asked to name one cryptosystem that used public and private keys, I'd definitely say RSA first and not elliptic curves.

Spooky23• 2 years ago

If you interact with government or some large entities that do business with government, they have to comply with FIPS 140-2, and cannot use ed25519.

pantalaimon2• 2 years ago

3. There are some systems out there that don't support ed25519, though they are becoming rarer. If you have to deal with those systems then you're forced to use RSA (at least for that system).

Azure Devops is a big one.

loudmax• 2 years ago

When I run `ssh-keygen`, I can remember the options `-t rsa` or `-t dsa`. I simply cannot remember the flag `-t ed25519`. I have to look it up every time.

I just remember the flag as being vaguely similar the name of the monster robot from RoboCop.

upofadown• 2 years ago

Another article from the same blog about optimizing RSA:

* https://www.amazon.science/blog/formal-verification-makes-rs...

RSA signature verification is already very fast and TLS doesn't use RSA for encryption anymore so the problem reduces to optimizing signing operations.

SEJeff8• 2 years ago

The firedancer team at one of the better HFT firms wrote an AVX512 optimized implementation of ed25519 and X25519 that’s significantly faster than OpenSSL.

https://github.com/firedancer-io/firedancer/pull/716

Ditto for sha256: https://github.com/firedancer-io/firedancer/pull/778

And sha512: https://github.com/firedancer-io/firedancer/pull/760

If you’re an optimization nerd, this codebase is wild.

electricshampo1• 2 years ago

Completely agree re: firedancer codebase. There is a level of thought and discipline wrt performance that I have never seen anywhere else.

SEJeff8• 2 years ago

That team is full of world experts in high performance computing.

dhx2• 2 years ago

It's much more than just performance they've thought about. Here are some of the secure programming practices that have been implemented:

  /* All the functions in this file are considered "secure", specifically:
     - Constant time in the input, i.e. the input can be a secret[2]
     - Small and auditable code base, incl. simple types
     - Either, no local variables = no need to clear them before exit (most functions)
     - Or, only static allocation + clear local variable before exit (fd_ed25519_scalar_mul_base_const_time)
     - Clear registers via FD_FN_SENSITIVE[3]
     - C safety
  */

libsodium[4] implements similar mechanisms, and Linux kernel encryption code does too (example: use of kfree_sensitive)[5]. However, firedancer appears to better avoid moving secrets outside of CPU registers, and [3] explains that libraries such as libsodium have inadequate zeroisation, something which firedancer claims to improve upon.

[1] https://github.com/firedancer-io/firedancer/blob/main/src/ba...

[2] https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplic...

[3] https://eprint.iacr.org/2023/1713

[4] https://libsodium.gitbook.io/doc/internals#security-first

[5] https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/lin...

syzygyhack• 2 years ago

I laughed a little at calling Firedancer contributors "a team at a HFT firm".

Not that you are technically wrong, not at all, that's where Jump came from. It's just that this is all completely blockchain-driven optimization, but the b-word is so dirty now that we've gotta go back to using TradFi for the rep.

SEJeff8• 2 years ago

It’s an optimization in hashing algorithms that is around twice as fast as the ones Amazon is posting in thus article for the same eliptic curves.

If the Amazon improvements are hacker news worthy (they are) this seems reasonable contextually.

Also, I worked for Jump for almost 12 years :)

webXL3• 2 years ago

What makes the “b-word” dirty?

4gotunameagain3• 2 years ago

So many manhours spent on finding better ways to shovel around money and pocket what falls from the cracks.

What a wasteful and unproductive enterprise, considering the vast majority of the devised improvements never see the public eye.

Still, impressive work. Imagine if those brilliant minds behind this were focused somewhere else.

posnet• 2 years ago

The greatest minds of our generation spend their time thinking about how to:

- make people click on ads

- make trading algos faster

- replace human artists

- build more efficient killing machines

- destroy any remaining concept of privacy

appendix-rock• 2 years ago

What do you work on?

almostgotcaught• 2 years ago

I'll never be able to figure out what people get from repeating the same thing over and over. I've seen this same exact comment 1000 times on hn and I'm 100% sure you have too (indeed I believe the reason you repeat is because you've seen it and agree with it).

toast03• 2 years ago

It doesn't seem wasteful and unproductive, given that the result of the HFT industry is smaller bid/ask spreads (lowering costs for all trades) and payment for order flow which is the mechanism that eliminated retail commissions and provides price improvement on many retail trades. And even so, HFT firms are making money.

It might not seem like real work, but making money by reducing costs of market participants sounds like a good thing. I admit though, block trades might be harder now than before the rise of HFT.

If you could do warehousing/distributing/coordinating fresh foods in a way that reduced the difference in price between the farmer and the consumer and make money doing it, that would clearly be good work.

pantalaimon2• 2 years ago

That looks really neat, but I still don't understand what firedancer actually is - what is a validator client for Solana and why does it need it's own crypto library?

SEJeff8• 2 years ago

It’s a new from scratch implementation of a validator for Solana the fastest blockchain by several orders of magnitude. The slowest part is signature verification so they sped up hashing to improve performance of the entire system.

They follow a first principles approach (the lead has a few physics degrees) and opted to speed up the cryptography. The beauty of this, despite the bad views on blockchain, is that they freaking sped up the cryptography of commonly used algorithms more than anything open or closed source that I personally am aware of.

It’s a win in cryptography, much like this Amazon post is, except it’s slower than the firedancer implementation.

nly• 2 years ago

A lot of slowness comes typically comes from wanting to avoid methods that enable side-channel timing attacks

inopinatus• 2 years ago

I see they learned clang’s dirty little secret over intrinsics viz. that in producing the IR it deviates (sometimes dramatically when AVX-512 is concerned) from the documented opcodes and the results are inevitably detrimental.

astrange2• 2 years ago

This is why ffmpeg uses assembly, and people get extremely mad when you say it's done for a reason, because they always want to come up with a fancier abstraction (usually cross-platform) which then defeats the purpose because it doesn't actually work.

nb those abstractions do make sense when you can only afford to write a single implementation of the algorithm; then you're just talking about a high level programming language. But they frequently fail to achieve their goal when you're writing a second implementation for the sole purpose of being faster.

slt2021• 2 years ago

wow amazing, nobody is gonna edit that code ever again...

londons_explore• 2 years ago

Does 25519 suffer from key/data-dependant execution time?

Is this implementation resistant to that?

If it isn't, it's kinda a footgun which shouldn't be published for general use.

vitus3• 2 years ago

Does 25519 suffer from key/data-dependant execution time?

I mean, when implemented naively, yes, but the industry has been aware of timing attacks for decades such that this is table stakes for any crypto implementations.

From the article:

We also do our best to execute the algorithms in constant time, to thwart side-channel attacks that infer secret information from the durations of computations.

https://github.com/awslabs/s2n-bignum (where most of the heavy lifting is done, per the article) further explicitly states that "Each function is moreover written in a constant-time style to avoid timing side-channels."

justinwsmith• 2 years ago

The next paragraph makes a slightly stronger statement about its constant-time'ness:

Our implementations of x/Ed25519 are designed with constant time in mind. They perform exactly the same sequence of basic CPU instructions regardless of the input values, and they avoid any CPU instructions that might have data-dependent timing.

deathanatos• 2 years ago

but the industry has been aware of timing attacks for decades such that this is table stakes for any crypto implementations.

When I see CVE-fests like — https://people.redhat.com/~hkario/marvin/ — … I just do not come away with that impression.

[Widely used] Cryptographic Rust crates offering "constant time" operations in "pure Rust" — but Rust has no primitives for doing constant time operations, so it's only through hopes and prayers that it might actually work, and with no guarantee anywhere that it actually should.

(Other, less timing attack related stuff, but e.g., major companies still not supporting anything beyond RSA.)

syncsynchalt2• 2 years ago

Curve25519 is designed to be resistant to timing attacks, such as clamping the 254th bit in x25519 keys to 1 so that implementors can not optimize away a multiplication round.

That doesn't mean that this implementation doesn't have timing attacks, but the implementors claim they chose mechanisms which should be constant-time.

fefe23• 2 years ago

Holy shit these claims are wild! It's not just a percent more performance here and there, the graphs look more like 50% more throughput on the same hardware (depending on the cpu architecture).

My immediate fear was that they optimized away the security features like absence of timing side channels, but they say they still have those.

They also claim to have formal proof of correctness, which is even more amazing, because they are not doing it on a symbolic level but on a machine instruction level. Apparently they tought their reasoning system the semantics of all the CPU instructions used in the assembler implementation.

I'll still wait what djb has to say about this, but it looks freaking amazing to me.

jonmon66912• 2 years ago

I'm assuming when they say that this improves user experience, that it implies the use case is primarily TLS. In which case store-now-decrypt-later attacks are already considered an urgent threat with regard to post quantum crypto. With FIPS 203 being released and Chrome is already using an implementation based on the draft standard, this seems like this algo (at least for TLS) should be on its way out.

dlgeek• 2 years ago

The industry is moving to a hybrid that mixes classic crypto (including ECC) with post-quantum crypto. AWS has even turned this on in some places - https://aws.amazon.com/about-aws/whats-new/2022/03/aws-kms-a... from 2022 and https://docs.aws.amazon.com/kms/latest/developerguide/pqtls.... for some details.

jonmon66912• 2 years ago

Thanks I forgot about that. So if understand it right, the idea is to provide some insurance in the case that these relatively young algorithms are broken as they get exposed to more and more cryptanalysis

adgjlsfhk1• 2 years ago

No one other than NIST is recommending phasing out pre-quantum crypto. Everyone else is using a combination of pre-quantum and post-quantum because trust in the security and robustness of the post-quantum ecosystem is fairly low.

aseipp• 2 years ago

I was aware of s2n-bignum which is a very cool project, but apparently there is a larger sister project, aws-lc, that aims for broader set of APIs including OpenSSL compatibility, while retaining the general approach and vibe (lots of formal verification + performance work): https://github.com/aws/aws-lc

That's pretty sweet. I'm currently using BoringSSL in a project as a supplement to OpenSSL (mostly because it is much easier to build for Windows users than requiring them to fiddle with msys2/vcpkg etc; the alternative is to rely on the Windows CNG API, but it lacks features like ed25519 support.) I wonder how much effort it would take to use aws-lc instead... Not that I'm that interested, BSSL is pretty good, but free performance and heavy automated verification is always nice :)

Related: one of the authors of this post, John Harrison, wrote a really good book about automated theorm proving about 15 years ago while working on floating point verification at Intel -- there's still no other book quite like this one, I think https://www.cl.cam.ac.uk/~jrh13/

newman314• 2 years ago

Upon hearing about AWS-LC, I immediately thought about tying it to nginx to see if it will work.

Turns out someone else has already tried: https://github.com/aws/aws-lc/issues/1827

notfed3• 2 years ago

The x25519 algorithm also plays a role in post-quantum safe cryptographic solutions, having been included as the classical algorithm in the TLS 1.3 and SSH hybrid scheme specifications for post-quantum key agreement.

Really though? This mostly-untrue statement is the line that warrants adding hashtag #post-quantum-cryptography to the blogpost?

westurner3• 2 years ago

Actually, e.g. rustls added X25519Kyber768Draft00 support this year: https://news.ycombinator.com/item?id=41534500

/?q X25519Kyber768Draft00: https://www.google.com/search?q=X25519Kyber768Draft00

notfed3• 2 years ago

Kyber768 is the post-quantum algorithm in that example, not x25519.

webXL3• 2 years ago

Why don't they just focus on making a Gravitron variant with those algorithms in the circuitry?

AgentOrange1234• 2 years ago

"just"?

Better-performing “25519” elliptic-curve cryptography

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