RSA is hard to implement and requires a lot of key material to change hand.
On the flipside, a Ed25519 or Ed448 key can be reasonably dictated over phone (though you might need three minutes) and put into small low-res QR codes.
Additionally, Ed25519/448 are dead simple to implement; following the reference from the RFC documentation, you can implement a safe cryptographic method (encrypt/decrypt/sign/verify). You actually have to go out of your way and do things the standard doesn't include to make it unsafe.
Compare with RSA, where such a naive implementation will make you suffer through atleast 30 CVEs of the "padding oracle" or "leak private key" type.
While RSA is fine from a mathematical standpoint, Ed25519/448 are much simpler to implement with much less code and are designed to be reasonably safe. They provide the same security as a ~3500 bit (or about 4500 bit for 448) RSA key, so it's on the safe side of things.
There is no Post-QC algorithm yet, atleast none that made it through the NIST competition, some of them do involve using RSA with absurd key sizes and they'll likely fail the competition.
I don't understand the argument of dictating a key over the phone. If you care about that use case, you can just a well dictate the hash of an RSA public key.
Nobody knowns of the NIST curves have backdoors. Nobody know s if Dan Bernstein's curve has issues.
The advantage of RSA, is that we actually know how it works. I continue to be amazed that so many people advocate curves that we don't undertstand.
Of course, the big problem with RSA, is that is seems simple enough that people try to implement it themselves and get it wrong. With EC, you basically have to use one of the standard libraries.
>Nobody knowns of the NIST curves have backdoors. Nobody know s if Dan Bernstein's curve has issues.
There are still some differences. NIST provides some curves and doesn't explain much about them. You can read up how DJB choose the curves. It's a very neat and tidy process that is easy to follow and very reasonable.
ECurve isn't terribly more complicated than RSA, they both rely on multiplication, though EC does it in 2D space and RSA in Modulo space. I have implemented EC myself, the underlying math isn't that much more complicated, really, than RSA.
>I don't understand the argument of dictating a key over the phone. If you care about that use case, you can just a well dictate the hash of an RSA public key.
Not only dictating over phone but for example typing a SSH key over a serial line while not being able to copy-paste directly. I've had to suffer than with my RSA4096 key once and it's NOT pleasant at all.
it also means you have much less overhead for the protocol (DH and KEX with Ed25519 only need 32 bytes of space per step instead of kilobytes)
> There are still some differences. NIST provides some curves and doesn't explain much about them. You can read up how DJB choose the curves. It's a very neat and tidy process that is easy to follow and very reasonable.
You're not wrong, but to paraphrase a famous quotation: No body every got fired for following Suite B.
AES, SHA-2, and the NIST curves are approved for government crypto, and are also probably in many industry regulations. If there's ever an incident and a post-mortem audit, then it's a lot easier to explain the choice of Suite B algorithms.
> Meanwhile I would gladly fire someone for using AES128 or the NSA-sponsored curves, despite being in Suite B.
Why? Pointing SSL Labs at my bank, it's what they use (ECDH secp256r1). What does your bank use? Or is there a site that you consider more important than that one?
Would you fire the folks at Let's Encrypt, who only offer certs of RSA and P-{256,384}? Gmail, where they do offer x25519, but where most browsers use secp256r1?
Banks are not known for using the best/safest solutions. Just take 4 digit pins and 3DES into account for example.
> who only offer certs of RSA and P-{256,384}?
I am pretty sure that nginx and openssl only recently added support for ed25519 certificates. Although to be honest I don't really like the idea of let's encrypt. The addressing system that tor uses has solved that issue already.
> but where most browsers use secp256r1?
This is an issue. Browser vendors should prioritize the djb algorithms.
Which aspect of elliptic curves would you like to understand better? The original paper for Curve25519 contains a dedicated subsection for attack models, for example, and leaves only marginal room for hidden backdoors with its detailed reasoning about curve parameter choice. The implementation of EdDH or EdDSA is specified in RFCs that are explicitly written to be "fool-proof", as others already commented.
Compare the NIST curves to RSA. For RSA we know there cannot be any backdoors. If you generate good quality primes you are in business (assuming you don't make mistakes elsewhere).
For NIST we cannot say anything about backdoors. We don't use those curves because we don't trust NIST. Not because we have any prove they are bad.
So to avoid that, there is a parameter selection process that supposedly leaves no room for backdoors, though at some CCC congress DJB described how you could use a similar process to add backdoors.
So basically, EC is based on magic. We cannot prove it is bad, we just have to hope there is no hidden magic.
Note you say 'only marginal room'. Soon the whole world will use exactly one curve. With 'only marginal room for hidden backdoors'.
I feel way more comfortable to know that with RSA what you see is what you get.
Even Bernstein doesn't really believe the NIST p-curves are backdoored, and the Koblitz/Menezes paper makes a pretty decent case that they couldn't be, but if you want to tinfoil hat it, just do what every modern system does and use Curve25519.
If any of this is new to you, though, you shouldn't be designing cryptosystems. Most people shouldn't! I sure shouldn't! It's an extremely specialized skill, and the world doesn't need that many new ones. Just use Nacl.
> but if you want to tinfoil hat it, just do what every modern system does and use Curve25519.
What is your take on the NIST curves being "officially" blessed for government data via Suite B (or whatever they're calling it)?
If it's good enough for government work, would it be good enough for us in the private sector? What are the chances the the NSA know weaknesses in Curve25519 or ChaCha like they knew about differential cryptanalysis attacks DES ahead of everyone else?
Frankly I think the kremlinology is a lot less interesting and useful than the engineering facts, which are that Curve25519 is more misuse-resistant, faster, and easier to implement in constant time. People shouldn't be using the P-curves anymore.
On the flipside, a Ed25519 or Ed448 key can be reasonably dictated over phone (though you might need three minutes) and put into small low-res QR codes.
Additionally, Ed25519/448 are dead simple to implement; following the reference from the RFC documentation, you can implement a safe cryptographic method (encrypt/decrypt/sign/verify). You actually have to go out of your way and do things the standard doesn't include to make it unsafe.
Compare with RSA, where such a naive implementation will make you suffer through atleast 30 CVEs of the "padding oracle" or "leak private key" type.
While RSA is fine from a mathematical standpoint, Ed25519/448 are much simpler to implement with much less code and are designed to be reasonably safe. They provide the same security as a ~3500 bit (or about 4500 bit for 448) RSA key, so it's on the safe side of things.
There is no Post-QC algorithm yet, atleast none that made it through the NIST competition, some of them do involve using RSA with absurd key sizes and they'll likely fail the competition.