X448 Key Exchange

[Joseph S. Testa II]

On 09/13/2018 08:18 PM, Damien Miller wrote:
> We have any plans to add more crypto options to OpenSSH without a strong
> justification, and I don't see one for X448-SHA512 ATM.

What I like about it is that it offers ~224 bit security level, whereas 
X25519 offers ~128 bits (according to RFC7748).  Hence, pairing X448 
with AES256 would provide a full chain of security in the ~224 bit 
level, no?

It also provides an alternative to the NIST P-curves (like P-521), which 
some people suspect are back-doored by the NSA.  P-521 in ECDSA has been 
supported by OpenSSH for awhile now.


> It's hard to imagine a world where X25519-SHA256 is broken but
> X448-SHA512 is unaffected.

Ok, but still... X448 provides a higher security margin that pairs well 
with AES256.  That's a benefit users can enjoy immediately.


> AFAIK The most likely ways that X25519-SHA256
> could fail are:
> 
> 1) discovery of weaknesses in prime field EC crypto. This would almost
> certainly affect both X25519/X448.

The same could happen with the NIST P-curves, which OpenSSH already 
supports.


> 2) working quantum computers. Exciting times, everything breaks.
> 
> 3) a weakness in SHA256. Online key agreement protocols like SSH KEX are
> the last thing affected by collisions, because the attacker has such a
> limited window in which to generate one and limited degrees of freedom
> to manipulate the colliding data.

(Did you mean SHA-512 here?)

Again, this can happen with the P-curves/SHA-256/384/512/ECDSA that is 
already supported.

While we're daydreaming about this, what about SHA3-512? (note the "3")


> Personally, I'm more interested in a post-quantum KEX than another of the
> same species...

I'm very interested in this too.  They're not exclusive to each other, 
however.

I haven't stayed on top of post-quantum crypto lately, but isn't that 
still years away?  X448, on the other hand, is fully defined and was 
recently put into TLS 1.3.

It wouldn't be hard to convince me that X448 is still a little too new; 
perhaps we could wait a year and see how well it does with the new 
scrutiny it gets from being in the TLS spec.  If it survives its 
field-testing, then we could move forward.  And/or we make X448 a 
last-priority KEX for a year or two and patiently see what happens.

Again, if this gets the green light, I'll be happy to write the initial 
implementation.

   Thanks,
   - Joe

-- 
Joseph S. Testa II
Founder & Principle Security Consultant
Positron Security