[HN Gopher] Eccfrog512ck2: An Enhanced 512-Bit Weierstrass Ellip...
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       Eccfrog512ck2: An Enhanced 512-Bit Weierstrass Elliptic Curve [pdf]
        
       Author : bikenaga
       Score  : 39 points
       Date   : 2025-04-16 18:31 UTC (4 days ago)
        
 (HTM) web link (arxiv.org)
 (TXT) w3m dump (arxiv.org)
        
       | commandersaki wrote:
       | Why this over Curve448 and Ed448. Does the curve lend itself to
       | an easier implementation? From what I can see there doesn't seem
       | to be a compelling story here.
        
         | geocar wrote:
         | No. The claim is that it's about as fast as 22519 but stronger
         | than 448, and might be resistant to some specific attacks. If
         | that's true, that is a good thing.
         | 
         | But please do not take this as endorsement: I don't think you
         | or anyone else should use this.
         | 
         | 448 and 22519 go to great lengths to "nothing-up-my-sleeves"
         | the parameters, and this one just keeps saying "custom
         | designed" parameters.
         | 
         | This might be my failing to find it, but it's something I've
         | come to expect in serious crypto papers front-and-centre.
         | 
         | It might also be the subject of another paper the author is
         | working on, mere naivete (on the authors part or mine), or part
         | of a deliberate attempt to infiltrate some other/popular piece
         | of software (like OpenSSL).
        
           | commandersaki wrote:
           | I only see performance comparisons with NIST P-521? I don't
           | even see a claim for performance on par with Curve25519.
        
             | geocar wrote:
             | That's my bad. I was getting blurry after Table 4.
        
       | kevvok wrote:
       | With the industry pivoting towards focussing on post-quantum
       | algorithms, I'd be surprised if yet another elliptic curve gains
       | much traction.
        
         | Retr0id wrote:
         | The industry is mostly pivoting to hybrid schemes, and it's
         | sensible to want a higher-security curve to pair with a higher-
         | security PQ algorithm.
        
           | ryao wrote:
           | The pivot is occurring on both key agreement and signatures.
           | Hybrid schemes currently only exist for key agreement.
           | Perfect forward secrecy means that as long as the key
           | agreement schemes are secure against Shor's algorithm, we can
           | afford to do a much more leisurely roll out of PKI with PQ
           | signing algorithms. Whether people will opt for "hybrid"
           | signatures is yet to be seen.
        
         | ryao wrote:
         | That seems like a mistake, since PQAs are an objective
         | downgrade from ECC in everything except for immunity to Shor's
         | algorithm. It is not clear that machines with the tens of
         | millions of qubits needed to run Shor's algorithm will be
         | constructed since there is no quantum moore's law that gives us
         | a clear roadmap to making them. If they never are made, then
         | all of these PQAs will have been a waste and we will have
         | missed opportunities for improvements from improved curves. For
         | example, the failure to deploy EdDSA certificates in PKI has
         | been a missed opoortunity. I hope the industry reverses course
         | and deploys them, since they are a clear improvement over the
         | current ECDSA certificates.
         | 
         | I can see using hybrid PQAs for key agreement as a hedge
         | against quantum machines actually being constructed, but with
         | the upcoming 47 day certificates, there really is no need to
         | avoid EdDSA. If we come anywhere near constructing a quantum
         | computer that can crack the public keys, the industry could
         | pivot to ML-DSA with the older EdDSA certificates expiring
         | before there is any risk of them being cracked.
        
           | Retr0id wrote:
           | If we assume cryptographically-relevant quantum computers
           | will one day exist, you don't just need to worry about certs
           | being cracked before they expire, but also the ECDH-
           | established session keys being cracked. These keys are
           | ephemeral, but if you store the ciphertexts long-term, you
           | can crack them at any point in the future (aka
           | https://en.wikipedia.org/wiki/Harvest_now,_decrypt_later).
        
             | ryao wrote:
             | Perfect forward secrecy means harvest now, decrypt later
             | does not apply to signature algorithms when ephemeral keys
             | are used and TLSv1.3 mandates ephemeral keys. If the
             | ephemeral keys are cracked, that would be the fault of the
             | key agreement algorithm, not the signature algorithm.
             | 
             | > If we assume cryptographically-relevant quantum computers
             | will one day exist
             | 
             | One day could be 10,000 years in the future, so what
             | meaning is there to such an assumption? You need to assume
             | much more than that such machines will be constructed one
             | day to suggest that there is a need for action. The
             | industry is switching to hybrid key agreement algorithms
             | out of an abundance of caution that it is not just one day
             | that such a machine will be made, but one day in our
             | lifetimes. It is not certain that will actually happen, but
             | if it does, having adopted hybrid key exchange algorithms
             | years in advance is enough. There is no need to switch
             | signature algorithms from ECC until the creation of such a
             | machine is imminent. Thus it is fine to proceed with EdDSA
             | adoption in PKI.
        
               | Retr0id wrote:
               | The Eccfrog512ck2 curve can be used for both signatures
               | and key agreement.
        
       | Retr0id wrote:
       | They say coefficient b is determined via BLAKE3, but unless I'm
       | missing it, they don't actually say how?
       | 
       | They also claim that the prime modulus was chosen "carefully",
       | and enumerate its favourable properties, but do not elaborate on
       | _how_ it was chosen. Presumably they had some code that looped
       | until they found a prime that gave them all the right properties,
       | but it would be good if they shared that process.
        
         | GoblinSlayer wrote:
         | Here is b:
         | https://github.com/victormeloasm/OpenFrogget/blob/main/src/e...
        
           | quesomaster9000 wrote:
           | And even with the constant `b=BLAKE("ECCFrog512CK2 forever")`
           | there is an open question, while not as problematic as it is
           | with the NIST & SEC curves, it's covered in "How to
           | manipulate curve standards: a white paper for the black
           | hat"[1]
           | 
           | I'm surprised they didn't include the constant in the paper
           | and at least a short justification for this approach, despite
           | stating "This ensures reproducibility and verifiable
           | integrity" in section 3.2, whereas several other curves take
           | the approach of 'smallest valid value that meets all
           | constraints'.
           | 
           | Really they should answer the question of "Why can't `b` be
           | zero... or 1" if they're going for efficiency, given they're
           | already using GLV endomorphisms.
           | 
           | Likewise with the generator, I see no code or mention in the
           | paper about how they selected it.
           | 
           | [1]: https://eprint.iacr.org/2014/571.pdf
        
       | quesomaster9000 wrote:
       | Well, I've tried manually verifying the curve parameters and I
       | don't trust this.
       | 
       | * The generator isn't selected deterministically
       | 
       | * The BLAKE3(seed) in the OpenFrogget code doesn't match what I
       | get with Python & Javascript implementation of Blake3, the index
       | & seed aren't specified in the paper
       | 
       | * The paper doesn't provide a reference for why `a=-7` was chosen
       | (presumably because of the GLV endomorphism)
       | 
       | * the various parameters differ between the reference
       | implementation and the paper and the spec...
       | 
       | There are enough many holes in this that I wouldn't touch it yet,
       | as a very quick glance into the spec & the code leaves me
       | wondering why their claims of reproducibility & determinism re:
       | the constants aren't true, and the documentation & code don't
       | match what I can reproduce locally.
       | 
       | So uhh yea... No
        
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