you
So that's all from my side in this little review
on the ellipticals itself and thinking
and the implementations in free software.
Hi.
You were talking about standardization of curves,
but with a lot of the new cryptography techniques
like zero knowledge, homomorphic encryption,
MPC, VDFs.
And then even when you start to amount recursion
and curve cycles and pairing friendly curves,
each time it seems we will try to standardize curves,
it then discover like, oh, there's some new property
like maybe unknown order groups or hyper elliptic.
I think the movement of this restrito and decath
goes in the direction in instead of
standardize an elliptic curve itself,
it's just standardizing a variety of elliptic curves.
Then you have the operations and the match
to work with any elliptic curves in this variety.
So this will bring us the possibility to have this,
like another service that is providing random elliptic curves
on the net and you can pick one over from there
and forget about the thing that we are sharing
the same elliptic curves.
The way that the current standards that exist
are fixing an elliptic curve one or another,
but fixing it in a specific way.
I have answered it because you say about homomorphic,
but the homomorphic is huge.
It's a very interesting field, but it's huge field.
Okay, I can see another question.
In many protocols and also in IoT devices,
you are bottlenecked by speed and also by signature size.
You said that with Jacobi Quartik curve,
you can go faster and also smaller.
How fast, how much faster and how much smaller?
I haven't, the paper of the Jacobi Quartik people,
it's the speed is explained.
I don't have the numbers on mine now.
I have the numbers on mine about the size
because the sizes in signatures in elliptic curves
are 64 bytes and the proposal,
the schema they propose for the Jacobi Quartik,
it's 84 bytes.
So it's like a third smaller.
But it's still bigger than BLS signatures
who are about 32 to 48
because you only need a single point on curve.
In the signature, in the signature,
you are not putting only the point.
There are three, if I remember correctly, there are three.
BLS signatures, it's only one point.
Which signature?
BLS from Dan Bonny.
Mm-hmm, but it's longer than, it's shorter than 48 bytes.
It depends on the base curve you use,
but it's only, so if you use, well,
32 bytes signatures are not deemed secure enough
because you have pairing issues,
but 48 provides 128 bytes of security, so, yeah.
What I know is in the ethyl curbs variety,
the signature is 64 bytes.
Okay, are there any questions?
No, then.
Okay.
Have you looked at jealous two curves
because I saw that they actually outperformed
a jealous two.
Yeah.
They outperformed the jealous one.
I saw DJB was really into that.
Hyper elliptic curves.
Yeah, the Picard group.
This is a very nice subject also.
I think banks are the ones
that are putting more money in hyper elliptic curves.
They are not using points.
They are using a matrix of the Jacobian of the point.
By now, I only heard about banks putting money there.
I haven't seen an implementation in open source.
Any other?
No, thank you.