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Results tagged with elliptic-curves
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user 18316
Elliptic curves are algebraic-geometric structures with applications in cryptography. Such a curve consists of the set of solutions to a cubic equation over a finite field equipped with a group operation. Questions relating to elliptic curves and derived algorithms should use this tag and might also consider more specific tags such as discrete-logarithm and ecdsa.
2
votes
Elliptic curves in Edwards form (or Edwards curve) and addition formulas
This is actually a reference request, anyway: according to Edwards "A Normal Form for Elliptic Curves", this addition law was introduced by Gauss with reference to Euler.
http://www.ams.org/journals/ …
- 2,317
2
votes
Understanding elliptic curve encryption
"Elliptic curve encryption" is somewhat popular wording; one better be specific like ElGamal encryption with a group of points on elliptic curve.
So, start with ElGamal to understand what kind of grou …
- 2,317
0
votes
Accepted
Construction of division polynomials
Leading coefficient of a rational function was defined at 5.3
on page 11 of Report 31
as another function (multiplied by (x/y)^d for some d)
evaluated at identity.
Handling the case of point at ident …
- 2,317
1
vote
Zero-knowledge integer comparison
Statement $a > c$
could be proved as $a - c - 1 = b_1^2 + b_2^2 + b_3^2 + b_4^2$.
According to Lagrange theorem,
a 4-tuple of integers exists for any non-negative integer such that it equals to the su …
- 2,317
1
vote
Choosing asymmetric pairing for Elliptic Curves
There are slim chances to "just choose proper $G_2$". There are families of specific curves such that $G_2$ will have proper number of points. Supersingular curves with $(p+1)$ points for the curve ov …
- 2,317
1
vote
How would I convert committed coordinates $x$ and $y$ to a commitment of the EC point withou...
My goal is to design a Zero Knowledge Proof of Knowledge of the private key associated with a public key which has been hashed (using the Bitcoin address hash) in such a way that the only public in …
- 2,317
0
votes
How to compute a smooth-degree isogeny given a generator point of its kernel?
Use Velu formula with all the points of the subgroup. Sure it would take too long for a large subgroup, and this is why group order is considered like $2^m 3^n$. I think you understand it ok with the …
- 2,317
3
votes
0
answers
234
views
Prime extension field encoding ASN.1
ASN.1 encoding for elliptic curve cryptography is recommended by Certicom, as explained at a related question, covering curves over prime fields and binary extension fields.
I'm looking for known rec …
- 2,317
0
votes
Exponentiation Problem of G2 in MNT curve
Please let me stand on shoulders of poncho who did his guess regarding the order of a random $G2$ element.
The question is hereby reduced to, how do we properly pick generators.
We start from,
$G1$ is …
- 2,317