ECC is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security. Elliptic curves are applicable for key agreement, digital signatures, pseudorandom generators, and other tasks. they can be used for encryption by combining the key agreement with an asymmetric encryption scheme.
Questions tagged [elliptic-curve-generation]
133 questions
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What is the relationship between p (prime), n (order) and h (cofactor) of an elliptic curve?
I am reading up on ECC and having trouble understanding how these are related.
In a finite field, all point operations are taken modulo $p$.
$n$ is the order of the generator $G$ — which apparently is the number of different points on the curve…
SFlow
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18
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How to calculate elliptic curve parameters?
I'm having a rough time understanding the math behind elliptic curves.
I want to implement ECDH where user can define a, b, and p parameters of elliptic curve.
How can I calculate generator base point G? Is it any point that satisfies elliptic curve…
marlenn
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15
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How to generate own secure elliptic curves?
I know that the algorithm used to generate the Brainpool curves and the NIST curves is published. The algorithm should be this one (RFC5639 Appendix A). From what it looks like it's rather slow to find secure parameters.
After some research I've…
SEJPM
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What is the curve type of SECP256K1?
This is possibly a dumb question. I'm trying to input SECP256K1 curve parameters to a system that expects any custom curve. The form is asking for "curve type". It offers three options:
Short Weierstrass
Twisted Edwards
Montgomery
What should I…
fernacolo
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11
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3 answers
What's up with unnamed elliptic curves in e-passports?
At my work I deal with the cryptographic aspects of the international E-Passport specification (the crypto chips embedded in your passports, the kiosks at airports that talk to them, and the certificate authorities that issue their certs).
The…
Mike Ounsworth
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10
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How do malware rely safely on ECDH algorithm to maintain secrecy of keys?
In traditional malware (especially ransomware) using RSA approach, the public key may be hard-coded in the malware binary and is used to encrypt a symmetric key generated on the system. The symmetric key itself is used to encrypt user files.
Some…
learnerX
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Why are there so many different elliptic curves?
There are Chinese, French and NIST curves. There's a Million Dollar one. The BADA55 Research Team studied 1 million variants. Some are based on widely different formulae. Indeed there are entire suites of curves, and we're still actively…
Paul Uszak
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9
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How to find the order of a generator on an elliptic curve?
I was looking out to find optimum generator for an elliptic curve $E$ over a prime field $\mathbb F_p$. I found the following algorithm:
Choose random point $P$ on the curve.
Find the order of a generator $\ell$.
Calculate the number of points…
Venkatesh
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9
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Curve25519 vs "Million Dollar Curve"
Quoting from the Million Dollar Curve website:
By using publicly verifiable randomness produced in February 2016 by many national lotteries from all around the world, we propose to generate a cryptographically secure elliptic curve for the ECDH…
Tim McLean
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Why Elliptic Curve Cryptography protocols depend on fixed curves?
I'm learning about Ed25519. It depends on a bunch of magic values: The finite field of order $2^{255}-19$, the specific elliptic curve over that field, a specific point on that curve. This is in contrast to Diffie-Hellman or RSA.
Why is that? And…
Jasiu
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8
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How can I generate a Koblitz curve?
Is there the way to generate new Koblitz curves, over $\mathbb F_{2^n}$ and $\mathbb F_p$?
The Certicom SEC 2 standard says:
The recommended parameters associated with a Koblitz curve were chosen by repeatedly selecting parameters admitting an…
Daniel Herbrych
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8
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2 answers
Do Weak Elliptic Curves Exist?
I'm running into very contradictory opinions when try to understand if weak elliptic curves exist. I'm not interested in the case when a curve's weakness is attributed to properties of an EC's prime, because those cases have been already explored,…
Oleg Gryb
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curve25519 by openSSL
How can i generate ec curve25519 keys using openSSL?
When I run
openssl ecparam -name curve25519 -genkey -noout -out private.ec.key
I have this message
unknown curve name (curve25519)
Vito Lipari
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6
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Cryptographically Secure Elliptic Curve
What are the properties a cryptographically secure Elliptic Curve must have?
I have started to create a list and wanted to know if I forgot some important points, and if it is correct so far:
A curve $E$ over a finite field $\mathbb{F}_q$ with…
Luca
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6
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What's wrong with this curve (generation algorithm)?
In this tweet, Paulo Barreto proposes the following elliptic curve over $\mathbb{F}_{2^{255}-19}$:
$$
E_\mathrm{PB} : y^2 = x^3 - 3x + 13318
$$
with $G_\mathrm{PB} = (-7, 114)$. Now I would like to try to verify the curve by trying to generate it…
dusk
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