Questions tagged [elliptic-curve-generation]

Filter by
Sorted by
Tagged with
0
votes
1answer
40 views

Division of Point in Elliptic Curve: Getting Back Point

Let $P=(x_p,y_p)$ be a point on elliptic curve $E (a, b) := y^2=x^3+ax+b$, for an integer $n$, there exists a point $Q=(x_q,y_q)=nP$ on $E (a, b)$. If $(x_q,y_q)$ and $n$ are given, what is the ...
1
vote
0answers
43 views

Elliptic Curve (Point Counting)

I am studying elliptic curves in particular point counting. If I have coordinates P and 2P, is there a way to calculate the total points in between P and 2P using either curve parameters or algorithm? ...
1
vote
0answers
38 views

Need help understanding SPAKE2 setup values

I am trying to write a simulation of the SPAKE2 protocol in python (just so I can get a better understanding of the protocol altogether). I am reading through the ietf draft here: Datatracker. There'...
0
votes
1answer
80 views

Order of subgroups formed by Elliptic Curves with a Cofactor

In this question: Why are the lower 3 bits of curve25519/ed25519 secret keys cleared during creation? The answer indicates that the order of all points on the curve over the finite field ...
0
votes
0answers
46 views

Difference in elliptic curve order and finite field size [duplicate]

Must the prime finite field, Fp, an elliptic curve is defined over always have a greater number of elements than the cardinality of an elliptic curve. For example, If I have ...
1
vote
1answer
76 views

Point doubling with only one coordinate

In many source codes that implement ECDH, there is a function that multiplies the base point of that curve with a constant. This function usually takes as arguments the constant and just one ...
3
votes
0answers
84 views

Check validity of generated parameters for SIDH

In section 4.1 of the paper Towards Quantum-Resistant Cryptosystems From Supersingular Elliptic Curve Isogenies by Feo, Jao and Plût it is described how you generate valid parameters for the SIDH ...
1
vote
1answer
811 views

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 ...
1
vote
1answer
42 views

Does any problem arise when the order of an elliptic curve is equal to its prime field modulus? [duplicate]

Regarding cryptographic schemes in elliptic curve cryptography, is there a problem with having the order of an elliptic curve being equal to its prime field modulus? That is, an elliptic curve where $...
0
votes
0answers
56 views

Modifying Elliptic Curve Parameters

For context, I was watching this bit of the video: which goes over this source code. The piece is about elliptic curve cryptography and how it works. I want to use some of this knowledge to make my ...
0
votes
0answers
28 views

What is the cryptography involved in the initial setup of a cryptocurrency?

I keep hearing that when a cryptocurrency is created it goes through an initial setup phase wherein cryptographic parameters are created that are used by the cryptocurrency network throughout its ...
0
votes
0answers
58 views

Isogeny of elliptic curve

If we have two elliptic curves $E$ and $E'$ and the points of both elliptic curves are same. Then all the points of $E$ map to all the points of another elliptic curve $E'$. For example $E$ has ...
2
votes
1answer
102 views

Generating a small EDDSA curve

I have an application that would benefit from very small (e.g. 16-20 byte) EDDSA keys and small signatures. It's an application where the goal is more to deter DOS attacks than "hard" security, so ...
2
votes
0answers
62 views

ECC - complex multiplication and key agreement

I'd like to ask three questions - 2 of them regard CM method. The last is regarding the ECC domain parameters generation on the fly, see https://eprint.iacr.org/2015/647.pdf What role has ...
2
votes
2answers
128 views

How to model a miniature elliptic curve?

For educational purposes I would need to work on an elliptic curve that has a small field, but holds the safety futures of a real curve. Is that possible to have such a curve!? For example for the ...
3
votes
0answers
190 views

What is Frobenius map of an elliptic curve?

I was reading about elliptic curves from this PDF. Page 44 defines Frobenius map. It defines the frobenius map as $f(x,y) = (x^p, y^p) \bmod p$. Isn't it just an identity map? What's the use of this ...
0
votes
0answers
104 views

NIST ECC Curves without pairings

NIST FIPS.186-4 has standardized 5 ECC curves on field $\mathbb{F}_p$ (P-192, P-224, P-256, P-384, P-521) and 10 elliptic curves on binary fields. I need to use ECC curves without pairings for my ...
0
votes
1answer
197 views

What math should I learn to get in depth with Elliptic Curve Cryptography research?

My background is computer scientist. I have done applied cryptography research for a while. Currently, I'm working on Elliptic curve cryptography. To understand the idea and how to use Elliptic curve ...
0
votes
1answer
304 views

C# equivalent of openssl ecparam -name prime256v1 -genkey -noout -out [closed]

I am having some issues generating a proper private key,I need it to be an Elliptic Curve private key suitable for use with NIST P-256 which i than need to convert to Base64-encoded private key in ...
2
votes
1answer
813 views

How were the P-256 parameters chosen?

In NIST FIPS 186-4 (page 90), it is said that $c$ is the output of SHA-1 on a seed that was chosen randomly. Then the parameter $b$ of the EC is chosen, according to the formula: $$b^2 \times c \equiv ...
5
votes
1answer
472 views

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 ...
1
vote
2answers
157 views

What are the properties of secure Elliptic Curves?

I have heard about the standard elliptic curves called NIST curves. What are the properties of such cryptographically secure elliptic curves? Are they standardized according to certain protocols? Also,...
3
votes
0answers
150 views

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 ...
10
votes
2answers
2k views

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 ...
8
votes
1answer
2k views

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 ...
4
votes
1answer
903 views

Curve point generators for ECC

I'm working on a cryptosystem based on ECC (elliptic curve cryptography). I need to choose several (~10) curve points which should be used as generators, and it's important that their relation is ...
1
vote
1answer
287 views

OpenSSL - creating random elliptic curve and measuring performance

I want to generate random elliptic curves (over $\mathbb F_p$ and $\mathbb F_{2^m}$) using OpenSSL, that's my task. At first curves over $\mathbb F_p$. Now I am able to generate prime $p$, $a$ and $b$...
0
votes
1answer
199 views

How is the precomputed table for 25519 Elliptic curve generated?

I am wondering how the precomputed table for scalar multiplication for elliptic curve (in my case 25519) is generated/precomputed? I am talking about this [https://github.com/WhisperSystems/...
1
vote
1answer
107 views

finding a from a*G

This might be a newbie question, In elliptic curve, I chosen a secret a and computed aG, where G is the base point. But here since I know G, I can compute inverse of G and multiply it with aG, to get ...
6
votes
1answer
805 views

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 ...
12
votes
1answer
2k views

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 ...
0
votes
2answers
332 views

Finding if two points on elliptic curve are related

On a given elliptic curve I have some points that are defined like this: Where $$A=a*G$$ $$B=b*G$$ $$C=(a+b)*G$$ $$D=d*G$$ $$E=(a+d)*G$$ So finally I have two equations like below: $$A+B=C$$ $$A+D=E$$ ...
1
vote
1answer
358 views

Bilinear Form: Weil pairing

I am doing an example on Weil pairings, and for that purpose I follow the thesis of Alex Edward Aftuck, The Weil Pairing on Elliptic Curves and Its Cryptographic Applications. By following his thesis,...
1
vote
1answer
628 views

How to check whether the given curve is Elliptic or not?

I've given a curve E5(2,3) over Zp. How to check this curve is Elliptic or not? I know the curve formed by this will be: (y2) mod 5 = (x3 + 2*x+3)mod 5.
9
votes
1answer
328 views

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 ...
-1
votes
1answer
118 views

Order of the curve and generator

Does the order of the curve and the order of generator should be coprime for an elliptic curve defined over a prime field?
2
votes
2answers
2k views

Security of elliptic curves

How can we say an elliptic curve is secure and can be used for cryptographic applications?
0
votes
1answer
161 views

Order of an elliptic curve defined over a prime field

I found the following algorithm to find the generator of an elliptic curve: Find the order of the curve - N. Choose any random point on the curve - P. Find the order of that point - n. Calculate co-...
8
votes
1answer
2k views

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 ...
4
votes
2answers
776 views

How can I find the generator of a composite group and $Z_p*$?

I was doing some research on elliptic curves. I know how to find the generator of $Z_p$ (this is a prime group). But I came across the term $Z_p*$ (group containing elements that relatively prime to $...
1
vote
2answers
124 views

Does the generator (base point) is preshared between the sender and receiver in elliptic curve cryptography?

Or the elliptic curve and the generator point are known to everyone?
3
votes
2answers
491 views

Is the prime P is fixed for an elliptic curve defined over a particular prime field F_p?

I have seen the NIST, SEC and Brainpool standards. They have used same prime for a particular bit curve (128,192,256,521). Is the prime value fixed for a particular security (field size)?
1
vote
2answers
866 views

Comparing elliptic curves over prime fields against EC over binary fields

In which scenarios we go for prime fields or binary fields? Please indicate why we would choose one over the other.
2
votes
1answer
4k views

How to find the generator of an elliptic curve? [duplicate]

If the elliptic curve has prime order of points, then all of its points are generator. Is this true? If so, how can I find the optimized generator(which generates more number of points) among them?
0
votes
1answer
441 views

Supersingular vs non-singular (Same or different)

I have a frustration for the term "supersingular" elliptic curve and "non-singular" elliptic curve. In some paper, performance evaluation is done using supersingular elliptic curve and in some cases, ...
4
votes
1answer
525 views

Security level difference: supersingular vs non-singular elliptic curve

In some evaluation of elliptic curve cryptography, it says that for same security level In supersingular curve over $F_p$ with group of prime order $q$, p=512, q=160 bits In non-singular curve , p=...
4
votes
1answer
271 views

Elliptic curves with field sizes that not byte-aligned

Why there are abnormal field size like 521, 571, 233, 283 bits in prime and binary fields that are defined by NIST?
3
votes
2answers
333 views

Elliptic curve with non-prime generator?

Suppose we need a special Elliptic curve on prime field $Fp$, for some reason, that the order of the generator must be $6*q$, where q could be a big prime, does this weak the ECC encryption? What's ...
3
votes
1answer
523 views

Short Weierstrass equation is non-singular for not 2 or 3 characteristic

Consider a field $K$ of characteristic $p \neq 2,3$. Consider a curve $E$ over $K$ defined by the equation $y^2 = x^3 + ax + b$. How can I show that: $E$ is not an elliptic curve (it is not ...
3
votes
0answers
245 views

TypeA pairing, elliptic curves in pairing based cryptography

I am beginner to pairing-based cryptography. After downloading jpbc library, curve parameters files are seen as properties file. For example, for type A curve, following parameters are given. type a ...