# Questions tagged [elliptic-curve-generation]

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### Probability of a prime number of points on an elliptic curve over a prime field

Suppose we have some elliptic curve defined over $\mathbb F_p$, with $p$ a large prime. Let $n$ be the number of points on the curve. I am interested in what is currently known about the probability* ...
57 views

### Elliptic curve of order $p = 2q + 1$

Does anyone know an example of an Elliptic Curve of caracteristic $p$ ($E_p$) that has a point generator $G$ that generates a subgroup of order $q$, with $p$, $q$ being prime numbers and $p = 2q + 1$?
48 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 ...
59 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? ...
47 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'...
100 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 ...
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 ...
93 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 ...
89 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 ...
1k 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 ...
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### 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?
510 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)?
919 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.
5k 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?
465 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, ...
584 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=...
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 ...