# Tagged Questions

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### What is rational point on elliptic curve over Galois field

It is clear what is a rational point on elliptic curve, when the curve is defined over real numbers. But if it is defined over Galois field, what is a rational point? If necessary, supply an example, ...
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### How to find primitive point on an elliptic curve?

Reading about Elliptic curve cryptography, i came across primitive point's or generator point's but found nothing on how to generate such points any help would be appriciated.
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### Lenstra's Elliptic Curve Algorithm

I am currently trying to understand Lenstra's Elliptic Curve Algorithm for factoring integers. As a source I use "Rational Points on Elliptic Curves" by Joseph H. Silverman and John Tate. They ...
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### Find coordinate $y$ of an elliptic curve point

If I have an elliptic curve over a finite filed $F_p$ ($p$ is prime) defined as $$y^2 \equiv x^3 + ax + b\pmod p,$$ such that $4a^2 + 27b^2 \neq 0$ and suppose I have only given the coordinate $x$, ...
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### What is an embedding degree of elliptic curve?

I am dealing with MOV algorithm to transform ECDLP to DLP in $GF(p^k)$, but at the first step I have to determine embedding degree k. I have read the definitions of embedding degree, but still I am ...
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### Uniqueness of points in Elliptic Curve addition

When working on a curve E, is the point yielded by P + Q (some P and Q on E) completely unique? What I mean is there are no other points on E sharing the same x or y value. Thanks!
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### Elliptic Curve Crypto

I had just read a primer about ECC, I see how it can be complicated. Something I haven't been able to determine is what information does the client machine get to help decrypt the data? The whole ...
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### Probability of an ECM factor

Suppose I have a composite number $N$ divisible by some prime $p\le x.$ What is the probability that one iteration of ECM finds $p$, given parameters B1 and B2? Usually people look for factors in ...
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### Addition a point on an elliptic curve with an integer value

Suppose $Q$ is a point in an elliptic curve such that $Q=dP$ and $d$ is an integer value, and $P$ is base point of that elliptic curve. Note $Q = dP$ means that $P+\cdots+P$ for $d$ times** and since ...
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### Diffie-Hellman key exchange for three user.

Assume that there are three users that have their own secret key $d_i$ and corresponding public key $Q_i = d_i G$ such that $Q_i$ is a point in an elliptic curve. Now I'm looking for a solution to ...
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### Adding points of an elliptic curve over a finite field

I'm a bit confused with how fractions are handled with adding points of elliptic curves over finite fields. Below is an example from the text which I am trying to understand: The part that ...
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### Is Hash(bG) equal to b(Hash(G))?

Assume b is an integer, G is a basepoint in an elliptic curve, and Hash is a one-way hash function. Is Hash(bG) equal to b(Hash(G)) ? or not? Note: A hash function is any algorithm or subroutine ...
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### How do you determine if an elliptic curve over a finite field is cyclic?

I know the group order and the points of the elliptic curve $y^2 = x^3 + Ax + B$, but I am confused on how to determine if they from a cyclic group The curve $y^2 = x^3 + 2x +2$ in $\Bbb F_{11}$ ...
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