Linked Questions

19 votes
1 answer
4k 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 ...
SFlow's user avatar
  • 465
5 votes
3 answers
5k views

What is the point at infinity on secp256k1 and how to calculate it?

I hear that there should be a point at infinity on secp256k1. I wounder how to calculate it and what does it even mean. I tried to calculate it as $P_{inf}=P+(-P)$ but this gives different results for ...
PouJa's user avatar
  • 314
2 votes
2 answers
2k views

Get the parameters of an elliptic curve's equation

I have a binary signed with ECDSA384 and I need to verify it using a particular cryptography library. The first thing that needs to be done is to initialize the EC ...
Dan's user avatar
  • 123
1 vote
1 answer
2k views

How to divide 2 coordinates on elliptic curve? [closed]

On the elliptic curves, there is no divide function, and I need divide coordinates - X/Y, o I need not divide but make (X minus or multiply to "modified" Y). How to modify Y?
Donald's user avatar
  • 53
3 votes
1 answer
936 views

Problem with point addition about [n-1]+[2]G and [n-1]+G on on Secp256k1

I apologize in advance for my question. I am trying to make my own simple Secp256k1 calculator, just addition and subtraction, and one thing keeps confusing me. When I add 2 points, and I know what ...
Franko's user avatar
  • 31
1 vote
1 answer
737 views

elliptic curve multiplication with negative factor

I'm learning the multiplication operation on EC. From most material I can found, the multiplication $nP$ is just: $$nP=P+P+\cdots +P+P$$ For negative factor, i.e. $(-n)P$, by above definition and the ...
qweruiop's user avatar
  • 326
2 votes
1 answer
1k views

What is the difference between anomalous elliptic curve and ordinary elliptic curve?

Probably this is a silly question but an anomalous curves and ordinary curves are the same things?
Renato Borseti's user avatar
1 vote
1 answer
615 views

EC scalar multiplication with zero scalar

Is the elliptic curve scalar multiplication $[n]G$ defined if $n=0$? I saw multiple software implementations with multiple results such that, $[0]G=0$ or $[0]G=G$. This made me wonder, how can i ...
Ashraf Yassin's user avatar
1 vote
1 answer
331 views

Why does point addition work on EC curves?

This may be more of a math question but I cannot find an intuitive answer. On an EC curve why is 2P+2P equal to P+P+P+P? The addition operation seems to a layman as some arbitrary sequence of steps. ...
Frank's user avatar
  • 113
1 vote
1 answer
657 views

Key size and finite fields in ECC (References)

So somehow I know that the key size in ECC is defined over the number of elements in a finite field or that it is almost equivalent to that (Correct me if I am wrong). However, other than on Wikipedia ...
user164324's user avatar
1 vote
1 answer
618 views

Shor's algorithm and ECDSA in Bitcoin - why is finding the private key still difficult when we know the base point?

I'm learning about Shor's algorithm and how it can be applied to break ECDSA. I've clearly missed something basic here - I thought I understood that the challenge ECDSA presented was to find the ...
compp's user avatar
  • 13
1 vote
0 answers
251 views

how calculate 2g ,3g ,

$y^2=x^3+9x+17$ over $\mathbb{F}_{23}$, what is the discrete logarithm $k$ of $Q=(4,5)$ to the base $P=(16,5)$? One (naï­ve) way to find k is to compute multiples of $P$ until $Q$ is found. The first ...
Ramin Najafi's user avatar
0 votes
1 answer
180 views

Fully understanding bitcoin transcation verifying and secp256k1

Hello fellow cryptographers. I have spent last few days trying to understand and find a way to generate secp256k1 private and public keys from scratch, but i failed. I have seen tons of videos and ...
Notaboredguy's user avatar
1 vote
0 answers
116 views

Converting a point in a finite field to its real (x, y) coordinate [closed]

Let curve $A: y^2 = x^3 + 7$ and curve $B: y^2 \equiv x^3 + 7 \pmod{p}$ Curve $B$ is secp256k1, assume the usual parameters for that curve. Let $k$ be any private key, and compute the corresponding ...
enriquejr99's user avatar