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 ...
• 465
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 ...
• 314
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 ...
• 123
1 vote
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?
• 53
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 ...
• 31
1 vote
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 ...
• 326
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?
1 vote
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 ...
1 vote
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. ...
• 113
1 vote
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 ...
1 vote
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 ...
• 13
1 vote
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 ...
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 ...