8k views

### In elliptic curve, what does the point at infinity look like?

We know that for each point $P$ on curve $E$ there exists a minimum scalar $k$ such that $kP$ equals the point at infinity. And the book Cryptography Theory and Practice by Douglas R. Stinson only ...
2k views

### How is the x coordinate of a "point at infinity" encoded in a Secp256k1 signature?

I'm testing an implementation of Bitcoin, which uses the curve Secp256k1 for ECDSA, and I want to see how it handles the point at infinity ($0$) if present in a signature. For example, r could be the ...
3k views

### How to represent point-at-infinity in affine coordinate

In projective coordinates point-at-infinity can be identified with z=0. How to identify the point-at-infinity in affine coordinate. Whether x=0 and y=0 can be considered as point-at-infinity in ...
2k views

### Can you tell me why doing scalar multiplication of a point on a Elliptic curve over a finite field gets to a point at infinity?

I am reading Programming Bitcoin. The author said: Another property of scalar multiplication is that at a certain multiple, we get to the point at infinity (remember, the point at infinity is the ...
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?
830 views

### Problem with point addition about [n-1]+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 ...
910 views

### Verify that a point belongs to secp256r1

I need to verify that the point in this public key ...
1 vote
683 views

### Proof that user public key corresponds the curve equation (secp256r1)

I'm currently stuck at a problem, where I'm supposed to proove that the user public key of a returned u2f token corresponds to an elliptic curve equation (secp256r1). The token looks as follows: ...
1 vote
312 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. ...
1 vote
529 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 ...
229 views

### Could a EC public key have zero coordinate?

Take secp256r1 as an example, the parameter of the curve is ...
1 vote
379 views

### How does this formula work $(aG + bG) = (a + b) G$ in ECDSA?

Please explain how does this formula $(aG + bG) = (a + b) G$ work in ECDSA? According to the source: $a$ and $b$ are different private keys Suppose $a = 3$ $b = 4$ then the public key is $Q = aG$...
378 views

### Is it possible to calculate multiplication inverse of a point on elliptic curve?

The title must be confusing. Imagine we have this curve: $y^2 = x^3 + 9x + 17$ over $\mathbb F_{23}$ And we know P = (19 , 20) P = (12 , 17) If we only have the value of $P$, Is it ...
1 vote
136 views

### What is the order of the Identity point on prime order elliptic curve groups?

I'm trying to understand how the identity point is represented in a group of prime order. What I think is correct: If the group has even order, then the identity point is in the group, because the ...
1 vote