Linked Questions

8 votes
2 answers
9k 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 ...
Iñaki Viggers's user avatar
8 votes
2 answers
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 ...
SDL's user avatar
  • 1,887
8 votes
1 answer
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 ...
Andy's user avatar
  • 181
3 votes
2 answers
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 ...
inherithandle's user avatar
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
982 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
3 votes
1 answer
1k views

Verify that a point belongs to secp256r1

I need to verify that the point in this public key ...
Anonymous's user avatar
1 vote
1 answer
899 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: ...
Steven's user avatar
  • 13
3 votes
2 answers
356 views

Could a EC public key have zero coordinate?

Take secp256r1 as an example, the parameter of the curve is ...
Jin.J's user avatar
  • 133
1 vote
1 answer
337 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
673 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
3 votes
1 answer
512 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 [4]P = (19 , 20) [8]P = (12 , 17) If we only have the value of $[8]P$, Is it ...
Lordi's user avatar
  • 53
1 vote
1 answer
163 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 ...
WeCanBeFriends's user avatar
1 vote
2 answers
399 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 $Q = aG$...
Rozwrcd's user avatar
  • 19
1 vote
1 answer
266 views

ECDH public keys restrictions

I know that Bob can calculate the shared DH key without knowing the private key. If he sends to Alice a public key = 1, then the the DH key would be 1. Can i achieve something like this in ECDH? where ...
Ashraf Yassin's user avatar

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