Linked Questions
22 questions linked to/from What is the point at infinity on secp256k1 and how to calculate it?
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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 ...
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2
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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 ...
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8
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1
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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 ...
- 181
3
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2
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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 ...
- 139
1
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1
answer
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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
3
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1
answer
830
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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 ...
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3
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1
answer
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1
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1
answer
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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:
...
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1
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1
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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
1
answer
529
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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 ...
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3
votes
2
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229
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Could a EC public key have zero coordinate?
Take secp256r1 as an example, the parameter of the curve is
...
- 133
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2
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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 $Q = aG$...
- 19
3
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1
answer
378
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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 ...
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1
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1
answer
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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 ...
- 1,303
1
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1
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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 ...