<blockquote>
<p>Let's say I found (I know, impossible) public key factors.</p>
</blockquote>
<p>Bitcoin public keys are coordinates of points on the secp256k1 elliptic curve. They are not integers, and thus factoring is not an operation that applies to them.</p>
<blockquote>
<p>What to do with them next to compute original private key for that public key?</p>
</blockquote>
<p>Bitcoin's (ECDSA) security is based on the hardness of computing the discrete logarithm of points on the secp256k1 curve, not on the difficulty of factoring large integers (like e.g. the RSA algorithm is). Having access to a fast integer factorization algorithm will not in any way help you compute private keys of Bitcoin public keys quickly.</p>

CC BY-SA 4.0
2023-09-29T20:16:47.887Z
Can you say what to do, not what is impossible?
pbies
CC BY-SA 4.0
2023-09-29T20:17:29.077Z
There is nothing to do. Factorization is just entirely unrelated to Bitcoin's security. This isn't a question of "hard" or "impossible"; the word "factorization" just has no meaning w.r.t. Bitcoin public keys.
Pieter Wuille
CC BY-SA 4.0
2023-09-29T20:05:46.280Z
2023-09-29T20:05:46.280Z
Pieter Wuille
<p>Let's say I found (I know, impossible) public key factors. What to do with them next to compute original private key for that public key?</p>

<private-key><public-key><cryptography><attack>
Public key factors - but what's next?
pbies
# Public key factors - but what's next?

(Asked by: username_0 on 2023-09-29)

Let's say I found (I know, impossible) public key factors. What to do with them next to compute original private key for that public key?

**Tags:** private-key, public-key, cryptography, attack


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## 1 answers

### Answer by username_1 on 2023-09-29. Score: 2

> Let's say I found (I know, impossible) public key factors.

Bitcoin public keys are coordinates of points on the secp256k1 elliptic curve. They are not integers, and thus factoring is not an operation that applies to them.

> What to do with them next to compute original private key for that public key?

Bitcoin's (ECDSA) security is based on the hardness of computing the discrete logarithm of points on the secp256k1 curve, not on the difficulty of factoring large integers (like e.g. the RSA algorithm is). Having access to a fast integer factorization algorithm will not in any way help you compute private keys of Bitcoin public keys quickly.

> **Comments:**
> **username_0**: Can you say what to do, not what is impossible?  
> **username_1**: There is nothing to do. Factorization is just entirely unrelated to Bitcoin's security. This isn't a question of "hard" or "impossible"; the word "factorization" just has no meaning w.r.t. Bitcoin public keys.  

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