<p>It cannot be done.</p>

<p>Every private key has exactly one public key, and every public key has exactly one address (ignoring compressed/uncompressed or normal vs P2SH address, which do not matter here).</p>

CC BY-SA 3.0
2016-06-16T22:24:29.353Z
any references, so i can prove it?
Albert S
CC BY-SA 3.0
2016-06-16T22:38:30.323Z
@fredsbend That is incorrect. There is an isomorphism between the multiplicative group of integers modulo n (to which the private keys belong) and the elliptic curve group (to which the public keys belong). There is provably exactly one point on the curve for every private key. *However* there are certainly multiple public keys with the same address, although finding them requires finding a hash collision, which is considered computationally infeasible.
Pieter Wuille
CC BY-SA 3.0
2016-06-17T14:29:50.503Z
@fredsbend You might be thinking of public keys with different addresses, which is also possible depending on whether the public key is expressed in compressed format or not.
Jestin
CC BY-SA 3.0
2016-06-16T22:01:12.637Z
2016-06-16T22:01:12.637Z
Pieter Wuille
<p>Nope, impossible.</p>

<p>The address is mathematically derived from the public key. The public key is mathematically derived from the private key.</p>

<p>Hence, there is a deterministic relationship tying the address to the private key. Every private key has exactly one address it belongs to.</p>

<p>Therefore, changing the private key will also change the address.</p>

CC BY-SA 3.0
2016-06-16T22:44:12.827Z
2016-06-16T22:44:12.827Z
Murch
<p>I would like a way to change the private key of a public address, for this you'd of course require the current private key.<br>
Is this at all possible?</p>

<p>I want to prove that it can be done, or prove that it cannot be done.</p>

<private-key><public-key><cryptography>
Changing a private key of a public Bitcoin address
Albert S
# Changing a private key of a public Bitcoin address

(Asked by: username_0 on 2016-06-16)

I would like a way to change the private key of a public address, for this you'd of course require the current private key.  
Is this at all possible?

I want to prove that it can be done, or prove that it cannot be done.

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


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## 2 answers

### Answer by username_1 on 2016-06-16. Score: 3

It cannot be done.

Every private key has exactly one public key, and every public key has exactly one address (ignoring compressed/uncompressed or normal vs P2SH address, which do not matter here).

> **Comments:**
> **username_0**: any references, so i can prove it?  
> **username_1**: @fredsbend That is incorrect. There is an isomorphism between the multiplicative group of integers modulo n (to which the private keys belong) and the elliptic curve group (to which the public keys belong). There is provably exactly one point on the curve for every private key. *However* there are certainly multiple public keys with the same address, although finding them requires finding a hash collision, which is considered computationally infeasible.  
> **username_2**: @fredsbend You might be thinking of public keys with different addresses, which is also possible depending on whether the public key is expressed in compressed format or not.  

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### Answer by username_3 on 2016-06-16. Score: 0

Nope, impossible.

The address is mathematically derived from the public key. The public key is mathematically derived from the private key.

Hence, there is a deterministic relationship tying the address to the private key. Every private key has exactly one address it belongs to.

Therefore, changing the private key will also change the address.


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