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Bitcoin => Development & Technical Discussion => Topic started by: krashfire on January 31, 2023, 05:44:57 AM


Title: secp256k1 formula calculations
Post by: krashfire on January 31, 2023, 05:44:57 AM
Hi, i need help to check my code.

Code:

import ecdsa

z = int(input("Enter value of z: "))
r = int(input("Enter value of r: "))
k = int(input("Enter value of k: "))
s = int(input("Enter value of s: "))

private_key = (z + (r * k)) / s

print("Private Key =", private_key)


and after giving my inputs, i got this output, Private Key = 2.378864885847563e+77
I just wanna make sur.  is my formula written correctly?

and how do i actually read that answer? i tried googling but i cant get an answer on how do I read it as integer.

Title: Re: secp256k1 formula calculations
Post by: garlonicon on January 31, 2023, 06:22:46 AM
It is invalid, because:

1. You have to calculate it modulo "n".
2. The correct formula is "s=(z+rd)/k", so your private key "d" is "(sk-z)/r".

Also, if 256-bit numbers are too big for you to start with, then compute everything on smaller numbers first: https://www.coindesk.com/markets/2014/10/19/the-math-behind-the-bitcoin-protocol/

Title: Re: secp256k1 formula calculations
Post by: witcher_sense on January 31, 2023, 06:31:23 AM
I already have given you  a link to a correct formula in your previous thread:
Quote from: witcher_sense on December 31, 2022, 09:14:16 AM
Quote from: krashfire on December 31, 2022, 06:03:08 AM
What is the formula to calculate private keys if you already have all the R,S,Z(H) K Value? 
Where d= private_key.


d = (k * s - z) * r-1 mod n

Source: https://learnmeabitcoin.com/technical/ecdsa (Why do you need to generate a random point each time? (Mathematical Explanation)
Why not just use it instead of inventing your own?

Also, your resulting private key shouldn't be a floating point number, which is why it is better to use floor division (//) instead of real division ( / ) that always gives you floats (even when you divide intehers without remainder)

Title: Re: secp256k1 formula calculations
Post by: krashfire on January 31, 2023, 06:51:38 AM
Quote from: garlonicon on January 31, 2023, 06:22:46 AM
It is invalid, because:

1. You have to calculate it modulo "n".
2. The correct formula is "s=(z+rd)/k", so your private key "d" is "(sk-z)/r".

Also, if 256-bit numbers are too big for you to start with, then compute everything on smaller numbers first: https://www.coindesk.com/markets/2014/10/19/the-math-behind-the-bitcoin-protocol/
thank you garlonicon. I got this answer from ChatGPT... Damn.

Title: Re: secp256k1 formula calculations
Post by: krashfire on January 31, 2023, 06:52:21 AM
Quote from: witcher_sense on January 31, 2023, 06:31:23 AM
I already have given you  a link to a correct formula in your previous thread:
Quote from: witcher_sense on December 31, 2022, 09:14:16 AM
Quote from: krashfire on December 31, 2022, 06:03:08 AM
What is the formula to calculate private keys if you already have all the R,S,Z(H) K Value? 
Where d= private_key.


d = (k * s - z) * r-1 mod n

Source: https://learnmeabitcoin.com/technical/ecdsa (Why do you need to generate a random point each time? (Mathematical Explanation)
Why not just use it instead of inventing your own?

Also, your resulting private key shouldn't be a floating point number, which is why it is better to use floor division (//) instead of real division ( / ) that always gives you floats (even when you divide intehers without remainder)
Quote from: witcher_sense on January 31, 2023, 06:31:23 AM
I already have given you  a link to a correct formula in your previous thread:
Quote from: witcher_sense on December 31, 2022, 09:14:16 AM
Quote from: krashfire on December 31, 2022, 06:03:08 AM
What is the formula to calculate private keys if you already have all the R,S,Z(H) K Value? 
Where d= private_key.


d = (k * s - z) * r-1 mod n

Source: https://learnmeabitcoin.com/technical/ecdsa (Why do you need to generate a random point each time? (Mathematical Explanation)
Why not just use it instead of inventing your own?

Also, your resulting private key shouldn't be a floating point number, which is why it is better to use floor division (//) instead of real division ( / ) that always gives you floats (even when you divide intehers without remainder)
yeah yeah...I forgot about that ..thanks for reminding.

Title: Re: secp256k1 formula calculations
Post by: krashfire on January 31, 2023, 07:15:42 AM
ChatGPT also gave me this formula to find K nonce Value

Code:
k= (z + r*s) % n

Title: Re: secp256k1 formula calculations
Post by: garlonicon on January 31, 2023, 03:48:56 PM
Quote
Code:
k= (z + r*s) % n
But there is no private key "d" here, so I am certain this formula is invalid. If it would be possible to calculate "k" from publicly known values r,s,z, then you could do that for every signature, and move any coins in this way.

Quote
ChatGPT also gave me this formula
ChatGPT is already banned in Stack Overflow, because of bad answers it gave for technical questions. Who knows, if there will be more such cases here, then maybe we will get "automatically generated post" as one of the reasons to report such posts. Because now, the quality of that bot is far from perfect, and even worse, typical answers seems to be correct, but are often misleading.

Title: Re: secp256k1 formula calculations
Post by: witcher_sense on January 31, 2023, 04:01:45 PM
Quote from: garlonicon on January 31, 2023, 03:48:56 PM
Quote
Code:
k= (z + r*s) % n
But there is no private key "d" here, so I am certain this formula is invalid. If it would be possible to calculate "k" from publicly known values r,s,z, then you could do that for every signature, and move any coins in this way.

Just for reference, the correct formula is the following (we still need private key to obtain nonce value):

k = (z + d * r) * s-1 mod n


Title: Re: secp256k1 formula calculations
Post by: krashfire on January 31, 2023, 07:31:58 PM
Quote from: witcher_sense on January 31, 2023, 04:01:45 PM
Quote from: garlonicon on January 31, 2023, 03:48:56 PM
Quote
Code:
k= (z + r*s) % n
But there is no private key "d" here, so I am certain this formula is invalid. If it would be possible to calculate "k" from publicly known values r,s,z, then you could do that for every signature, and move any coins in this way.

Just for reference, the correct formula is the following (we still need private key to obtain nonce value):

k = (z + d * r) * s-1 mod n




Just to be sure, I again ask ChatGPT

Code:

The mathematical formula to calculate k nonce from r,s,z signatures is:

k = (z + r*s) / s mod n 

where n is the order of the elliptic curve.

Yeah


This forum should ban CHATGPT as well.

Title: Re: secp256k1 formula calculations
Post by: Critical_Thoughts on February 01, 2023, 08:23:08 AM
OP you need to understand chatGPT is not a computational operated model, it just generates answers based on a limited database, we don't know the source of it's outputs, they could be wrong in many cases. chatGPT is an experimental project, don't expect much from it.

Title: Re: secp256k1 formula calculations
Post by: NotATether on February 02, 2023, 04:45:51 AM
Quote from: garlonicon on January 31, 2023, 03:48:56 PM
Quote
Code:
k= (z + r*s) % n
But there is no private key "d" here, so I am certain this formula is invalid. If it would be possible to calculate "k" from publicly known values r,s,z, then you could do that for every signature, and move any coins in this way.

The divisor is also missing here, instead the s is being multiplied instead of divided.

Quote
ChatGPT is already banned in Stack Overflow, because of bad answers it gave for technical questions. Who knows, if there will be more such cases here, then maybe we will get "automatically generated post" as one of the reasons to report such posts. Because now, the quality of that bot is far from perfect, and even worse, typical answers seems to be correct, but are often misleading.

Alternatively you can feed the input of a post into ChatGPT and prompt it to explain why it's a bad bitcointalk post, and you will get an automated report message out of it.


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