Dockeyhunt Private Key Calculator

The software running the formula for calculating the private key X to a Bitcoin wallet looks like this:

X=hex(((S⋅K−Z)⋅modinv(R,N))modN)

• S  and  R  are the values ​​from the transaction signature (RawTX).
• Z  is the transaction signature hash.
• K  is the secret key (nonce).
• N  is the order of the elliptic curve group.
• modinv( R , N ) is the modular inverse function of  R  modulo  N .

Explanation of the formula

1. Input parameters :
   • S  and  R : These values ​​are obtained from the transaction signature. They are needed to recover the private key.
   • Z : This is the signature hash, which is also used in the process.
   • K : A secret key (nonce) that should only be known to the wallet owner.
2. Calculations :
   • First we  multiply S  by  K.
   • Then we subtract  Z .
   • The result is multiplied by the modular inverse  of R  modulo  N . This allows us to “cancel” the influence of  R to obtain a value that can be used to calculate the private key.
   • Finally, the result is taken modulo  N to ensure that it is within the acceptable range for private key values.
3. Convert to hexadecimal format :
   • After all the mathematical operations are performed, the result is converted to hexadecimal format using the function  hex(), which is the standard representation of private keys in Bitcoin.

We examined the formula X=hex(((S⋅K−Z)⋅modinv(R,N))modN)  using the software Dockeyhunt Private Key Calculator to compute the private key X for a Bitcoin wallet. Additionally, we explained in detail all the input parameters and steps necessary for its application, including the values S and R, which are extracted from the transaction signature, the hash of the signature Z, the secret key K, and the order of the elliptic curve group N. Each step of the calculations, starting from multiplying S by K and ending with converting the result into hexadecimal format, was described to ensure a complete understanding of the process. The modular inverse function used in the formula plays a crucial role in recovering the private key by allowing us to “cancel out” the influence of the value R.

Understanding how a private key is calculated is an important aspect of working with Bitcoin and cryptocurrencies in general. This information can be useful for both developers and users who want to gain a deeper understanding of how the Bitcoin blockchain works.