Step by Step solution about How to resolve the algorithm Bitcoin/address validation step by step in the Mathematica / Wolfram Language programming language

Purpose: The provided Wolfram code is an implementation of a hashing algorithm for converting an input string into a 32-byte hashed value. It operates on the principle of converting an input string to a sequence of integers, hashing that sequence twice using SHA256, and extracting the first 32 bytes of the double-hashed result as the final hash.

Detailed Explanation:

Step 1: Character Conversion

• The chars variable contains a string of characters from '1' to 'z' (excluding 'I', 'l', and 'O').
• For each character in the input string, the StringPosition function finds its position in the chars string.
• The position is decremented by 1 to produce an integer value between 0 and 61.

Step 2: Integer Digits

• The list of integer values generated in Step 1 is converted to a base-58 integer using IntegerDigits.

Step 3: First Hash

• The base-58 integer is converted back to a string using FromDigits.
• The resulting string is hashed using the SHA256 algorithm with a 256-bit output size.

Step 4: Second Hash

• The first 32-bit (4-byte) portion of the first hash is converted to a string.
• The string is hashed again using SHA256.

Step 5: Final Hash

• The first 32-bit portion of the second hash is extracted. This is the final hash result.

Step 6: Comparison

• The final 32-bit hash result is compared to the 32-bit hash calculated from the first 32-bit portion of the first hash. They should be equal if the algorithm is working correctly.

Note:

• The purpose of excluding 'I', 'l', and 'O' in the chars string is to avoid confusion with '1', '0', and 'l' in the output string.
• The choice of a base-58 integer representation is arbitrary and could be replaced with other base representations.
• The use of double hashing with SHA256 is for increased security by reducing the likelihood of hash collisions.

chars = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"; data = 
 IntegerDigits[
  FromDigits[
   StringPosition[chars, #][[1]] - 1 & /@ Characters[InputString[]], 
   58], 256, 25];
data[[-4 ;;]] == 
 IntegerDigits[
   Hash[FromCharacterCode[
     IntegerDigits[Hash[FromCharacterCode[data[[;; -5]]], "SHA256"], 
      256, 32]], "SHA256"], 256, 32][[;; 4]]