Update README.md

Author: helloissac

README.md

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-# sha-256-hash-algorithm-bitcoin-miner
-SHA-256 Cryptographic Hash Algorithm for Bitcoin Miner 
+# SHA-256 Cryptographic Hash Algorithm for Bitcoin Miner
+Description of SHA256: https://eips.ethereum.org/assets/eip-2680/sha256-384-512.pdf
+- An n-bit hash is a map from arbitrary length messages to n-bit hash values. 
+- An n-bit cryptographic hash is an n-bit hash which is one-way and collision-resistant. Such functions are important cryptographic primitives used for such things as digital signatures and password protection.
+- Current popular hashes produce hash values of length n = 128 (MD4 and MD5) and n = 160 (SHA-1), and, therefore can provide no more than 64 or 80 bits of
+security, respectively, against collision attacks. Since the goal of the new Advanced Encryption Standard (AES) is to offer, at its three cryptovariable sizes, 128, 192, and 256 bits of security, there is a need for companion hash algorithms which provide similar levels of enhanced security. 
+- SHA-256 is a 256-bit hash that provides 128 bits of security against collision attacks.
+
+## Overview
+- The Bitcoin miner and SHA256 hashing algorithm were written from scratch in C++.
+- SHA-256 operates in the manner of MD4, MD5, and SHA-1: The message to be hashed is first
+  - (1) padded with its length in such a way that the result is a multiple of 512 bits long, and then
+  - (2) parsed into 512-bit message blocks <i>M</i><sup>1</sup>, <i>M</i><sup>2</sup>,..., <i>M</i><sup><i>N</i></sup></i>
+  - The message blocks are processed one at a time: Beginning with a fixed initial hash value <i>H</i>^0, sequentially compute: 
+    - <i>H</i><sup><i>i</i></sup> = <i>H</i><sup>(<i>i</i>-1)</sup> + <i>C</i><sub><i>M</i><sup><i>i</i></sup></sub> (<i>H</i><sup>(<i>i</i>-1)</sup>)
+  - where C is the SHA-256 compression function and + means word-wise mod 2<sup>32</sup> addition. <i>H</i><sup>(<i>N</i>)</sup> is the hash of of <i>M</i>
+
+## Function
+The SHA-256 compression function operates on a 512-bit message block and a 256-bit intermediate hash value. It is a 256-bit block cypher algorithm that encrypts the intermediate hash value using the message block as the key. Hence there are two main components to describe: (1) the SHA-256 compression function and (2) the SHA-256 message schedule.
+
+<img src="https://github.com/issacjohannli/sha-256-hash-algorithm-bitcoin-miner/blob/main/diagrams/sha-256-compression-function.png">
+
+## Diagrams
+The SHA-256 compression function is shown below, where the square tile symbols denote mod 2<sup>32</sup> addition.
+
+Figure 1: <i>j</i><sup>th</sup> internal step of the SHA-256 compression function <i>C</i>.
+
+## Sample Hash Computations
+The result of hashing the 24-bit message "abc". After padding, the message becomes (in hexadecimal):\
+61626380 00000000 00000000 00000000 00000000 00000000 00000000 00000000\
+00000000 00000000 00000000 00000000 00000000 00000000 00000000 00000018;\
+and the hash value is\
+ba7816bf 8f01cfea 414140de 5dae2223 b00361a3 96177a9c b410ff61 f20015ad.