Paper Implementation : SHA-256 NSA Patent Whitepaper

Implementing the patented National Security Agency official SHA 256 paper

Official SHA-256 Paper Frontpage

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Introduction

It’s 2025, and the President of the United States has just launched a Solana meme coin called $TRUMP. Bitcoin is making a comeback, and so it’s time to dive into the SHA-256 hash function, the backbone of Bitcoin’s value.

$TRUMP Meme Coin from Donald Trump’s Official Twitter Account

SHA-256, or Secure Hash Algorithm 256-bit, was developed in 2001 by the National Security Agency (NSA). The official patent for SHA-256 is held by Glenn Lilly, who served as the director of the NSA’s mathematical research group.

Official Patent for SHA-256 awarded to NSA Director Glenn M. Lilly

Part 1 : Important Definitions

Definitions from the SHA-256 white paper

From the paper, SHA-256 utilizes these boolean and arithmetic operations:

• AND denoted by ∧.

• XOR denoted by ⊕.

• OR denoted by∨.

• Bitwise complement denoted by ¯.

• Integer addition denoted by A + B.

• Circular Right Shift of A by n bits. RotR(A, n)

• Regular Right Shift of A by n bits. ShR(A, n)

• Concatenation of Integers denoted by A || B

SHA-256 makes use of thse contants:

• The first 32 bits of the fractional parts of the cube roots of the first 64 prime numbers.

NOTE

• All integer operations are perfomed within the range 0 and 2^32. Upo overflow, the operations wrap around like a finite field

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Section goals

1. Implement Regular Right Shift.

2. Implement Circular Right Shift.

3. Create an array of constants.

4. Implement LittleToBig endian conversion function

Function 1 : RegularRightShift Coding Guide + Solution

1. Write a function called RegularRightShift.

2. The function takes two inputs.

• An unsigned integer called A.

• An unsigned integer called n.

3. The function should return an unsigned integer.

4. The function shifts an integer A to the right, by n bits .

• Depending on your language choice, this could be a simple >> or integer division by 2 for n times.