How Does SHA-256 Work? @learnmeabitcoin

learnmeabitcoin An explanation of how SHA-256 works, with animations of the operations used inside the hash function.

I'm not a cryptographer though, so I can't explain the reasons behind the design (at the moment).

00:00 - Introduction
↳ 02:20 - Bitcoin Mining
05:05 - Basic Operations
08:27 - Functions
10:58 - Constants
12:23 - Hash Computation
↳ 12:41 - Message
↳ 13:19 - Padding
↳ 14:24 - Message Blocks
↳ 14:58 - Message Schedule
↳ 17:42 - Compression
↳ 22:30 - Final Hash Value

Source code for animations (and text guide): github.com/in3rsha/sha256-animation

Official specification: nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf

====
FAQs:
====

=== What setup are you using for your computer? ===

* Operating System = Ubuntu (Xubuntu)
* Desktop Environment = XFCE
* Appearance Style = Arc-Dark
* Appearance Icons = Papirus-Dark
* Window Manager Style = Numix
* Wallpaper = A simple gradient from dark grey to grey.
* Shell = zsh (using zsh-autosuggestions)
* Terminal Font = Hack Regular

=== How do you work out the constants? ===

The constants are created using the first 32 bits from the fractional part of the cube roots of prime numbers.

For example, the first constant is the cube root of the first prime number (2), so:

∛2 = 1.2599210498948732

The fractional part of this is:

= 0.2599210498948732

However, we want 32 bits' worth of this fractional part. To get these 32 bits, we multiply the fraction by 2^32:

= 1116352408.8404646

The integer part of this is our 32-bit constant, which we can convert to binary:

= 1116352408
= 0b01000010100010100010111110011000

Here's some code showing how it works: github.com/in3rsha/sha256-animation/blob/master/constants.rb

=== How does the padding work if my message is X bits in length? ===

Lets say we have a message that is exactly 448 bits.

We always need to include the `1` separator and the 64 bit message size in the padding, which takes the message+padding up to 513 bits. This exceeds the 512 bit message block size we're after, so we pad with 511 zeros to take us up to 1024 bits (the next multiple of 512).

The zeros go between the separator and the size, like so:

[message] [separator] {zeros} [size]

So in other words, if your message and the initial padding takes you beyond the size of a message block, you pad all the way up to the next multiple of 512.

updated 6 years ago

How Does SHA-256 Work?

learnmeabitcoin 2020-05-12 | An explanation of how SHA-256 works, with animations of the operations used inside the hash function.

I'm not a cryptographer though, so I can't explain the reasons behind the design (at the moment).

00:00 - Introduction
↳ 02:20 - Bitcoin Mining
05:05 - Basic Operations
08:27 - Functions
10:58 - Constants
12:23 - Hash Computation
↳ 12:41 - Message
↳ 13:19 - Padding
↳ 14:24 - Message Blocks
↳ 14:58 - Message Schedule
↳ 17:42 - Compression
↳ 22:30 - Final Hash Value

Source code for animations (and text guide): github.com/in3rsha/sha256-animation

Official specification: nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf

====
FAQs:
====

=== What setup are you using for your computer? ===

* Operating System = Ubuntu (Xubuntu)
* Desktop Environment = XFCE
* Appearance Style = Arc-Dark
* Appearance Icons = Papirus-Dark
* Window Manager Style = Numix
* Wallpaper = A simple gradient from dark grey to grey.
* Shell = zsh (using zsh-autosuggestions)
* Terminal Font = Hack Regular

=== How do you work out the constants? ===

The constants are created using the first 32 bits from the fractional part of the cube roots of prime numbers.

For example, the first constant is the cube root of the first prime number (2), so:

∛2 = 1.2599210498948732

The fractional part of this is:

= 0.2599210498948732

However, we want 32 bits' worth of this fractional part. To get these 32 bits, we multiply the fraction by 2^32:

= 1116352408.8404646

The integer part of this is our 32-bit constant, which we can convert to binary:

= 1116352408
= 0b01000010100010100010111110011000

Here's some code showing how it works: github.com/in3rsha/sha256-animation/blob/master/constants.rb

=== How does the padding work if my message is X bits in length? ===

Lets say we have a message that is exactly 448 bits.

We always need to include the `1` separator and the 64 bit message size in the padding, which takes the message+padding up to 513 bits. This exceeds the 512 bit message block size we're after, so we pad with 511 zeros to take us up to 1024 bits (the next multiple of 512).

The zeros go between the separator and the size, like so:

[message] [separator] {zeros} [size]

So in other words, if your message and the initial padding takes you beyond the size of a message block, you pad all the way up to the next multiple of 512.

Bitcoin Lesson | Script

learnmeabitcoin 2018-05-09 | A simple yet full explanation of how the Script language in Bitcoin works.

Includes examples of the most commonly used locking scripts (and unlocking scripts), with animations showing how they are run to unlock bitcoins for spending.

00:38 - Introduction (Catch-up)
06:38 - Basics
↳ 13:52 - Running
↳ 18:02 - Pay To Pubkey (P2PK)
↳ 19:41 - Pay To Pubkey Hash (P2PKH)
↳ 26:45 - Pay To Multisig (P2MS)
↳ 34:32 - Pay To Script Hash (P2SH)
↳ 42:21 - Null Data
45:31 - Non-Standard Scripts
53:37 - Technical Details / Decoding Transaction Data
58:08 - Summary

1:01:33 - Code, Examples, References

* github.com/in3rsha/learnmeabitcoin-code/blob/master/scriptdecoder.rb
* http://learnmeabitcoin.com/glossary/script

* https://en.bitcoin.it/wiki/Script
* github.com/siminchen/bitcoinIDE

Buy me a beer: 3Beer3irc1vgs76ENA4coqsEQpGZeM5CTd

Bitcoin Lesson | Keys & Addresses

learnmeabitcoin 2018-03-09 | A developer's explanation of how Keys & Addresses work in Bitcoin, including a tutorial on how you can create your own. http://learnmeabitcoin.com

00:18 - Outline
02:03 - Introduction (Catch-up)
07:10 - Where do keys come from?
08:28 - Basic Key Generation

10:42 - Private Key
15:37 - Public Key
↳ 22:05 - Digital Signatures
↳ 26:41 - Signing
↳ 31:54 - Verifying
↳ 36:30 - Summary
39:02 - Address
↳ 39:37 - Extra Security (Hash160)
↳ 43:20 - Locking Mechanism
↳ 48:54 - Address

56:48 - Technical Walkthrough
↳ 1:09:35 - Code
↳ 1:11:03 - Example
↳ 1:12:41 - Useful Links

1:13:51 - Outro

Source Code:
http://learnmeabitcoin.com/code/keygenerator.rb.txt

Links:
royalforkblog.github.io/2014/08/11/graphical-address-generator/#learnmeabitcoin
http://www.secg.org/sec2-v2.pdf

Resources:
youtube.com/watch?v=iB3HcPgm_FI

For more simple explanations of how bitcoin works, visit my website: http://learnmeabitcoin.com

If you found this video helpful, please buy me a beer: 3Beer3irc1vgs76ENA4coqsEQpGZeM5CTd

Bitcoin Lesson | Transactions

learnmeabitcoin 2018-01-15 | An explanation of how bitcoin transactions work.

01:27 - Transaction Basics
↳ 08:45 - Change
↳ 12:49 - Graph
↳ 15:10 - Coinbase Transaction
↳ 17:24 - Fees
20:00 - Transaction Data
↳ 35:22 - Signing
↳ 48:20 - Summary
54:20 - Live Example
↳ 1:02:45 - Code

http://learnmeabitcoin.com/code - Transaction Builder & Command-Line Tools

For more simple explanations of how bitcoin works, visit my website: http://learnmeabitcoin.com

If you found this video helpful, please buy me a beer: 3Beer3irc1vgs76ENA4coqsEQpGZeM5CTd

Bitcoin Lesson | Mining

learnmeabitcoin 2017-11-14 | A simple technical explanation of how Mining works in Bitcoin.

00:49 - What is Mining?
08:39 - Hash Function
13:55 - Mining Basics
↳ 23:03 - Target
↳ 28:08 - Mining Simulator
33:20 - Mining Technical
54:46 - Live Coding Example

For more simple explanations of how bitcoin works, visit my website: http://learnmeabitcoin.com

http://learnmeabitcoin.com/code - Mining Simulator & Command-Line Tools
http://learnmeabitcoin.com/glossary/block-header - Block Header

If you found this video helpful, please buy me a beer: 3Beer3irc1vgs76ENA4coqsEQpGZeM5CTd

learnmeabitcoin Live Stream

learnmeabitcoin 2017-10-13 | ...