How do you perform double-SHA-256 encoding?

Question

The Bitcoin Protocol-specification gives an example of double-SHA-256 encoding.

hello
2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824 (first round of sha-256)
9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50 (second round of sha-256)

I've tried various SHA256 calculators and the first encoding matches no problem, but the second always resolves to

d7914fe546b684688bb95f4f888a92dfc680603a75f23eb823658031fff766d9

I've also tried UPPERCASE and swapping the byte endianness.

Answer 1

You're hashing the hexadecimal representation of the first hash. You need to hash the actual hash -- the binary data that the hex represents.

Try this:

$ echo -n hello |openssl dgst -sha256 -binary |openssl dgst -sha256

Answer 2

You want to work with the digests, not the hex strings.

Here's some Ruby:

require 'digest'
d = Digest::SHA2.new 256
d2 = Digest::SHA2.new 256
d << 'hello'
d.to_s
d2 << d.digest
d2.to_s

This will be the output from irb:

1.9.3p194 :001 > require 'digest'
 => true 
1.9.3p194 :003 >   d = Digest::SHA2.new 256
 => #<Digest::SHA2:256 e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855> 
1.9.3p194 :004 > d2 = Digest::SHA2.new 256
 => #<Digest::SHA2:256 e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855> 
1.9.3p194 :005 > d << 'hello'
 => #<Digest::SHA2:256 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824> 
1.9.3p194 :006 > d.to_s
 => "2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824" 
1.9.3p194 :007 > d2 << d.digest
 => #<Digest::SHA2:256 9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50> 
1.9.3p194 :008 > d2.to_s
 => "9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50"

Here's the same thing in Python:

import hashlib
d = hashlib.sha256(b"hello")
d2 = hashlib.sha256()
d.hexdigest()
d2.update(d.digest())
d2.hexdigest()

And the output from within a Python shell:

>>> d = hashlib.sha256(b"hello")
>>> d2 = hashlib.sha256()
>>> d.hexdigest()
'2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824'
>>> d2.update(d.digest())
>>> d2.hexdigest()
'9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50'

Answer 3

For the second round of sha256, you need to hash the raw binary output from the first round, not the textual version.

A sha256 hash is 256 bits, or 32 bytes. Thus for the second round you should be hashing a piece of data that's 32 bytes. When hashing a hexadecimal string as the literal input for the second round, your data is 64 bytes.

Try a hashing tool that can interpret hexadecimal input. For example see here, copy/paste the hash to the input field and check the 'Hex' checkbox.

Answer 4

For easy reference, lets name the various inputs and outputs from your question like so:

pre-image 1:                     hello
                                   |
                                   v
hash operation 1:                SHA256
                                   |
                                   v
hash output 1 (aka pre-image 2): 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824
                                   |
                                   v
hash operation 2:                SHA256
                                   |
                                   v
hash output 2:                   9595c9df90075148eb06860365df33584b75bff782a510c6cd4883a419833d50

Pre-image 1 is binary (ASCII) data. We know this because the range of hexadecimal characters is 0-9 and a-f, and there are characters beyond f in pre-image 1. So hash operation 1 must be performed using a binary input.

By definition, a SHA256 hash operation always produces a 256 bit integer. We typically represent this in hexadecimal format, however it could just as correctly be written in decimal format and nothing would change:

hex:     2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824
decimal: 20329878786436204988385760252021328656300425018755239228739303522659023427620

(Decimal conversion using Wolfram Alpha)

Since we know that pre-image 2 is a hexadecimal number, then hash operation 2 must be performed upon a number, rather than upon binary data.

In Javascript, using the Stanford Javascript Crypto Library, the two hashes would be done like so:

var preImage1 = 'hello';
var hashOutput1 = sjcl.hash.sha256.hash(preImage1);
console.log('hash output 1: ' + sjcl.codec.hex.fromBits(hashOutput1));
var preImage2 = hashOutput1;
var hashOutput2 = sjcl.hash.sha256.hash(preImage2);
console.log('hash output 2: ' + sjcl.codec.hex.fromBits(hashOutput2));

The SJCL is clever enough to figure out the pre-image formats and perform the hash correctly in each case.

You can also do these hash operations live on my blog, here: https://analysis.null.place/how-do-the-bitcoin-mining-algorithms-work/#form10

Note how the hash output changes when you click the pre-image is hexadecimal checkbox (this only works when hexadecimal characters are present in the input).

Answer 5

Late to the party, but here is a Node.js implementation using the built-in crypto module:

const crypto = require('crypto');
/**
 *
 * @param {Buffer} data
 * @returns {Buffer}
 */
function doubleSHA256(data) {
  return crypto.createHash('sha256').update(crypto.createHash('sha256').update(data).digest()).digest();
}