In Part 1, we explained the padding step of SHA-256.

In this part, we move to the next step: the Message Schedule.

┌───────┐    ┌─────────┐    ┌──────────────────┐    ┌──────────────┐    ┌──────┐
│ Input │ -> │ Padding │ -> │ Message Schedule │ -> │ Compression  │ -> │ Hash │
└───────┘    └─────────┘    └──────────────────┘    └──────────────┘    └──────┘
                 ↑                    ↑
             Part 1               Part 2 (current)

Reminder:Reminder:

After padding, the message becomes a single 512-bit block.

Now this block goes into the message schedule step.

Input ("bitcoin")
        │
        ▼
┌─────────┐ ---> ┌────────────────────────────────────┐ ---> ┌──────────────────┐
│ Padding │ ---> │ 512-bit padded block               │ ---> │ Message Schedule │
└─────────┘ ---> └────────────────────────────────────┘ ---> └──────────────────┘
                 │  01100010011010010111010001100011  │
                 │  01101111011010010110111010000000  │
                 │  00000000000000000000000000000000  │
                 │  00000000000000000000000000000000  │
                 │  00000000000000000000000000000000  │
                 │  00000000000000000000000000000000  │
                 │  00000000000000000000000000000000  │
                 │  00000000000000000000000000111000  │

Step 1: Split Block Into WordsStep 1: Split Block Into Words

The padded block has:
512 bits total

We split it into:
16 pieces

Each piece is:
32 bits

And each piece is called a word.

So we get: W0, W1, W2, ..., W15

These come directly from the padded message.

w0 = 01100010011010010111010001100011
w1 = 01101111011010010110111010000000
w2 = 00000000000000000000000000000000
w3 = 00000000000000000000000000000000
w4 = 00000000000000000000000000000000
w5 = 00000000000000000000000000000000
w6 = 00000000000000000000000000000000
w7 = 00000000000000000000000000000000
w8 = 00000000000000000000000000000000
w9 = 00000000000000000000000000000000
w10 = 00000000000000000000000000000000
w11 = 00000000000000000000000000000000
w12 = 00000000000000000000000000000000
w13 = 00000000000000000000000000000000
w14 = 00000000000000000000000000000000
w15 = 00000000000000000000000000111000

Step 2: Notice We Need More WordsStep 2: Notice We Need More Words

The compression step needs:

W0 → W63 (64 words total)

But we only have:
W0 → W15

So we must compute 48 additional words:
W16 → W63

Step 3: How New Words Are BuiltStep 3: How New Words Are Built

Each new word is computed from four earlier words

So every new word depends on previous schedule values.

Example for W16:
W16 = W0 + σ0(W1) + W9 + σ1(W14)

We reuse earlier words to generate new ones.

Step 4: Bit Mixing Functions σ0 and σ1Step 4: Bit Mixing Functions σ0 and σ1

The functions σ0 and σ1 mix bits using rotations and shifts:

σ0(x) = ROTR7(x) XOR ROTR18(x) XOR SHR3(x)
σ1(x) = ROTR17(x) XOR ROTR19(x) XOR SHR10(x)

These operations spread information across bits.

Check https://hashexplained.com/ for more details about σ0 and σ1

Step 5: General Rule for All Remaining WordsStep 5: General Rule for All Remaining Words

All later words are computed using:

W[t] = W[t-16] + σ0(W[t-15]) + W[t-7] + σ1(W[t-2])

Repeat this until: W63 is computed

After computing everything:

w16 = 10111000111111010101100100111010
w17 = 01101111100001000110111010000000
w18 = 00000111100101000011010000110111
w19 = 10111010100010111101101100101001
w20 = 10011100100111001000011000110101
w21 = 10010110110111110100100011100010
w22 = 11010011111110110101101100110100
w23 = 00000110010001100000011110100000
w24 = 00110110010011000111101111010100
w25 = 11001010101110011100011010100001
w26 = 01101101001010001110101000011010
w27 = 01111000010100101111100010101111
w28 = 11111111001101000111100111101101
w29 = 11110111010101111010001011010001
w30 = 00101010010010001001010100001001
w31 = 10001111011111001000110001011111
w32 = 11110010011101011110000100001111
w33 = 00011000001001011011000100010111
w34 = 01111111011011111100100101100011
w35 = 10000001100101111000101001111101
w36 = 10110111010001010010011011101000
w37 = 10011010100011101001110000110100
w38 = 01011100001010001101000100000000
w39 = 01000110110001101000000001111110
w40 = 11101100100100111001011010000111
w41 = 11011110010001001100000111111100
w42 = 10011000001110011100100011000101
w43 = 00000010111100100001110101110100
w44 = 11001100110011111010111001010100
w45 = 11010010111101000111101010001010
w46 = 00100001110010010110110011101000
w47 = 10101000000110100101110010011110
w48 = 10101110000011010100010011011010
w49 = 01010001101000011111101011011010
w50 = 10010110111011100010011010101011
w51 = 10011110110001010100011010101100
w52 = 00111111010010001000101110110010
w53 = 00000111011110011101001110001111
w54 = 10101101001011101000010011001011
w55 = 11000000011101100011000101011000
w56 = 10100011000110001010000000100001
w57 = 00111101111100000111101011100111
w58 = 11101010010000011101101001100000
w59 = 11001111111100000000100000100011
w60 = 10111011111010100100110100011010
w61 = 00010100100010100001100010001111
w62 = 00010000101101010110001110000111
w63 = 10001100001100010110000010100010

At this point, the message schedule is complete.

Next StepNext Step

Now the 64 words are ready.

They are passed into the compression function, which produces the final hash state.

┌───────┐    ┌─────────┐    ┌──────────────────┐    ┌──────────────┐    ┌──────┐
│ Input │ -> │ Padding │ -> │ Message Schedule │ -> │ Compression  │ -> │ Hash │
└───────┘    └─────────┘    └──────────────────┘    └──────────────┘    └──────┘
                 ↑                    ↑                     ↑
             Part 1                Part 2               Part 3 (next)

SummarySummary

Padding step ✔
Message schedule ✔
Next: Compression step

Learn MoreLearn More

You can see the message schedule step animated here:

https://hashexplained.com