Lesson 15 · Expanding the full schedule - Build SHA-256 from Scratch

Expanding the full schedule

Applying the recurrence 48 times fills out the complete 64-word message schedule for a block. Today you wrap it in one function and pin the last word for the "abc" block.

The goal

Expand a 64-byte block into the full 64-word message schedule W0 through W63.

Start here - the target

TO DO

Scenario: The full schedule for the "abc" block

Giventhe "abc" block and the recurrence from the previous lesson

WhenExpandSchedule(block) returns all 64 words, W[0..15] read from the block and W[16..63] grown by the recurrence in order

Thenthe array has exactly 64 words, with W[0] still 0x61626380 and W[16] still 0x61626380

Andthe final word W[63] is 0x12b1edeb

Background

Growing the schedule is just applying last lesson’s recurrence in a loop from t = 16 to t = 63, each step reading four words that already exist. Because the words are computed strictly in order, every reference W[t-2], W[t-7], W[t-15], W[t-16] points at a word filled earlier in the same loop - the recurrence never looks ahead. Sixteen seed words in, sixty-four words out.

This is the per-block input the compression function will consume: one schedule word per round. Pin the tail, W[63] = 0x12b1edeb, because it depends on the entire chain of 48 recurrence steps - if any small sigma amount, index offset, or modular add is off anywhere along the way, this last word will not match. Getting W[63] right for the “abc” block is strong evidence the whole schedule is correct before you build the rounds that rely on it.

Make it work

func ExpandSchedule(block []byte) [64]uint32 {
  var w [64]uint32
  first := MessageWords(block)
  copy(w[:16], first[:])
  for t := 16; t < 64; t++ {
    // w[t] = SmallSigma1(w[t-2]) + w[t-7] + SmallSigma0(w[t-15]) + w[t-16]
    // (fill in, all mod 2^32)
  }
  return w
}

CheckpointDONE

You can expand a block into its full 64-word schedule. The schedule is complete. Commit and stop here.