Lesson 18 · Running all sixty-four rounds - Build SHA-256 from Scratch

Running all sixty-four rounds

One round becomes the whole compression core by looping it 64 times, feeding round t its own constant K[t] and schedule word W[t]. Today you run the full loop and pin the working-variable state after the last round.

The goal

Run all 64 compression rounds over a block's schedule.

Start here - the target

TO DO

Scenario: Sixty-four rounds over the "abc" schedule

Givenworking variables a..h set to the initial hash values, the full 64-word schedule of the "abc" block, and the 64 round constants

Whenthe round from the previous lesson runs for t = 0 to 63, each using K[t] and W[t]

Thenafter round 63, a is 0x506e3058 and e is 0x5ef50f24

Andthe remaining working variables are b=0xd39a2165, c=0x04d24d6c, d=0xb85e2ce9, f=0xfb121210, g=0x948d25b6, h=0x961f4894

Background

Turning one round into the compression core is nothing more than a 64-iteration loop, but the whole security of SHA-256 lives in that repetition: 64 passes of mixing, each pulling in a different round constant K[t] and a different schedule word W[t], until every output bit depends on every input bit in a way that is practically impossible to run backward. The loop body is exactly last lesson’s round, unchanged, with t indexing both tables.

Pin the end state for the “abc” block: after round 63 the eight working variables are a = 0x506e3058, b = 0xd39a2165, c = 0x04d24d6c, d = 0xb85e2ce9, e = 0x5ef50f24, f = 0xfb121210, g = 0x948d25b6, h = 0x961f4894. These are not the digest yet - they are the fully stirred state that still has to be combined with where it started. That final combination is the next lesson, and it is what makes the whole function a one-way mixing of block into hash.

Make it work

for t := 0; t < 64; t++ {
  t1 := Add32(Add32(Add32(h, BigSigma1(e)), Add32(Ch(e, f, g), K[t])), W[t])
  t2 := Add32(BigSigma0(a), Maj(a, b, c))
  h, g, f = g, f, e
  e = Add32(d, t1)
  d, c, b = c, b, a
  a = Add32(t1, t2)
}

CheckpointDONE

You can run the full 64-round compression core. Commit and stop here.