Stage 3 of 7v2 · e462126c

Message schedule

Expand sixteen initial words into the sixty-four words for each block.

Build it in your language

The tester treats your program as a black box: any language works. These are just the most convenient ones for this project.

Message Schedule Expansion ( $sigma_0$ and $sigma_1$ )

From the initial 16 words ( $W_0 \dots W_{15}$ ), SHA-256 expands the schedule to 64 words ( $W_0 \dots W_{63}$ ) using bitwise rotations and shifts.

Mental Model: Schedule Recurrence Relation

For any index $i \ge 16$ :

W_i = sigma_1(W_{i-2}) + W_{i-7} + sigma_0(W_{i-15}) + W_{i-16} pmod{2^{32}}

Where:

$sigma_0(x) = \text{ROTR}^7(x) \oplus \text{ROTR}^{18}(x) \oplus \text{SHR}^3(x)$
$sigma_1(x) = \text{ROTR}^{17}(x) \oplus \text{ROTR}^{19}(x) \oplus \text{SHR}^{10}(x)$ All additions are modulo $2^{32}$ .

Your Goal in this Stage

Read a JSON object from stdin with op: "schedule-word", previous words, and target index. Compute $W_i$ under "word".

Input Format

json

{
  "op": "schedule-word",
  "words": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24],
  "index": 16
}

Output Format

json

{
  "word": 0
}

Step-by-Step Implementation Guide

Bitwise helpers: Define 32-bit ROTR and SHR.
Define $sigma_0$ and $sigma_1$ : Apply XOR bitwise combinations.
Calculate word: Sum mod $2^{32}$ using >>> 0.
Emit output: Print JSON with word.

Acceptance Criteria

✅ Exact implementation of $sigma_0$ and $sigma_1$ .
✅ Strict modulo $2^{32}$ unsigned arithmetic.

Output and errors

Multiline examples are formatted for readability. Emit compact JSON without optional spaces, with properties in the order shown by the output examples, and a final newline. Keep logs off stdout. Tests compare exact text. Invalid inputs use stderr containing error, empty stdout, and exit 1. Valid inputs exit 0. Serialize integer results as JSON integers.