Lesson 23 · A multi-block vector and length extension

A multi-block vector and length extension

Today you confirm a longer, two-block message against its official digest through the public API, then meet length extension - a real property of the Merkle-Damgard design that explains why a raw hash is not a message authentication code.

The goal

Hash a two-block message end to end and match the published digest.

Start here - the target

TO DO

Scenario: The 56-byte multi-block vector

Giventhe 56-byte message "abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq" (which pads into two blocks)

Whenit is hashed with Sum256 through padding, blocking, and the compression loop

ThenHex of it is "248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1"

Andthis is a published NIST test vector, and hashing it exercises the full two-block chaining path end to end

Background

This 56-byte message is a published NIST test vector chosen precisely because it crosses a block boundary: as you saw in lesson 11, 56 bytes forces padding into a second block, so hashing it end to end exercises the full chaining path - Compress running twice with the state threaded between. Matching its digest, 248d6a61...19db06c1, confirms your whole pipeline works on real multi-block input, not just the single-block “abc”.

The chaining that makes this work also has a famous consequence worth understanding: length extension. Because the digest is the internal hash state after the last block, anyone who knows Sum256(message) and the message’s length can keep hashing from that state, computing Sum256(message || padding || extra) without knowing the original message. That is why you must never authenticate a message by hashing a secret key in front of it (Sum256(key || message)) - an attacker can extend it. The correct fix is HMAC, a keyed construction built on top of the hash, which is exactly what the next lesson builds.

Make it work

msg := []byte("abcdbcdecdefdefgefghfghighijhijkijkljklmklmnlmnomnopnopq")
want := "248d6a61d20638b8e5c026930c3e6039a33ce45964ff2167f6ecedd419db06c1"
// Hex(msg) == want

CheckpointDONE

Your SHA-256 matches a multi-block NIST vector. Commit and stop here.