8.02 Lab 5: Hashing and Signatures

Week 8 · 38 points · about 90 minutes · submit in Canvas

Goal

Work out what a hash proves, what a signature proves, and (the part people get wrong) what neither of them proves. Then compare a shared-secret MAC with a public-key signature and say when you would reach for each.

You run a provided script and change two values in it. No code to write.

Objectives assessed

• 3.3: Compare symmetric and public-key cryptography by key distribution, performance, and typical use.
• 3.4: Verify a digital signature and explain what a verification failure does and does not prove.

(TLO 3)

Time estimate

Step	Time
Step 1: run it	10 min
Step 2: hashing	25 min
Step 3: signing and tampering	30 min
Step 4: MAC vs. signature	25 min
Total	90 min

Before you start

• CyBOK §10.4.3 (printed pages 332-334), hash functions.
• CyBOK §10.6 (printed pages 338-341), public key encryption.
• CyBOK §10.7 (printed pages 341-343), public key signatures.
• Nakov, Practical Cryptography for Developers, the hash functions and digital signatures pages: https://cryptobook.nakov.com/cryptographic-hash-functions
• Download data/sign_demo.py from Canvas Files.
• Needs the cryptography package from Lab 0.

Steps

Step 1: Run it

python3 sign_demo.py

Save the full output. The key pairs and the HMAC secret are generated fresh each run, so your signature and tag values will differ from your classmates'. Your Part 1 digests will not: that is expected, and it is itself worth noticing.

Step 2: What a hash does

Part 1 hashed two messages that differ by one character.

1. Quote both digests and the "Bits that differ" line.
2. The two inputs differ by one character out of twenty. The digests differ in roughly half their bits. Why is that the desired behavior and not a flaw? About 100 words.
3. The script hashed the same input twice and got the same answer. A hash takes no key. Given that, explain in two or three sentences why a hash by itself cannot tell you who wrote a message.
4. Change HASH_INPUT_B so it differs from HASH_INPUT_A by one different character (for example, Transfer $100 to Rob), run again, and paste the new "Bits that differ" number. Then change it to something completely different and paste that number too. What do you notice?
5. Suppose a download page publishes a file and its SHA-256 digest next to it. What attack does that digest stop, and what attack does it not stop? Two or three sentences each. This is the question the rest of the lab answers properly.

Step 3: Signing, tampering, and what verification proves

Part 2 signed a message, verified it, then verified the same signature against a tampered message. Part 3 verified a valid signature against the wrong public key.

1. Quote the Part 2 output: both the valid and the invalid result.
2. The attacker in Part 2 could see the message and the signature, and could change the message. Why can they not just produce a new signature to match? Two or three sentences.
3. Set TAMPERED_MESSAGE equal to SIGNED_MESSAGE and run it again. What does Part 2 print now, and why? Then set it back.
4. Part 3 verified the correct signature over the correct message against a different person's public key, and it failed. State precisely what a successful verification does establish. Two things, both of them narrow. Then state three things it does not establish: the script names them, but write them in your own words with an example for each.
5. The gap this leaves. A signature verifies against a public key. Nothing so far tells you that the public key belongs to the person you think it does. Describe one concrete way an attacker exploits exactly that gap. Name what the attacker has to control to make it work. (Week 10 is about the machinery built to close this gap. You are describing the problem it solves.)

Step 4: Shared secret or key pair

Part 4 produced an HMAC tag and an Ed25519 signature over the same message.

1. Quote both, and note the size of each in bytes.

2. Alice and Bob share an HMAC key. Alice sends Bob a message with a valid tag. Bob later claims Alice authorized a payment; Alice says she did not. Can the tag settle the argument? Explain why or why not, then say what would change if Alice had signed with a private key instead.

3. Key distribution. Fill in this table and explain each number in one sentence:

   Parties, all of whom must talk securely to each other	Shared secrets needed	Key pairs needed
   2
   10
   1,000

4. Public-key operations are far more expensive than symmetric ones. Given the table above, why does nearly every real protocol use both? Two or three sentences, citing CyBOK §10.6 or §10.8.

5. Pick the right tool for each of these and give one sentence of justification:

   • A phone app checking that a firmware update really came from the manufacturer.
   • Two servers inside one company verifying messages on a private link between them.
   • A university proving to a student that a transcript it issued has not been altered.
   • A web session cookie that a server issues and later checks itself.

What to submit

One Canvas submission containing your full first-run output and your numbered answers to Steps 2, 3, and 4, including the modified-run outputs the steps ask for.

Rubric

Row	What is assessed	Points
1	Step 2: digests quoted, avalanche behavior correctly explained, both modified runs shown, and the download-digest question answered on both sides	10
2	Step 3, questions 1-3: outputs quoted, and why the attacker cannot forge a new signature explained correctly	10
3	Step 3, questions 4-5: exactly what verification does and does not establish, with examples, and a concrete attack on the key-identity gap	12
4	Step 4: repudiation question answered correctly, key-distribution table correct, hybrid rationale given, and all four tools chosen with justification	6
	Total	38

AI disclosure

You may use AI tools on this assignment. If you do, add one or two sentences saying which tool and what for, per the AI policy.

The hex values you quote must come from your own run.