Digital Signatures
1. What Is a Signature? (beginner — court-proof seal!)
Sign = encrypt HASH with PRIVATE key (!). Verify = decrypt with PUBLIC + compare hashes! Only key-holder could make it (authenticity!) — anyone verifies (public!) — signer can't deny (non-repudiation!).
2. Flow (exam diagram!)
SIGN (Alice): hash m → H(m) → encrypt with PRIVATE → (m, sig)!
VERIFY (Bob): hash received m → H'(m); decrypt sig with PUBLIC → H(m); equal? accept!
Tamper → hashes differ → REJECT! (integrity + source + proof!)
3. Schemes (exam list!)
| Scheme | Hard problem | Note |
|---|---|---|
| RSA sign | factoring | sign hash (PSS padding!) |
| DSA | discrete log | signing-only, smaller! |
| ECDSA | elliptic DL | tiny keys (256-bit ≈ RSA-3072!) |
Always sign HASH (fast + fixed!), never raw message! Random padding/k (RSA-PSS, DSA per-message secret — reuse leaks key!).
4. Direct vs Arbitrated (exam terms!)
Direct: Alice→Bob only (shared trust in keys!). Arbitrated: trusted third party timestamps/witnesses (dispute-proof!).
5. Exam Points
- Sign/verify flow + hash role — 7 marks, very frequent.
- Schemes + non-repudiation vs MAC — 5 marks, favourite contrast.