gen-define-a-digital-signature-and-give-one-short-worked-example-781b

Define a digital signature and give one short worked example.

# Digital Signature ## Definition A **digital signature** is a mathematical scheme that verifies the authenticity and integrity of a digital message or document. It provides: - **Authentication** (proves who sent it) - **Integrity** (proves it wasn't altered) - **Non-repudiation** (sender cannot deny signing it) It works like a handwritten signature but uses cryptographic techniques (typically public-key cryptography). ## Short Worked Example (RSA-based) **Setup:** - Alice chooses primes: p = 11, q = 13 - n = p × q = 143 - φ(n) = (11-1)(13-1) = 120 - Public key: e = 7 - Private key: d = 103 (since 7 × 103 ≡ 1 mod 120) **Signing:** 1. Alice's message: m = 5 2. Alice signs: s = m^d mod n = 5^103 mod 143 = **47** 3. Alice sends: (message: 5, signature: 47) **Verification:** 1. Bob receives (5, 47) 2. Bob verifies: s^e mod n = 47^7 mod 143 = **5** ✓ 3. Since 5 matches the original message, the signature is valid! If anyone altered the message or signature, the verification would fail, proving tampering occurred.