Ch2. Cryptography — The Mathematics of Secrets

Cryptographic Goals

Cryptography achieves four security objectives:

Confidentiality: Data is unreadable to unauthorized parties
Integrity: Tampering is detectable
Authentication: Identity is verifiable
Non-repudiation: Actions cannot be later denied

Symmetric Encryption

Same key for encryption and decryption. Fast but has key distribution problem.

Algorithm	Key Length	Status
DES	56-bit	Broken (retired)
3DES	112/168-bit	Legacy
AES-128	128-bit	Current standard
AES-256	256-bit	Maximum strength

Asymmetric Encryption

Public key (encrypt) + Private key (decrypt) pair. Slow but solves key distribution.

Sender: Encrypt with recipient's public key
Recipient: Decrypt with their own private key

Algorithms:

RSA: Most widely used, based on integer factorization difficulty
ECC (Elliptic Curve): Same security with smaller keys
Diffie-Hellman: Key exchange protocol

Hybrid encryption (TLS pattern): Asymmetric is too slow for bulk data. In practice: use asymmetric to exchange a session key, then encrypt all data with fast symmetric (AES). This is exactly how TLS works.

Hash Functions

One-way function: Input → Fixed-length output (digest). Not reversible.

Properties: Deterministic, avalanche effect (1-bit input change → completely different output), collision resistance.

Algorithms:

MD5: 128-bit, broken (collisions found)
SHA-1: 160-bit, deprecated
SHA-256/SHA-3: Current standard

PKI (Public Key Infrastructure)

Trust system for issuing and managing digital certificates.

CA (Certificate Authority): Issues and signs certificates. Root CA → Intermediate CA → End-Entity Certificate

Digital certificate (X.509): Public key + Owner info + CA signature.

Digital signatures:

Sender: Hash document → Sign with private key
Recipient: Verify signature with public key → Confirms integrity + authentication + non-repudiation

Key Concept Cards

Symmetric vs. Asymmetric ★★★★★ : Symmetric=fast (AES, data encryption), Asymmetric=slow (RSA, key exchange). TLS combines both.

Hash Functions ★★★★★ : One-way, fixed-length output. SHA-256 is the current standard. MD5/SHA-1=broken.

PKI and Digital Signatures ★★★★★ : CA vouches for public key authenticity. Digital signatures = integrity + authentication + non-repudiation.

Practice Quiz

Q1. To verify a received file hasn’t been tampered with, what cryptographic tool do you use?

Hash function. The sender computes a SHA-256 hash of the file and transmits it alongside the file. The recipient recomputes the hash upon receipt and compares. A match confirms integrity. No encryption is needed for integrity verification — hashing alone suffices.

Q2. Why do digital signatures provide non-repudiation?

A digital signature uses the signer’s private key — a key only they possess. The resulting signature mathematically proves the signer created it. To deny signing, the signer would have to claim their private key was stolen, which is difficult to establish retroactively. This is what makes digital signatures legally binding in many jurisdictions.