Wallet Types:

1. Custodial vs Non-Custodial
   - Custodial: Keys held by third party
   - Non-Custodial: User controls keys

2. Hot vs Cold Wallets
   - Hot: Connected to internet
   - Cold: Offline storage

3. Software Wallets
   - Mobile: Phone apps
   - Desktop: Computer applications
   - Web: Browser-based

4. Hardware Wallets
   - Physical devices
   - Secure element
   - Offline signing

5. Paper Wallets
   - Printed keys
   - Offline storage
   - Physical security

HD Wallet Hierarchy:

Seed (12/24 words)
     │
     ▼
Master Private Key (m)
     │
     ├─── m/0' (Hardened)
     │      │
     │      ├─── m/0'/0 (Address 1)
     │      ├─── m/0'/1 (Address 2)
     │      └─── ...
     │
     ├─── m/1' (Hardened)
     │      │
     │      ├─── m/1'/0 (Address 1)
     │      └─── ...
     │
     └─── m/2' (Hardened)
            │
            └─── ...

BIP-44 Path: m/44'/coin'/account'/change/address_index

Examples:
- Bitcoin: m/44'/0'/0'/0/0
- Ethereum: m/44'/60'/0'/0/0
- Solana: m/44'/501'/0'/0/0

Master Key Generation:
1. Seed → HMAC-SHA512 → Master Private Key
2. Master Private Key → Extended Key (xprv)

Child Key Derivation (BIP-32):
1. Parent Key + Chain Code + Index
2. HMAC-SHA512 → Child Key + Chain Code
3. Child Private Key: (parent + hash) mod n
4. Chain Code: Used for further derivation

Hardened vs Normal:
- Hardened: Uses parent private key
- Normal: Uses parent public key
- Hardened: More secure (no parent key exposure)
- Normal: Public derivation possible

BIP-39 Word List (2048 words):
- Carefully chosen list
- 3-8 characters per word
- Unique prefixes (4 letters)
- Language-specific lists

Examples (English):
abandon, ability, able, about, above, absent, absorb, abstract, abuse...

Mnemonic Generation:

1. Generate entropy:
   - 12 words: 128 bits entropy
   - 24 words: 256 bits entropy

2. Add checksum:
   - 12 words: 4 bits checksum
   - 24 words: 8 bits checksum

3. Map to words:
   - 11 bits per word
   - Lookup in word list

4. Seed Generation (PBKDF2):
   - Key: mnemonic phrase
   - Salt: "mnemonic" + passphrase
   - Iterations: 2048
   - HMAC-SHA512
   - Output: 512-bit seed

5. Add passphrase (optional):
   - Additional security layer
   - Different passphrase = Different wallet
   - "25th word"

Security Model:
- Private Key: Access to funds
- Seed Phrase: Backup and recovery
- Passphrase: Additional security

Threats:
1. Private key theft (malware, phishing)
2. Seed phrase compromise (physical, digital)
3. Side-channel attacks
4. Social engineering
5. Physical theft

Protection Layers:
1. Encryption (password protected)
2. Hardware security (secure element)
3. Multi-factor authentication
4. Multi-signature (M-of-N)
5. Time locks (delayed transactions)

Hardware Wallet Architecture:

┌─────────────────────────────────────────────────────────────────────┐
│                     Hardware Wallet                               │
│                                                                   │
│  Secure Element (SE):                                             │
│  ┌─────────────────────────────────────────────────────────────┐   │
│  │  • Private key storage                                     │   │
│  │  • Cryptographic operations                                │   │
│  │  • Tamper-resistant                                        │   │
│  │  • Physical unclonability                                  │   │
│  └─────────────────────────────────────────────────────────────┘   │
│                                                                   │
│  Microcontroller:                                                 │
│  ┌─────────────────────────────────────────────────────────────┐   │
│  │  • Communication interface                                 │   │
│  │  • Display control                                         │   │
│  │  • Button input                                            │   │
│  │  • Firmware management                                     │   │
│  └─────────────────────────────────────────────────────────────┘   │
│                                                                   │
│  Display:                                                         │
│  ┌─────────────────────────────────────────────────────────────┐   │
│  │  • Transaction verification                                │   │
│  │  • Address confirmation                                    │   │
│  │  • PIN entry                                               │   │
│  └─────────────────────────────────────────────────────────────┘   │
└─────────────────────────────────────────────────────────────────────┘

1. Seed Phrase Recovery:
   - Most common method
   - Enter seed phrase in new wallet
   - Recover all keys and funds

2. Multi-Sig Recovery:
   - Use threshold of keys
   - M-of-N scheme
   - Protection against key loss

3. Social Recovery:
   - Trusted individuals
   - Shamir Secret Sharing
   - Distributed recovery

4. Inheritance Planning:
   - Dead Man's Switch
   - Timed locks
   - Transfer on death
   - Legal documentation

Extended Key (xprv/xpub):
- Version bytes: 4 bytes
- Depth: 1 byte
- Parent Fingerprint: 4 bytes
- Child Number: 4 bytes
- Chain Code: 32 bytes
- Key: 33 bytes (compressed public/private)

Total: 78 bytes
Base58Check encoding (111 characters)

Example:
xprv9s21ZrQH143K31xYSDQpPDxsXRTUcvj2iNHm5NUtrGiGG5e5Tx...

Private Derivation:
CKDpriv((k_par, c_par), i):
1. If i ≥ 2³¹ (hardened):
   - data = 0x00 || k_par || i
   - Hardened derivation
2. Else (normal):
   - data = pubkey_par || i
   - Normal derivation
3. I = HMAC-SHA512(c_par, data)
4. k_i = (k_par + I_L) mod n
5. c_i = I_R

Public Derivation:
CKDpub((K_par, c_par), i):
1. Must be normal (i < 2³¹)
2. data = K_par || i
3. I = HMAC-SHA512(c_par, data)
4. K_i = K_par + I_L × G
5. c_i = I_R

Checksum Calculation (12 words):

1. Entropy: 128 bits (16 bytes)
2. SHA-256: 256 bits
3. Take first 4 bits as checksum
4. Total: 132 bits
5. Split into 11-bit words (12 words)

Example:
Entropy: 0x0102030405060708090a0b0c0d0e0f10
Checksum: 0x1
Bits: 128 + 4 = 132 bits
Words: 12 × 11 bits = 132 bits

1. Seed Phrase:
   ☐ Store offline (no digital copies)
   ☐ Multiple physical copies
   ☐ Different locations
   ☐ Protection from fire/water

2. Passphrase:
   ☐ Strong, memorable
   ☐ Separate from seed
   ☐ Backup separately

3. Multi-Sig:
   ☐ Consider for large holdings
   ☐ Geographic distribution
   ☐ Different custodians

4. Hardware:
   ☐ Purchase from trusted source
   ☐ Verify firmware
   ☐ Update regularly

5. Encrypted Backup:
   ☐ Encrypt digital backups
   ☐ Use strong encryption
   ☐ Store encryption key separately