Table of Contents
Foreword. . . xi
Preface. . . xiii
1. Finite Fields. . . 1
Learning Higher-Level Math 1
Finite Field Definition 2
Defining Finite Sets 3
Constructing a Finite Field in Python 3
Exercise 1 5
Modulo Arithmetic 5
Modulo Arithmetic in Python 7
Finite Field Addition and Subtraction 8
Exercise 2 9
Coding Addition and Subtraction in Python 9
Exercise 3 10
Finite Field Multiplication and Exponentiation 10
Exercise 4 11
Exercise 5 11
Coding Multiplication in Python 12
Exercise 6 12
Coding Exponentiation in Python 12
Exercise 7 13
Finite Field Division 13
Exercise 8 15
Exercise 9 16
Redefining Exponentiation 16
Conclusion 17
2. Elliptic Curves. . . 19
Definition 19
Coding Elliptic Curves in Python 26
Exercise 1 27
Exercise 2 27
Point Addition 27
Math of Point Addition 31
Coding Point Addition 33
Exercise 3 34
Point Addition for When x1≠x2 35
Exercise 4 36
Coding Point Addition for When x1≠x2 36
Exercise 5 36
Point Addition for When P1 = P2 37
Exercise 6 38
Coding Point Addition for When P1 = P2 38
Exercise 7 39
Coding One More Exception 39
Conclusion 40
3. Elliptic Curve Cryptography. . . 41
Elliptic Curves over Reals 41
Elliptic Curves over Finite Fields 42
Exercise 1 44
Coding Elliptic Curves over Finite Fields 44
Point Addition over Finite Fields 45
Coding Point Addition over Finite Fields 47
Exercise 2 47
Exercise 3 47
Scalar Multiplication for Elliptic Curves 47
Exercise 4 49
Scalar Multiplication Redux 50
Mathematical Groups 51
Identity 51
Closure 52
Invertibility 53
Commutativity 54
Associativity 55
Exercise 5 56
Coding Scalar Multiplication 57
Defining the Curve for Bitcoin 58
Working with secp256k1 60
Public Key Cryptography 61
Signing and Verification 62
Inscribing the Target 63
Verification in Depth 65
Verifying a Signature 66
Exercise 6 67
Programming Signature Verification 67
Signing in Depth 68
Creating a Signature 68
Exercise 7 69
Programming Message Signing 70
Conclusion 72
4. Serialization. . . 73
Uncompressed SEC Format 73
Exercise 1 75
Compressed SEC Format 75
Exercise 2 79
DER Signatures 79
Exercise 3 81
Base58 81
Transmitting Your Public Key 81
Exercise 4 83
Address Format 83
Exercise 5 84
WIF Format 84
Exercise 6 85
Big- and Little-Endian Redux 85
Exercise 7 86
Exercise 8 86
Exercise 9 86
Conclusion 86
5. Transactions. . . 87
Transaction Components 87
Version 90
Exercise 1 90
Inputs 90
Parsing Script 95
Exercise 2 96
Outputs 96
Exercise 3 97
Locktime 98
Exercise 4 98
Exercise 5 98
Coding Transactions 99
Transaction Fee 100
Calculating the Fee 102
Exercise 6 102
Conclusion 102
6. Script. . . 103
Mechanics of Script 103
How Script Works 105
Example Operations 105
Coding Opcodes 106
Exercise 1 107
Parsing the Script Fields 107
Coding a Script Parser and Serializer 108
Combining the Script Fields 111
Coding the Combined Instruction Set 111
Standard Scripts 111
p2pk 112
Coding Script Evaluation 115
Stack Elements Under the Hood 117
Exercise 2 118
Problems with p2pk 118
Solving the Problems with p2pkh 120
p2pkh 120
Scripts Can Be Arbitrarily Constructed 124
Exercise 3 127
Utility of Scripts 127
Exercise 4 127
SHA-1 Piñata 128
Conclusion 128
7. Transaction Creation and Validation. . . 129
Validating Transactions 129
Checking the Spentness of Inputs 130
Checking the Sum of the Inputs Versus the Sum of the Outputs 130
Checking the Signature 131
Exercise 1 135
Exercise 2 135
Verifying the Entire Transaction 135
Creating Transactions 136
Constructing the Transaction 136
Making the Transaction 139
Signing the Transaction 141
Exercise 3 141
Creating Your Own Transactions on testnet 141
Exercise 4 142
Exercise 5 142
Conclusion 142
8. Pay-to-Script Hash. . . 143
Bare Multisig 143
Coding OP_CHECKMULTISIG 148
Exercise 1 148
Problems with Bare Multisig 148
Pay-to-Script-Hash (p2sh) 149
Coding p2sh 156
More Complicated Scripts 157
Addresses 157
Exercise 2 158
Exercise 3 158
p2sh Signature Verification 158
Exercise 4 161
Exercise 5 161
Conclusion 161
9. Blocks. . . 163
Coinbase Transactions 164
Exercise 1 164
ScriptSig 165
BIP0034 165
Exercise 2 166
Block Headers 166
Exercise 3 167
Exercise 4 167
Exercise 5 167
Version 168
Exercise 6 169
Exercise 7 169
Exercise 8 169
Previous Block 169
Merkle Root 169
Timestamp 169
Bits 170
Nonce 170
Proof-of-Work 170
How a Miner Generates New Hashes 171
The Target 172
Exercise 9 173
Difficulty 173
Exercise 10 173
Checking That the Proof-of-Work Is Sufficient 174
Exercise 11 174
Difficulty Adjustment 174
Exercise 12 176
Exercise 13 176
Conclusion 176
10. Networking. . . 177
Network Messages 177
Exercise 1 179
Exercise 2 179
Exercise 3 179
Parsing the Payload 179
Exercise 4 181
Network Handshake 181
Connecting to the Network 181
Exercise 5 184
Getting Block Headers 184
Exercise 6 185
Headers Response 185
Conclusion 188
11. Simplified Payment Verification. . . 189
Motivation 189
Merkle Tree 190
Merkle Parent 191
Exercise 1 192
Merkle Parent Level 192
Exercise 2 193
Merkle Root 193
Exercise 3 194
Merkle Root in Blocks 194
Exercise 4 195
Using a Merkle Tree 195
Merkle Block 197
Merkle Tree Structure 199
Exercise 5 199
Coding a Merkle Tree 199
The merkleblock Command 205
Exercise 6 206
Using Flag Bits and Hashes 206
Exercise 7 210
Conclusion 210
12. Bloom Filters. . . 211
What Is a Bloom Filter? 211
Exercise 1 213
Going a Step Further 214
BIP0037 Bloom Filters 215
Exercise 2 216
Exercise 3 216
Loading a Bloom Filter 216
Exercise 4 217
Getting Merkle Blocks 217
Exercise 5 218
Getting Transactions of Interest 218
Exercise 6 220
Conclusion 220
13. Segwit. . . 221
Pay-to-Witness-Pubkey-Hash (p2wpkh) 221
Transaction Malleability 222
Fixing Malleability 222
p2wpkh Transactions 223
p2sh-p2wpkh 226
Coding p2wpkh and p2sh-p2wpkh 231
Pay-to-Witness-Script-Hash (p2wsh) 235
p2sh-p2wsh 239
Coding p2wsh and p2sh-p2wsh 244
Other Improvements 246
Conclusion 246
14. Advanced Topics and Next Steps. . . 247
Suggested Topics to Study Next 247
Wallets 247
Payment Channels and Lightning Network 248
Contributing 248
Suggested Next Projects 249
Testnet Wallet 249
Block Explorer 249
Web Shop 249
Utility Library 250
Finding a Job 250
Conclusion 250
