The document provides a comprehensive overview of Bitcoin fundamentals, focusing on the structure and functionality of its blockchain. It defines key components like blocks, transactions, and addresses while emphasizing Bitcoin's status as the first and most secure blockchain. The document also touches on the relationship between private keys, public keys, and Bitcoin addresses.

1. Bitcoin Fundamentals
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

2. Topics Covered

3. Topics Covered
•Blockchain

4. Topics Covered
•Blockchain
•Blocks

5. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses

6. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses
•Scripting

7. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses
•Scripting
•Transactions

8. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses
•Scripting
•Transactions
•Proof-Of-Work & Mining

9. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses
•Scripting
•Transactions
•Proof-Of-Work & Mining
•Attacks

10. Topics Covered
•Blockchain
•Blocks
•Keys & Addresses
•Scripting
•Transactions
•Proof-Of-Work & Mining
•Attacks
•Quantum Computing Threats ?

11. Blockchain
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

12. What Is A Blockchain?
Several Definitions:

13. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand

14. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database

15. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database
•A database that can't be tampered with

16. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database
•A database that can't be tampered with
•An append-only database

17. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database
•A database that can't be tampered with
•An append-only database
•A cryptographically verified database

18. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database
•A database that can't be tampered with
•An append-only database
•A cryptographically verified database
•A chain of blocks

19. What Is A Blockchain?
Several Definitions:
•Over-used buzzword that many people don't understand
•A very slow database
•A database that can't be tampered with
•An append-only database
•A cryptographically verified database
•An immutable, append-only, hashed, cryptographically verified, singly-linked chain of blocks

20. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.

21. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)

22. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate

23. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain

24. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain
•Not the biggest blockchain (Ethereum is far bigger)

25. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain
•Not the biggest blockchain (Ethereum is far bigger)
•Each block contains block header plus N transactions where 0 ≤ N

26. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it
certainly fits the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain
•Not the biggest blockchain (Ethereum is far bigger)
•Each block contains block header plus N transactions where 0 ≤ N
•Each block is limited to 1MB*

27. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it certainly fits
the description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain
•Not the biggest blockchain (Ethereum is far bigger)
•Each block contains block header plus N transactions where 0 ≤ N
•Each block is limited to 1MB*
•New block generated every 10 minutes**

28. What about Bitcoin's blockchain?
Since "blockchain" is an overloaded term, let's examine Bitcoin's blockchain alone, since it certainly fits the
description.
•World's first blockchain (and always will be)
•World's most secure blockchain I.e. highest hash rate
•World's most famous blockchain
•Not the biggest blockchain (Ethereum is far bigger)
•Each block contains block header plus N transactions where 0 ≤ N
•Each block is limited to 1MB*
•New block generated every 10 minutes**
* Technically not true anymore, but block size still has a small, hard limit ** On average

29. What about Bitcoin's blockchain?
HashMerkleRoot
Block 0
HashPrevBlock HashMerkleRoot
Block 1
HashPrevBlock HashMerkleRoot
Block 2
HashPrevBlock HashMerkleRoot
Block 3
The Times
03/Jan/2009
Chancellor on
brink of
second
bailout for
banks

30. Blocks
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

31. Structure Of A Bitcoin Block
Each Bitcoin block consists of:

32. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance

33. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size

34. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header

35. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter

36. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselves

37. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:

38. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version

39. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version
• HashPrevBlock – Hash of the previous block's header

40. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version
• HashPrevBlock – Hash of the previous block's header
• HashMerkleRoot – Hash of the merkle root of the
transactions in this block. Just think of it as a hash of all
the transactions treated as one blob of data

41. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version
• HashPrevBlock – Hash of the previous block's header
• HashMerkleRoot – Hash of the merkle root of the
transactions in this block. Just think of it as a hash of all
the transactions treated as one blob of data
• Time

42. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version
• HashPrevBlock – Hash of the previous block's header
• HashMerkleRoot – Hash of the merkle root of the
transactions in this block. Just think of it as a hash of all
the transactions treated as one blob of data
• Time
• Bits – Current difficulty target (more on this later)

43. Structure Of A Bitcoin Block
Each Bitcoin block consists of:
• Magic Number – Used to identify block as a bitcoin block. No
cryptographic significance
• Block Size
• Block header
• Transaction counter
• The transactions themselvesEach Bitcoin block contains a block header. This is what is
hashed and gives rise to the blockchain. The transactions
themselves are not hashed, only the merkle root of the
transactions. So technically it's a blockheader chain. Each
block header contains:
• Version
• HashPrevBlock – Hash of the previous block's header
• HashMerkleRoot – Hash of the merkle root of the
transactions in this block. Just think of it as a hash of all
the transactions treated as one blob of data
• Time
• Bits – Current difficulty target (more on this later)
• Nonce – Related to mining (more on this later)

44. Keys & Addresses
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

45. Keys & Addresses

46. Keys & Addresses
P2PKH bitcoin address

47. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?

48. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?
Answer: No

49. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?
Answer: No
Each address is derived from a public key.

50. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?
Answer: No
Each address is derived from a public key.
Each public key is derived from a private key.

51. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?
Answer: No
Each address is derived from a public key.
Each public key is derived from a private key.
Private Key Public Key Address

52. Keys & Addresses
What is a Bitcoin address? Is it just a random string of characters?
Answer: No
Each address is derived from a public key.
Each public key is derived from a private key.
Private Key Public Key Address
Private Key Public Key Address

53. Keys & Addresses

54. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097

55. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1

56. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

57. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.

58. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb

59. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb
PubkeyHash = SHA256(RipeMD160(Public Key)) = 0xd8e5899f2589b7fa9df2513bf2366d2031f2d478

60. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb
PubkeyHash = SHA256(RipeMD160(Public Key)) = 0xd8e5899f2589b7fa9df2513bf2366d2031f2d478
VersionByte (0x00) | PubkeyHash = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d478

61. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb
PubkeyHash = SHA256(RipeMD160(Public Key)) = 0xd8e5899f2589b7fa9df2513bf2366d2031f2d478
VersionByte (0x00) | PubkeyHash = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d478
SHA2562(VersionByte | PubkeyHash)[:4] (Checksum) = 0x08c131a4

62. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb
PubkeyHash = SHA256(RipeMD160(Public Key)) = 0xd8e5899f2589b7fa9df2513bf2366d2031f2d478
VersionByte (0x00) | PubkeyHash = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d478
SHA2562(VersionByte | PubkeyHash)[:4] (Checksum) = 0x08c131a4
VersionByte | PubkeyHash | Checksum = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d47808c131a4

63. Keys & Addresses
Private Key: 0x69bc69641bd3111e47d55c40b8f1e912577c78edabb1c8ca5d2907bff7a93097
Private key is just a random number between 0 and 2256 - 232 - 29 - 28 - 27 - 26 - 24 – 1
Generator point: 0x0279be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
To get the unique public key for this private key, we add the generator point to itself private key times.
Public key: 0x0380864b7759a43923d2d0c99b142843fc306199a94995e55cb204d9a91fa09feb
PubkeyHash = SHA256(RipeMD160(Public Key)) = 0xd8e5899f2589b7fa9df2513bf2366d2031f2d478
VersionByte (0x00) | PubkeyHash = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d478
SHA2562(VersionByte | PubkeyHash)[:4] (Checksum) = 0x08c131a4
VersionByte | PubkeyHash | Checksum = 0x00d8e5899f2589b7fa9df2513bf2366d2031f2d47808c131a4
Base58CheckEncode(0x00d8e5899f2589b7fa9df2513bf2366d2031f2d47808c131a4)
= 1LmqvzD5KgNs1a8tcibuiNNM1MfZxLr5pw

64. Scripting
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

65. Script

66. Script
• Bitcoin comes with its own scripting language called "script"

67. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds

68. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds

69. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds
• Script is non-turing-complete, which means it has no loops

70. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds
• Script is non-turing-complete, which means it has no loops
• Script is a stack-based language which runs in (what some people call) a VM

71. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds
• Script is non-turing-complete, which means it has no loops
• Script is a stack-based language which runs in (what some people call) a VM
• VM is basically a giant switch statement (EvalScript in src/script/interpreter.cpp)

72. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds
• Script is non-turing-complete, which means it has no loops
• Script is a stack-based language which runs in (what some people call) a VM
• VM is basically a giant switch statement (EvalScript in src/script/interpreter.cpp)
• Giant switch statement is about 800 lines of C++

73. Script
• Bitcoin comes with its own scripting language called "script"
• Script is used to lock and unlock funds
• All bitcoin transactions must use script. There is no other way to lock/unlock funds
• Script is non-turing-complete, which means it has no loops
• Script is a stack-based language which runs in (what some people call) a VM
• VM is basically a giant switch statement (EvalScript in src/script/interpreter.cpp)
• Giant switch statement is about 800 lines of C++
• Consensus-critical code !!!

74. Script
Let's run a script!

75. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL

76. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
3

77. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
5
3

78. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
ADD
5
3

79. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
8

80. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
8
8

81. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
OP_EQUAL
8
8

82. Script
Interpreter Stack
OP_3 OP_5 OP_ADD OP_8 OP_EQUAL
TRUE

83. Transactions
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

84. Transactions

85. Transactions
Each transaction contains 1 or more
inputs and 1 or more outputs.

86. Transactions

87. Transactions
• Each input contains a reference to exactly one output
in a previous transaction.

88. Transactions
• Each input contains a reference to exactly one output
in a previous transaction.
• This is known as an "outpoint".

89. Transactions
• Each input contains a reference to exactly one output
in a previous transaction.
• This is known as an "outpoint".
• Each input also contains a script.

90. Transactions
• Each input contains a reference to exactly one output
in a previous transaction.
• This is known as an "outpoint".
• Each input also contains a script.

91. Transactions
• Each output contains a value in satoshis. (1 satoshi = 10-8BTC)
• Each input contains a reference to exactly one output
in a previous transaction.
• This is known as an "outpoint".
• Each input also contains a script.

92. Transactions
• Each output contains a value in satoshis. (1 satoshi = 10-8BTC)
• Each output also contains a script
• Each input contains a reference to exactly one output
in a previous transaction.
• This is known as an "outpoint".
• Each input also contains a script.

93. Transactions

94. Transactions
• In a transaction, a scriptSig from a TxIn (input) is contatenated with a scriptPubKey from a
TxOut (output) to form a full script.

95. Transactions
• In a transaction, a scriptSig from a TxIn (input) is contatenated with a scriptPubKey from a
TxOut (output) to form a full script.
• This script is run by the script interpreter and if there's a TRUE at the top of the stack after
the script is run, the transaction is a success and the funds can be unlocked and transferred
to somebody else.

96. Transactions
• In a transaction, a scriptSig from a TxIn (input) is contatenated with a scriptPubKey from a
TxOut (output) to form a full script.
• This script is run by the script interpreter and if there's a TRUE at the top of the stack after
the script is run, the transaction is a success and the funds can be unlocked and transferred
to somebody else.
• If there's anything other than a TRUE at the top of the stack, the transaction is deemed a
failure and the funds remain locked.

97. Transactions
• In a transaction, a scriptSig from a TxIn (input) is contatenated with a scriptPubKey from a
TxOut (output) to form a full script.
• This script is run by the script interpreter and if there's a TRUE at the top of the stack after
the script is run, the transaction is a success and the funds can be unlocked and transferred
to somebody else.
• If there's anything other than a TRUE at the top of the stack, the transaction is deemed a
failure and the funds remain locked.
• A transaction containing a scriptSig which fails to unlock funds will not be broadcast by
nodes, and even some wallets may not broadcast it. This is an important spam-prevention
mechanism which ensures only transactions which spend bitcoin in the form of fees, use
network resources.

98. Script
P2PKH Transaction Verification Script

99. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG

100. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
ScriptSig (part of Input)

101. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
ScriptPubKey (part of Output)

102. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<SIG>

103. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<PUBKEY>
<SIG>

104. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
OP_DUP
<PUBKEY>
<SIG>

105. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<PUBKEY>
<PUBKEY>
<SIG>

106. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
OP_HASH160
<PUBKEY>
<PUBKEY>
<SIG>

107. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<PUBKEYHASH>
<PUBKEY>
<SIG>

108. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<PUBKEYHASH>
<PUBKEYHASH>
<PUBKEY>
<SIG>

109. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
OP_EQUALVERIFY
<PUBKEYHASH>
<PUBKEYHASH>
<PUBKEY>
<SIG>

110. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
<PUBKEY>
<SIG>

111. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
OP_CHECKSIG
<PUBKEY>
<SIG>

112. Script
Interpreter Stack
<SIG> <PUBKEY> OP_DUP OP_HASH160
<PUBKEYHASH> OP_EQUALVERIFY OP_CHECKSIG
TRUE

113. Proof-of-Work & Mining
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

114. Proof-Of-Work & Mining

115. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)

116. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4

117. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash

118. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header

119. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty

120. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found

121. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward

122. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes

123. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined

124. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined
• Difficulty adjusted every 2,016 blocks

125. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined
• Difficulty adjusted every 2,016 blocks
• Block reward halved every 210,000 blocks

126. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined
• Difficulty adjusted every 2,016 blocks
• Block reward halved every 210,000 blocks
• Bitcoin mining uses the SHA-256 hash algorithm

127. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined
• Difficulty adjusted every 2,016 blocks
• Block reward halved every 210,000 blocks
• Bitcoin mining uses the SHA-256 hash algorithm
• All bitcoin Block IDs can be calculated with sha256(sha256(BlockHeader))

128. Proof-Of-Work & Mining
• Every bitcoin block has a 256-bit block ID (also called a block hash)
• Ex. Block hash: 00000000000000000005b5a0046b4e542a11f790b3fca15964bc58ad7b4386a4
• Technically it’s a block header hash
• To get different block hashes, a miner changes the nonce field in the block header
• Only block hashes below a threshold are accepted - this threshold is known as the difficulty
• This process continues until a hash below the threshold is found
• First miner to find this hash gets 12.5 BTC (EUR 82,818.68) - this is known as the block reward
• This happens every 10 minutes
• Each day ~ EUR 5,962,800.95 of new BTC is mined
• Difficulty adjusted every 2,016 blocks
• Block reward halved every 210,000 blocks
• Bitcoin mining uses the SHA-256 hash algorithm
• All bitcoin Block IDs can be calculated with sha256(sha256(BlockHeader))
• Mining can be done on any kind of hardware but is best done on specialized hardware

129. Mining Hardware Comparison

130. Mining Hardware Comparison
5.2 MH/sCore i7 3930k ($220)

131. Mining Hardware Comparison
749.23 MH/s
5.2 MH/sCore i7 3930k ($220)
Tesla S2070 ($18,995)

132. Mining Hardware Comparison
749.23 MH/s
5.2 MH/s
16 TH/s
Core i7 3930k ($220)
Tesla S2070 ($18,995)
Antminer S9 (about $300)

133. Mining Hardware Comparison
749.23 MH/s
5.2 MH/s
16 TH/s
Core i7 3930k ($220)
Tesla S2070 ($18,995)
Antminer S9 (about $300)
Tesla is 144 X faster than i7

134. Mining Hardware Comparison
749.23 MH/s
5.2 MH/s
16 TH/s
Core i7 3930k ($220)
Tesla S2070 ($18,995)
Antminer S9 (about $300)
Tesla is 144 X faster than i7
S9 is 21,355 X faster than Tesla

135. Bitcoin Mining Farm
(Somewhere on Earth)

136. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s

137. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth

138. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations

139. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations

140. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations
• Usually in cold countries with cheap electricity

141. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations
• Usually in cold countries with cheap electricity
• Bitcoin mining uses enough electricity to power 3
Irelands

142. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations
• Usually in cold countries with cheap electricity
• Bitcoin mining uses enough electricity to power 3
Irelands
• Many rumors about who is mining Bitcoin

143. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations
• Usually in cold countries with cheap electricity
• Bitcoin mining uses enough electricity to power 3
Irelands
• Many rumors about who is mining Bitcoin
• One thing we do know: more mining farms are
springing up because the hash rate is growing

144. Bitcoin Mining Farm
(Somewhere on Earth)
3,075,120 i7s
• Many such mining farms on earth
• Often in secret locations
• Impossible to find their locations
• Usually in cold countries with cheap electricity
• Bitcoin mining uses enough electricity to power 3
Irelands
• Many rumors about who is mining Bitcoin
• One thing we do know: more mining farms are
springing up because the hash rate is growing
• How do we know this ?

145. Finding The Network Hash Rate

146. Finding The Network Hash Rate

147. Finding The Network Hash Rate

148. Finding The Network Hash Rate
The "Great Crash" of 2017

149. Finding The Network Hash Rate
1,923,076,923,077 i7s

150. Finding The Network Hash Rate
But how does blockchain.info know the hash rate ?

151. Finding The Network Hash Rate
But how does blockchain.info know the hash rate ?
Nobody knows where all the mining farms are.

152. Finding The Network Hash Rate
But how does blockchain.info know the hash rate ?
Nobody knows where all the mining farms are.
Answer: They use math

153. Proof-Of-Work & Mining

154. Proof-Of-Work & Mining
PBH = 1

155. Proof-Of-Work & Mining
PBH = 1
"The mining equation"

156. Proof-Of-Work & Mining
PBH = 1
"The mining equation"
P = probability of mining block below difficulty target in 1 try

157. Proof-Of-Work & Mining
PBH = 1
"The mining equation"
P = probability of mining block below difficulty target in 1 try
B = block time (s)

158. Proof-Of-Work & Mining
PBH = 1
"The mining equation"
P = probability of mining block below difficulty target in 1 try
B = block time (s)
H = # of tries per second, a.k.a. hash rate (h/s)

159. Proof-Of-Work & Mining
PBH = 1
"The mining equation"
P = probability of mining block below difficulty target in 1 try
B = block time (s)
H = # of tries per second, a.k.a. hash rate (h/s)
P = 1/BH
B = 1/PH
H = 1/PB

160. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?

161. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1

162. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1
H = 10

163. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1
H = 10
B = 1/PH

164. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1
H = 10
B = 1/PH
B = 1/(0.1 × 10)

165. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1
H = 10
B = 1/PH
B = 1/(0.1 × 10)
B = 1/1

166. Example Hash Rate Calculation
Probability of mining a block in single attempt is 0.1. I'm trying 10 hashes per
second, what is my block time?
P = 0.1
H = 10
B = 1/PH
B = 1/(0.1 × 10)
B = 1/1
Average block time is 1 second

167. Example Hash Rate Calculation
Let's try a real example!

168. Example Hash Rate Calculation
The home page of blockchain.info looks like this: What is the current network hash rate?

169. Example Hash Rate Calculation
We have:

170. Example Hash Rate Calculation
We have:
• 8 most recent block hashes:
• 000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
• 0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
• 0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
• 0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
• 0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
• 00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
• 00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
• 000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b

171. Example Hash Rate Calculation
We have:
• 8 most recent block hashes:
• 000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
• 0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
• 0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
• 0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
• 0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
• 00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
• 00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
• 000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
• 8 most recent block timestamps:
• 2019-12-06 02:37
• 2019-12-06 02:19
• 2019-12-06 02:12
• 2019-12-06 01:46
• 2019-12-06 01:44
• 2019-12-06 01:26
• 2019-12-06 01:24
• 2019-12-06 01:15

172. Example Hash Rate Calculation
We want:
• P (probability of finding correct hash in one try)
• B (block time)
• So we can solve H = 1/PB

173. Example Hash Rate Calculation
B is easier to find so we'll start with it.

174. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37
• 2019-12-06 02:19
• 2019-12-06 02:12
• 2019-12-06 01:46
• 2019-12-06 01:44
• 2019-12-06 01:26
• 2019-12-06 01:24
• 2019-12-06 01:15

175. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37 => 1575599820
• 2019-12-06 02:19 => 1575598740
• 2019-12-06 02:12 => 1575598320
• 2019-12-06 01:46 => 1575596760
• 2019-12-06 01:44 => 1575596640
• 2019-12-06 01:26 => 1575595560
• 2019-12-06 01:24 => 1575595440
• 2019-12-06 01:15 => 1575594900

176. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37 => 1575599820
• 2019-12-06 02:19 => 1575598740
• 2019-12-06 02:12 => 1575598320
• 2019-12-06 01:46 => 1575596760
• 2019-12-06 01:44 => 1575596640
• 2019-12-06 01:26 => 1575595560
• 2019-12-06 01:24 => 1575595440
• 2019-12-06 01:15 => 1575594900
Step 2: Calculate intervals
• 1575599820 – 1575598740
• 1575598740 – 1575598320
• 1575598320 - 1575596760
• 1575596760 - 1575596640
• 1575596640 - 1575595560
• 1575595560 - 1575595440
• 1575595440 - 1575594900

177. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37 => 1575599820
• 2019-12-06 02:19 => 1575598740
• 2019-12-06 02:12 => 1575598320
• 2019-12-06 01:46 => 1575596760
• 2019-12-06 01:44 => 1575596640
• 2019-12-06 01:26 => 1575595560
• 2019-12-06 01:24 => 1575595440
• 2019-12-06 01:15 => 1575594900
Step 2: Calculate intervals
• 1575599820 – 1575598740 = 1080
• 1575598740 – 1575598320 = 420
• 1575598320 - 1575596760 = 1560
• 1575596760 - 1575596640 = 120
• 1575596640 - 1575595560 = 1080
• 1575595560 - 1575595440 = 120
• 1575595440 - 1575594900 = 540

178. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37 => 1575599820
• 2019-12-06 02:19 => 1575598740
• 2019-12-06 02:12 => 1575598320
• 2019-12-06 01:46 => 1575596760
• 2019-12-06 01:44 => 1575596640
• 2019-12-06 01:26 => 1575595560
• 2019-12-06 01:24 => 1575595440
• 2019-12-06 01:15 => 1575594900
Step 2: Calculate intervals
• 1575599820 – 1575598740 = 1080
• 1575598740 – 1575598320 = 420
• 1575598320 - 1575596760 = 1560
• 1575596760 - 1575596640 = 120
• 1575596640 - 1575595560 = 1080
• 1575595560 - 1575595440 = 120
• 1575595440 - 1575594900 = 540
Step 3: Compute median: 120 120 420 540 1080 1080 1560

179. Example Hash Rate Calculation
B is easier to find so we'll start with it.
Step 1: Convert 8 timestamps into seconds:
• 2019-12-06 02:37 => 1575599820
• 2019-12-06 02:19 => 1575598740
• 2019-12-06 02:12 => 1575598320
• 2019-12-06 01:46 => 1575596760
• 2019-12-06 01:44 => 1575596640
• 2019-12-06 01:26 => 1575595560
• 2019-12-06 01:24 => 1575595440
• 2019-12-06 01:15 => 1575594900
Step 2: Calculate intervals
• 1575599820 – 1575598740 = 1080
• 1575598740 – 1575598320 = 420
• 1575598320 - 1575596760 = 1560
• 1575596760 - 1575596640 = 120
• 1575596640 - 1575595560 = 1080
• 1575595560 - 1575595440 = 120
• 1575595440 - 1575594900 = 540
Step 3: Compute median: 120 120 420 540 1080 1080 1560
• => B = 540

180. Example Hash Rate Calculation
To find P, we can average the block hashes of the last 8 blocks, then multiply by 2 to get the difficulty target. We then express that as a
fraction of 2256.
•

181. Example Hash Rate Calculation
To find P, we can average the block hashes of the last 8 blocks, then multiply by 2 to get the difficulty target. We then express that as a
fraction of 2256.
Reasoning: If I keep asking to choose numbers between 1 and 100, and write down only the numbers below 10, the average of the
numbers I write down will be 5.
•

182. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b

183. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8

184. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8
÷ 0x04

185. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8
÷ 0x04
0x1b5b46da81afe669700e0162a8c7bb47ae361e294553f2

186. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8
÷ 0x04
0x1b5b46da81afe669700e0162a8c7bb47ae361e294553f2
÷ 0x020x100

187. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8
÷ 0x04
0x1b5b46da81afe669700e0162a8c7bb47ae361e294553f2
÷ 0x020x100
0.0000000000000000000000226...

188. Example Hash Rate Calculation
0x000000000000000000156ef4be0d0c90b655f9fb08fac67aa151032bfcdfa51a
0x0000000000000000000dd8b04dcf588433bbb4838d20ea8e3682c5b5328f3934
0x0000000000000000000ba39636a6dd75584f400da3217c5aec4d91116307243c
0x0000000000000000000c65f787061574865988894a721900fe46dbbe85580950
0x0000000000000000000825524292c9ad4938a85c3a0cd08965182272912d087d
0x00000000000000000013f660755e5aa1f9daf8eaa0663a4ecddd17d75e608d05
0x00000000000000000010f252e6a289adcdcce0577afa29d9f62082b7a416bc41
+ 0x000000000000000000050de301e9b99dcc253f51b186a3d6333ae5c5f9a2f22b
0x6d6d1b6a06bf99a5c038058aa31eed1eb8d878a5154fc8
÷ 0x04
0x1b5b46da81afe669700e0162a8c7bb47ae361e294553f2
÷ 0x020x100
0.0000000000000000000000226...
=> P = 0.0000000000000000000000226

189. Example Hash Rate Calculation
H = 1/PB

190. Example Hash Rate Calculation
H = 1/PB
H = 1/(0.0000000000000000000000226 × 540)

191. Example Hash Rate Calculation
H = 1/PB
H = 1/(0.0000000000000000000000226 × 540)
H = 81836032937956668986

192. Example Hash Rate Calculation
H = 1/PB
H = 1/(0.0000000000000000000000226 × 540)
H = 81836032937956668986
H = 81,836,032,937,956,668,986

193. Example Hash Rate Calculation
H = 1/PB
H = 1/(0.0000000000000000000000226 × 540)
H = 81836032937956668986
H = 81,836,032,937,956,668,986
H = 81.8 EH/s

194. Example Hash Rate Calculation
H = 1/PB
H = 1/(0.0000000000000000000000226 × 540)
H = 81836032937956668986
H = 81,836,032,937,956,668,986
H = 81.8 EH/s
Within 10% of the correct answer.
Only out by a few quintillion !

195. Attacks
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

196. Key Guessing Attack

197. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin

198. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security

199. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero

200. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure

201. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!

202. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:

203. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD

204. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37

205. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE

206. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets

207. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets
• Bots use massive hash tables of pre-computed brain wallets

208. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets
• Bots use massive hash tables of pre-computed brain wallets
• I lost about 500 euros to one such bot

209. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets
• Bots use massive hash tables of pre-computed brain wallets
• I lost about 500 euros to one such bot
• Best kind of wallet is a hardware wallet

210. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets
• Bots use massive hash tables of pre-computed brain wallets
• I lost about 500 euros to one such bot
• Best kind of wallet is a hardware wallet
• Hardware wallets are resistant to any intrusion on your computer including viruses, remote attackers, etc

211. Key Guessing Attack
• If you can successfully guess somebody's private key, you can take all their bitcoin
• Individual addresses have 256-bit security
• Assuming a good RNG was used, the chance of correctly guessing are virtually zero
• Not the case if you use "brain wallets" which are insecure
• Don't use brain wallets!
• Famous brain wallets:
• "bitcoin": 1E984zyYbNmeuumzEdqT8VSL8QGJi3byAD
• "hello": 1HoSFymoqteYrmmr7s3jDDqmggoxacbk37
• "satoshi": 1ADJqstUMBB5zFquWg19UqZ7Zc6ePCpzLE
• Bots are running 24/7 ready to take any bitcoin sent to brain wallets
• Bots use massive hash tables of pre-computed brain wallets
• I lost about 500 euros to one such bot
• Best kind of wallet is a hardware wallet
• Hardware wallets are resistant to any intrusion on your computer including viruses, remote attackers, etc
• Hardware wallet stores private key and signs transactions on behalf of the user

212. Key Guessing Attack

213. 51% Attack

214. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power

215. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)

216. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)

217. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain

218. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize

219. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)

220. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised

221. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible

222. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:

223. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed

224. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending

225. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption

226. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:

227. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins

228. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:

229. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners

230. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)

231. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition

232. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:

233. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen

234. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen
• December 2018: Vertcoin was 51% attacked - $100,000 stolen

235. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen
• December 2018: Vertcoin was 51% attacked - $100,000 stolen
• Unlikely to happen to Bitcoin because:

236. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen
• December 2018: Vertcoin was 51% attacked - $100,000 stolen
• Unlikely to happen to Bitcoin because:
• Hash-power is massive and well-diversified

237. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen
• December 2018: Vertcoin was 51% attacked - $100,000 stolen
• Unlikely to happen to Bitcoin because:
• Hash-power is massive and well-diversified
• Hash-power distribution is well known

238. 51% Attack
• To perform this attack, attacker must possess over 50% of the hashing power
1. Attacker pays somebody in bitcoin for goods or services in transaction T, spending coin C to address A (recipient)
2. Attacker begins privately mining alternative blockchain which contains transaction T' instead, spending coin C to address A' (himself)
3. Once goods/services have arrived, attacker broadcasts alternative blockchain
4. Since attacker's private blockchain will have higher height, network will be forced to accept it and re-organize
5. Attacker will still have his bitcoin in alternative address, plus goods or services ("goods" are usually $$$)
• Any blockchain where one entity controls over 50% of hashing power should be considered compromised
• Small blockchains are susceptible
• Can be used for:
• Preventing certain transactions from being confirmed
• Double-spending
• Network interruption
• Cannot be used to:
• Steal coins
• Best protected against with:
• Many miners
• Incentivizing mining pools (where individual miners are free to choose transactions)
• Competition
• Real-life examples:
• May 2018: Bitcoin Gold was 51% attacked - $18,000,000 stolen
• December 2018: Vertcoin was 51% attacked - $100,000 stolen
• Unlikely to happen to Bitcoin because:
• Hash-power is massive and well-diversified
• Hash-power distribution is well known
• Miners want Bitcoin to succeed and price to go up. 51% attack would cause price crash

239. Quantum Computing
Threats ?
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

240. Quantum Computing Threats ?

241. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography

242. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)

243. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits

244. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required

245. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment

246. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits

247. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system

248. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm

249. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)

250. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).

251. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)

252. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?

253. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027

254. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.

255. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.

256. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:

257. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)

258. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers

259. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers

260. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers
• If QC does break Bitcoin tomorrow, it will break everything else too. Banks, Governments, Hospitals, Airlines, Military, Big Tech...

261. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers
• If QC does break Bitcoin tomorrow, it will break everything else too. Banks, Governments, Hospitals, Airlines, Military, Big Tech...
• Such a QC would be the greatest weapon imaginable in information warfare

262. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers
• If QC does break Bitcoin tomorrow, it will break everything else too. Banks, Governments, Hospitals, Airlines, Military, Big Tech...
• Such a QC would be the greatest weapon imaginable in information warfare
• No palpable sense of urgency from these entities to upgrade to post-quantum cryptography

263. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers
• If QC does break Bitcoin tomorrow, it will break everything else too. Banks, Governments, Hospitals, Airlines, Military, Big Tech...
• Such a QC would be the greatest weapon imaginable in information warfare
• No palpable sense of urgency from these entities to upgrade to post-quantum cryptography
• As things stand – a tiny computer such as an Apple watch is far better at breaking crypto and prime factorization than today's multi-million dollar QCs

264. Quantum Computing Threats ?
• Bitcoin uses 256-bit EC cryptography
• To break a n-bit EC key a QC with 9n + 2 log2(n) + 10 qubits are needed (arXiv:1706.06752v3)
• These need to be stable qubits
• To "break bitcoin", this means 2,000 stable qubits are required
• It's very difficult to build QCs with stable qubits, this is due to decoherence when entangled qubits interact with their environment
• It's much easier to go from 1 to 2 qubits than to go from 100 to 101 qubits
• Adding qubit n introduces n – 1 new interactions to the system
• Breaking bitcoin requires a QC that can run Shor's algorithm
• Most QCs can't run Shor's Algorithm except with a tiny number of qubits (like 5)
• Largest number ever factored on a real QC using Shor's is 21 (5 bits, 2012).
• Largest number ever factored on a real QC is 4,088,459 (22 bits) using IBM's 5-qubit processor (Grover's algorithm)
• How could a 22-bit number be factored on a 5-bit QC?
• Answer: 2088459 = 2017 × 2027
• 2017 and 2027 differ by 2 bits; only 2 qubits of the 5 were used.
• Numbers were cherry-picked.
• More promising results with quantum annealing:
• 376,289 = 571 × 659 was factored on D-wave 2000Q quantum annealer by Shuxian Jiang, Keith A. Britt, Travis S. Humble, and Sabre Kais (2018)
• Not cherry-picked, but these are still tiny numbers
• Does not use Shor's algorithm, but variant of Grover's algorithm. Doubtful if the method used can scale to large numbers
• If QC does break Bitcoin tomorrow, it will break everything else too. Banks, Governments, Hospitals, Airlines, Military, Big Tech...
• Such a QC would be the greatest weapon imaginable in information warfare
• No palpable sense of urgency from these entities to upgrade to post-quantum cryptography
• As things stand – a tiny computer such as an Apple watch is far better at breaking crypto and prime factorization than today's multi-million dollar QCs
• Basically there's nothing to worry about.

265. The End
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY

266. Questions?
BITCOIN FUNDAMENTALS
N. P. O'DONNELL, MAYNOOTH UNIVERSITY