blockchain - indian statistical institutercbose/blockchain2017/... · blockchain the foundation...
TRANSCRIPT
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BLOCKCHAINThe foundation behind Bitcoin
Sourav Sen GuptaIndian Statistical Institute, Kolkata
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CRYPTOGRAPHYBackbone of Blockchain Technology
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Component 1 : Cryptographic Hash Functions
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Map variable-length input to constant-length output.
HASH FUNCTIONS
h yx101011101011001…0010110100101 101110101001000110111100010101
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Finding the pre-image of a given output is not easy.
HASH FUNCTIONS
h y?101011101011001…0010110100101 101110101001000110111100010101
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Finding a colliding twin of a given input is not easy.
HASH FUNCTIONS
h yx1101011101011001…0010110100101
101110101001000110111100010101
x21100101001011001…110010100110
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Finding any colliding pair of inputs is not easy.
It is of course possible, but not easy.
HASH FUNCTIONS
h yx1101011101011001…0010110100101
x21100101001011001…110010100110
101110101001000110111100010101
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Minor input-mismatch to major output-mismatch.
HASH FUNCTIONS
hy1x1101011101011001…0010110100101 101110101001000110111100010101
x2101010101011001…0010110100101 y2 110010100101100100110010100110
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Merkle-Damgard Construction Example : SHA 256 — used in Bitcoin
CONSTRUCTIONS
f
m1
IV f
m2
f
mn
h
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Sponge Construction Example : SHA 3 — used in Ethereum
CONSTRUCTIONS
f
m1
f
m2
f
mn
f
h1
c
r
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Provably secure scheme for tamper-detection
APPLICATION
h yx
record(x) : c = h(x)
verify(c,x) : h(x) == c
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Tamper-evident data pointer = Hash Pointer
Hash Pointer
DATA STRUCTURES
h hash(data)data
addr(data)
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Tamper-evident linked data structure = Block
DATA STRUCTURES
h
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
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Tamper-evident linked-list = Blockchain
DATA STRUCTURES
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
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Tamper-evident linked-list = Blockchain
DATA STRUCTURES
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
Block
HP(block)
data
timestamp
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DATA STRUCTURESProperties Blockchain Merkle Tree Merkle Trie
Size of Commitment O(1) O(1) O(1)
Append a Block/Node O(1) O(log n) O(k)
Update a Block/Node O(n) O(log n) O(k)
Proof of Membership O(n) O(log n) O(k)
Structural Abstraction List of Objects Set of Objects Set of (key, value)
Used for Construction Bitcoin Bitcoin Ethereum
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Component 2 : Digital Signature Schemes
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(sk, pk) = keygen(n) verify(pk,m,sign(sk,m)) = True
DIGITAL SIGNATURE
pksk
?
s = sign(sk,m) verify(pk,m,s)keygen(n)
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Given pk and access to sign(mi) as an oracle, an adversary should not be able to create a valid fresh message-signature pair (m,s)
DIGITAL SIGNATURE
pksk
?
s = sign(sk,m) verify(pk,m,s)keygen(n)
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Elliptic Curve Digital Signature Algorithm (ECDSA)
ECDSA on curve E(Fp) : { (x,y) in Fp x Fp | y2 = x3 + 7 } with base prime p = 2256 - 232 - 29 - 28 - 27 - 26 - 24 - 1
CONSTRUCTIONFpQ
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Elliptic Curve group of size |E(Fp)| = q ~ p ~ 2256
ECDSA on curve E(Fp) : { (x,y) in Fp x Fp | y2 = x3 + 7 } with base prime p = 2256 - 232 - 29 - 28 - 27 - 26 - 24 - 1
CONSTRUCTION
Parameters Format Range Bit-sizesk random Zq 256pk sk x G E(Fp) 512m hash(M) Zq 256
Signature (r, s) Zq x Zq 512
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Publish the public key pk as your Identity Use the secret key sk to prove your identity
APPLICATIONpk
sksk
verify(pk,m,sign(sk,m))
sk?
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BITCOINBlockchain in Practice
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ANONYMOUS E-CASH
35624
Zero-Knowledge Proof and Blind Signature
35624
35624
35624 35624
35624
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BLIND SIGNATURE
First Concept of Untraceable e-Payments and e-Cash
David Chaum, 1984
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CYPHERPUNKS
De-Centralize e-Cash
Anonymity is not Enough!
?!
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CYPHERPUNKS
DavidChaum
PhilZimmermann
DigiCash PGP RPOW
HalFinney
HashCash
AdamBack
B-Money
WeiDai
BitGold
NickSzabo
1990 1991 20041997 1998 1998
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BITCOINSatoshi Nakamoto31 October 2008
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BITCOINLedger of Transactions
between Pseudonymous Identities
Semi-Decentralised Publicly-Verifiable Tamper-Resistant Eventually-Consistent
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Economic Transaction that we are familiar with
NOT BITCOIN
Tx
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NOT BITCOIN
Tx
Centralised Account-based Ledger
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NOT BITCOIN
Tx
Decentralised Account-based Ledger
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Tx
NOT BITCOIN YET
Tx
Decentralised Transaction-based Ledger
Tx Tx Tx Tx TxTx
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TRANSACTION
Tx
Network verifies the Signature
TxSigned by
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TRANSACTION
Tx
Network verifies the Signature
TxSigned by
pk
sk
pk
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Input : Array of previous Transactions | Output : Array of recipient Addresses
R1
TRANSACTION
TxTxpk2
sk1
Txpk1
Txpk3
sk2 sk3
pk
R2pk
R3pk
Send
er(s)
Recipient(s)
Network verifies the Signature(s)
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Input : Array of previous Transactions | Output : Array of recipient Addresses
R1
TRANSACTION
Txpk2
sk1
Txpk1
Txpk3
sk2 sk3
pk
R2
pk
R3
pk
Tx
Recipients
SignaturesInpu
t Tra
nsac
tions
Network verifies the Signature(s)
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LEDGER
Tx
Decentralised Transaction-based Ledger
Tx Tx TxTx Tx Tx Tx
Tx Tx Tx TxTx Tx Tx Tx Tx Tx Tx Tx
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BITCOIN
Tx
Tx
Tx
Tx
MiningTransaction
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MINING
Tx
Tx
Tx
Tx
Computational Lottery (Puzzle)
Transaction
Winner writes the next block
Existing blocks at a given time
Find r such thathash(r || m) < C
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BITCOIN
Tx
Tx
Tx
Tx
MiningTransaction
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BITCOINFramework — Decentralised peer-to-peer collaborative networkGoal : All peers should agree on a sequence of transactions
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BITCOINPublicly-Verifiable
as the complete ledger and the hash function is public
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BITCOINTamper-Evident / Tamper-Resistant
as the ledger is connected through a chain of hash pointers
X X X
X
X X X
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BITCOINEventually-Consistent
as the longest chain eventually sustains as the main chain
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BITCOINSemi-Decentralised
as the mining is dominated by computational power
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BITCOINSemi-Decentralised Publicly-Verifiable Tamper-Resistant Eventually-Consistent
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BEYOND BITCOINExploiting the power of Blockchain Ecosystem
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Proof-of-Work Proof-of-Space Computation-hard challenge Memory-hard challenge
Proof-of-Stake Proof-of-Importance Depends on holdings Depends on involvement
MINING
PermaCoin, SpaceMint
OmiseGo, EOS
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De-Centralized Semi-Centralized Without any Authority With Trusted Authority
Almost all active Currency RSCoin (Bank of England)
NETWORK
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Pseudonymity Pure Anonymity Not easily Traceable Provably not Traceable
Mixing Services provide some guarantee of anonymity otherwise.
ANONYMITY
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Abstraction of Bitcointo the backbone protocol of blockchain
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APPLICATION