Lecture 2: Bitcoin and Cryptocurrency Ras DwivediIntroduction to Blockchain Lecture 2: Bitcoin and...

Introduction to BlockchainLecture 2: Bitcoin and Cryptocurrency

Ras Dwivedi

Indian Institute of Technology Kanpur

May 22, 2018

Ras Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 1 / 43

Outline

1 Recap

2 Hash Functions

3 Digital Signature

4 Cryptocurrency

Outline

1 Recap

2 Hash Functions

3 Digital Signature

4 Cryptocurrency

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, qcalculate n = pqcalculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ −→ e × d = 1 mod φ

Idea: me×d = med = m modulo nencryption: c = me mod ndecryption: p = cd mod n

proposed by Rivest,Shamir,Adleman

choose two large distinct prime number p, qcalculate n = pqcalculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ −→ e × d = 1 mod φ

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, q

calculate n = pqcalculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ −→ e × d = 1 mod φ

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, qcalculate n = pq

calculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ −→ e × d = 1 mod φ

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, qcalculate n = pqcalculate φ = lcm(p − 1, q − 1)

choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ −→ e × d = 1 mod φ

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, qcalculate n = pqcalculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1

calculate d such that d = e−1modφ −→ e × d = 1 mod φ

proposed by Rivest,Shamir,Adlemanchoose two large distinct prime number p, qcalculate n = pqcalculate φ = lcm(p − 1, q − 1)choose e such that gcd(e, φ) = 1calculate d such that d = e−1modφ

−→ e × d = 1 mod φ

Idea: me×d = med = m modulo n

encryption: c = me mod ndecryption: p = cd mod n

Idea: me×d = med = m modulo nencryption: c = me mod n

decryption: p = cd mod n

Digital signature Attempt 1

AIM: Convince everybody that Alice have signed the document

nobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuined is called Alice’s secret key and e is called Alice’s Public key

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the document

simple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuined is called Alice’s secret key and e is called Alice’s Public key

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not work

IDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuined is called Alice’s secret key and e is called Alice’s Public key

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSA

for document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuined is called Alice’s secret key and e is called Alice’s Public key

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuine

d is called Alice’s secret key and e is called Alice’s Public key

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and if m = se mod n, signature is genuined is called Alice’s secret key and e is called Alice’s Public key

Is the Scheme secure?

No!given (n, e) private key of Alice cannot be calculatedgiven document m, s = md could not be guessed.Problem: forging given m1,m2 as two document, and s1, s2 as theirdigital signature, one can find the valid signature of m1.m2 as s1.s2

Also the length of the signature is proportional to the size of thedocumentslow

What could we do now?

given (n, e) private key of Alice cannot be calculatedgiven document m, s = md could not be guessed.Problem: forging given m1,m2 as two document, and s1, s2 as theirdigital signature, one can find the valid signature of m1.m2 as s1.s2

No!given (n, e) private key of Alice cannot be calculated

given document m, s = md could not be guessed.Problem: forging given m1,m2 as two document, and s1, s2 as theirdigital signature, one can find the valid signature of m1.m2 as s1.s2

No!given (n, e) private key of Alice cannot be calculatedgiven document m, s = md could not be guessed.

Problem: forging given m1,m2 as two document, and s1, s2 as theirdigital signature, one can find the valid signature of m1.m2 as s1.s2

Also the length of the signature is proportional to the size of thedocument

slowWhat could we do now?

SHA: Secure Hash Functions

An Ideal Hash function is one which has following propertiesgiven f (x) it is impossible to guess x

given x1 its is impossible to find x2 such that f (x1) = f (x2)it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

An Ideal Hash function is one which has following propertiesgiven f (x) it is impossible to guess xgiven x1 its is impossible to find x2 such that f (x1) = f (x2)

it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

An Ideal Hash function is one which has following propertiesgiven f (x) it is impossible to guess xgiven x1 its is impossible to find x2 such that f (x1) = f (x2)it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

Merkle Demgrad Construction

Need of Padding message m?

m is prefix of PAD(m)if |m1| = |m2| then |PAD(m1)| = |PAD(m2)|if |m1| 6= |m2| then the last block of PAD(m1) 6= PAD(m2)

Need of Padding message m?m is prefix of PAD(m)

if |m1| = |m2| then |PAD(m1)| = |PAD(m2)|if |m1| 6= |m2| then the last block of PAD(m1) 6= PAD(m2)

Need of Padding message m?m is prefix of PAD(m)if |m1| = |m2| then |PAD(m1)| = |PAD(m2)|

if |m1| 6= |m2| then the last block of PAD(m1) 6= PAD(m2)

Need of Padding message m?m is prefix of PAD(m)if |m1| = |m2| then |PAD(m1)| = |PAD(m2)|if |m1| 6= |m2| then the last block of PAD(m1) 6= PAD(m2)

Hash Functions

Outline

1 Recap

2 Hash Functions

3 Digital Signature

4 Cryptocurrency

Hash Functions

Hash Function:

Figure: Hash FunctionRas Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 10 / 43

Hash Functions

Document integrity

If I have a document ”m” and I publish its hash ”H(m)”Can I change document later?Can I have two document with same Hash?Can I verify a document with incorrect Hash

Hash Functions

Document integrity

If I have a document ”m” and I publish its hash ”H(m)”

Can I change document later?Can I have two document with same Hash?Can I verify a document with incorrect Hash

Hash Functions

Document integrity

If I have a document ”m” and I publish its hash ”H(m)”Can I change document later?

Can I have two document with same Hash?Can I verify a document with incorrect Hash

Hash Functions

Document integrity

If I have a document ”m” and I publish its hash ”H(m)”Can I change document later?Can I have two document with same Hash?

Can I verify a document with incorrect Hash

Hash Functions

Document integrity

Hash Functions

Document integrity

Digital Signature

Outline

1 Recap

2 Hash Functions

3 Digital Signature

4 Cryptocurrency

Digital Signature

AIM: Convince everybody that Alice have signed the document

nobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuined problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

simple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuined problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not work

IDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuined problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSA

for document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuined problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuine

d problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentsimple pasting a copy of signature do not workIDEA: USE RSAfor document m Alice uses s = md as her digital signature. To verify,verifier calculates se and ifm = se mod n, signature is genuined problem: given s(m1) and s(m2) one could calculate s(m1.m2)

Digital Signature

Digital Signature: Another try

IDEA: publish hash of document m as h = H(m)IDEA: USE RSAfor document m Alice uses s = hd as her digital signature.To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuined given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentIDEA: publish hash of document m as h = H(m)

IDEA: USE RSAfor document m Alice uses s = hd as her digital signature.To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuined given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentIDEA: publish hash of document m as h = H(m)IDEA: USE RSA

for document m Alice uses s = hd as her digital signature.To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuined given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentIDEA: publish hash of document m as h = H(m)IDEA: USE RSAfor document m Alice uses s = hd as her digital signature.

To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuined given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentIDEA: publish hash of document m as h = H(m)IDEA: USE RSAfor document m Alice uses s = hd as her digital signature.To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuine

d given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

AIM: Convince everybody that Alice have signed the documentnobody should be able to forge the documentIDEA: publish hash of document m as h = H(m)IDEA: USE RSAfor document m Alice uses s = hd as her digital signature.To verify, verifier calculates se and ifH(m) = se mod n, signature isgenuined given s(m1) and s(m2) one can not calculate s(m1.m2)

Digital Signature

Summary

Symmetric vs asymmetric encryption system

RSASHA as tool for data integrityDigital signature

Digital Signature

Summary

Symmetric vs asymmetric encryption systemRSA

SHA as tool for data integrityDigital signature

Digital Signature

Summary

Symmetric vs asymmetric encryption systemRSASHA as tool for data integrity

Digital signature

Digital Signature

Summary

Symmetric vs asymmetric encryption systemRSASHA as tool for data integrityDigital signature

Digital Signature

Summary

Symmetric vs asymmetric encryption systemRSASHA as tool for data integrityDigital signature

Cryptocurrency

Outline

1 Recap

2 Hash Functions

3 Digital Signature

4 Cryptocurrency

Cryptocurrency

Figure: Barter Trade

Problem: Meet of Demand

Cryptocurrency

how to Meet Demand

Medium of Exchange

Cryptocurrency

how to Meet Demand

Medium of ExchangeGold

Cryptocurrency

Meet of Demand

Figure: Coins

Confidence of metal insideProblem: Difficult to carry

Cryptocurrency

Meet of Demand

Figure: Coins

Confidence of metal inside

Problem: Difficult to carry

Cryptocurrency

Meet of Demand

Figure: Coins

Confidence of metal insideProblem: Difficult to carry

Cryptocurrency

Solution: Paper note

Figure: paper note

problem: Paper alone do not have value

Cryptocurrency

Solution: Paper note

Figure: paper note

problem: Paper alone do not have valueRas Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 20 / 43

Cryptocurrency

What gives currency power?

Backed by RBI

RBI controls the flowstrong regulation against counterfeiting

Cryptocurrency

Backed by RBIRBI controls the flow

strong regulation against counterfeiting

Cryptocurrency

Backed by RBIRBI controls the flowstrong regulation against counterfeiting

Cryptocurrency

Backed by RBIRBI controls the flowstrong regulation against counterfeiting

Cryptocurrency

Digital currency

Figure: PoS machine

Cryptocurrency

Digital currency

Figure: PoS machineRas Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 22 / 43

Cryptocurrency

Digital currency

Backed by Central Bank to give legitimacyproblem: Double spendingsolution:Central server to record all the transactionEnter Banks: act as centralized server

Cryptocurrency

Digital currency

Backed by Central Bank to give legitimacy

problem: Double spendingsolution:Central server to record all the transactionEnter Banks: act as centralized server

Cryptocurrency

Digital currency

Backed by Central Bank to give legitimacyproblem: Double spending

solution:Central server to record all the transactionEnter Banks: act as centralized server

Cryptocurrency

Digital currency

Backed by Central Bank to give legitimacyproblem: Double spendingsolution:

Central server to record all the transactionEnter Banks: act as centralized server

Cryptocurrency

Digital currency

Backed by Central Bank to give legitimacyproblem: Double spendingsolution:Central server to record all the transaction

Enter Banks: act as centralized server

Cryptocurrency

Digital currency

Cryptocurrency

Digital currency

Cryptocurrency

2008 Recession

Figure: Caption

problem: cannot trust the banks

Cryptocurrency

Cryptocurrency: The Begining

problem: cannot trust bank

and their ledgersolution: Make decentralized ledger

Figure: The hindu

Cryptocurrency

problem: cannot trust bank and their ledger

solution: Make decentralized ledger

Figure: The hindu

Cryptocurrency

problem: cannot trust bank and their ledgersolution: Make decentralized ledger

Figure: The hindu

Cryptocurrency

problem: cannot trust bank and their ledgersolution: Make decentralized and permissionless ledger

Figure: Caption

Cryptocurrency

Problem solved?

No!It just exploded.

Cryptocurrency

Problem solved?No!

It just exploded.

Cryptocurrency

Problem solved?No!It just exploded.

Cryptocurrency

Problem 1: Identity

bank used to do the verification and assign an identity to the accountnumberfor India KYC normsWho would do identity management here?Think RSA !!

Cryptocurrency

Problem 1: Identity

bank used to do the verification and assign an identity to the accountnumber

for India KYC normsWho would do identity management here?Think RSA !!

Cryptocurrency

Problem 1: Identity

bank used to do the verification and assign an identity to the accountnumberfor India KYC norms

Who would do identity management here?Think RSA !!

Cryptocurrency

Problem 1: Identity

bank used to do the verification and assign an identity to the accountnumberfor India KYC normsWho would do identity management here?

Think RSA !!

Cryptocurrency

Problem 1: Identity

Cryptocurrency

Problem 1: Identity

Cryptocurrency

Identity: RSA a quick look

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to all

Secret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to none

Anybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt it

Idea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea:

What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identity

nobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,

but does that really matters?Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?

Anonymity comes for free

Cryptocurrency

Public key: Known to allSecret key: known to noneAnybody can use my public key to encrypt the text and only I candecrypt itIdea: What if I make Public key as Identitynobody would know my real identity,but does that really matters?Anonymity comes for free

Cryptocurrency

Problem 2: Authorization

How does Banks do it?

They provide you with some secret key like: Password, PIN, OTP, whichyou can use to verify your identityproblem: No trusted BanksSolution: use Digital signature with secret key of RSA :)

Cryptocurrency

How does Banks do it?They provide you with some secret key like: Password, PIN, OTP, whichyou can use to verify your identity

problem: No trusted BanksSolution: use Digital signature with secret key of RSA :)

Cryptocurrency

How does Banks do it?They provide you with some secret key like: Password, PIN, OTP, whichyou can use to verify your identityproblem: No trusted BanksSolution:

use Digital signature with secret key of RSA :)

Cryptocurrency

How does Banks do it?They provide you with some secret key like: Password, PIN, OTP, whichyou can use to verify your identityproblem: No trusted BanksSolution: use Digital signature with secret key of RSA

Cryptocurrency

How does Banks do it?They provide you with some secret key like: Password, PIN, OTP, whichyou can use to verify your identityproblem: No trusted BanksSolution: use Digital signature with secret key of RSA :)

Cryptocurrency

Problem 3: How to know your balance?

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?

They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.

Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger

and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every account

what could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do?

Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodes

Problem solved? No!

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved?

Cryptocurrency

How does Banks do it?They maintain each and every account and every transaction.Basically a ledger and a ledger for each and every accountwhat could we do? Maintain a ledger over distributed nodesProblem solved? No!

Cryptocurrency

Problem 3: How to update ledger

Solution 1allow any node to write it

Problem: how do you know that node is trustworthy?Solution: verify it by majoritycost for not trusting central bank

Cryptocurrency

Solution 1allow any node to write itProblem:

how do you know that node is trustworthy?Solution: verify it by majoritycost for not trusting central bank

Cryptocurrency

Solution 1allow any node to write itProblem: how do you know that node is trustworthy?

Solution: verify it by majoritycost for not trusting central bank

Cryptocurrency

Solution 1allow any node to write itProblem: how do you know that node is trustworthy?Solution:

verify it by majoritycost for not trusting central bank

Cryptocurrency

Solution 1allow any node to write itProblem: how do you know that node is trustworthy?Solution: verify it by majority

cost for not trusting central bank

Cryptocurrency

Solution 1allow any node to write itProblem: how do you know that node is trustworthy?Solution: verify it by majoritycost for not trusting central bank

Cryptocurrency

Solution 2allow any node to write it

and verify it by majorityProblem:Sybil AttackSybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majority

Problem:Sybil AttackSybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:

Sybil AttackSybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:Sybil Attack

Sybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:Sybil AttackSybil attack: Where one node have more than one identities

Solution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:Sybil AttackSybil attack: Where one node have more than one identitiesSolution:

Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:Sybil AttackSybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resources

What are the resources available?

Cryptocurrency

Solution 2allow any node to write it and verify it by majorityProblem:Sybil AttackSybil attack: Where one node have more than one identitiesSolution: Ask them to show proof of some limited resourcesWhat are the resources available?

Cryptocurrency

Proof of Work

Limited Resource is your computation power.

you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)

How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?

Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problems

What could be a difficult problem ?We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?

We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.

Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.Factoring

problem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We have seen one such problem before.Factoringproblem: how would you find such difficult problems again and again

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?

We know hash is uniformly distributedAsk them to find a hash of number, such that it has certain numberof leading zerosAdvantage: you can control the difficulty level of the problem

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We know hash is uniformly distributed

Ask them to find a hash of number, such that it has certain numberof leading zerosAdvantage: you can control the difficulty level of the problem

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We know hash is uniformly distributedAsk them to find a hash of number, such that it has certain numberof leading zeros

Advantage: you can control the difficulty level of the problem

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We know hash is uniformly distributedAsk them to find a hash of number, such that it has certain numberof leading zerosAdvantage: you can control the difficulty level of the problem

Cryptocurrency

Proof of Work

Limited Resource is your computation power. you cannot fake it :)How to implement it?Ask them to solve some very difficult problemsWhat could be a difficult problem ?We know hash is uniformly distributedAsk them to find a hash of number, such that it has certain numberof leading zerosAdvantage: you can control the difficulty level of the problem

Cryptocurrency

An Ideal Hash function f (x) : {0, 1}m → {0, 1}n is one which hasfollowing properties

given f (x) it is impossible to guess x

given x1 its is impossible to find x2 such that f (x1) = f (x2)it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

Cryptocurrency

given f (x) it is impossible to guess xgiven x1 its is impossible to find x2 such that f (x1) = f (x2)

it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

Cryptocurrency

given f (x) it is impossible to guess xgiven x1 its is impossible to find x2 such that f (x1) = f (x2)it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

Cryptocurrency

given f (x) it is impossible to guess xgiven x1 its is impossible to find x2 such that f (x1) = f (x2)it is impossible to find x1, x2, such that x1 6= x2 and f (x1) = f (x2)

Cryptocurrency

Problem 3: update the ledger

Ask every node to collect the transactions

verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify them

consolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then

guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random number

such that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zeros

then the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify it

Gossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocol

once verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Ask every node to collect the transactions verify themconsolidate them into a block and then guess a random numbersuch that hash of the block has certain leading zerosthen the successful node propagates the block to every other node,and they too verify itGossip Protocolonce verified they add it to their ledger

Cryptocurrency

Merkel tree

Figure: Merkle TreeRas Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 38 / 43

Cryptocurrency

What if two node are successful?accept the one which has better solution

Problem solved? No!

Cryptocurrency

Problem solved?

Cryptocurrency

Problem solved? No!

Cryptocurrency

Problem 4: how to know your balance

Assume that there is a public ledgerIt is not practical to maintain each and every account

Solution: modify transaction recording to get the balanceSuppose: A have to give B Rs. x . Initial balance of A was a and Bwas bwe record transaction as A→ B Rs xA→ A Rs a − xGain: you once you get to this transaction, you would never need tosee previous transactions to get balance of A

Cryptocurrency

Assume that there is a public ledgerIt is not practical to maintain each and every accountSolution: modify transaction recording to get the balance

Suppose: A have to give B Rs. x . Initial balance of A was a and Bwas bwe record transaction as A→ B Rs xA→ A Rs a − xGain: you once you get to this transaction, you would never need tosee previous transactions to get balance of A

Cryptocurrency

Assume that there is a public ledgerIt is not practical to maintain each and every accountSolution: modify transaction recording to get the balanceSuppose: A have to give B Rs. x . Initial balance of A was a and Bwas bwe record transaction as

A→ B Rs xA→ A Rs a − xGain: you once you get to this transaction, you would never need tosee previous transactions to get balance of A

Cryptocurrency

Assume that there is a public ledgerIt is not practical to maintain each and every accountSolution: modify transaction recording to get the balanceSuppose: A have to give B Rs. x . Initial balance of A was a and Bwas bwe record transaction as A→ B Rs xA→ A Rs a − x

Gain: you once you get to this transaction, you would never need tosee previous transactions to get balance of A

Cryptocurrency

Assume that there is a public ledgerIt is not practical to maintain each and every accountSolution: modify transaction recording to get the balanceSuppose: A have to give B Rs. x . Initial balance of A was a and Bwas bwe record transaction as A→ B Rs xA→ A Rs a − xGain: you once you get to this transaction, you would never need tosee previous transactions to get balance of A

Cryptocurrency

Problem 5: Double spending

Figure: Double SpendingRas Dwivedi (Indian Institute of Technology Kanpur) Introduction to Blockchain May 22, 2018 41 / 43

Cryptocurrency

Double spending

We have created blocks and verified them

integrity of each block is ensuredwe need to have integrity of all the block

Cryptocurrency

Double spending

We have created blocks and verified themintegrity of each block is ensured

we need to have integrity of all the block

Cryptocurrency

Double spending

We have created blocks and verified themintegrity of each block is ensuredwe need to have integrity of all the block

Cryptocurrency

Double spending

We have created blocks and verified themintegrity of each block is ensuredwe need to have integrity of all the block

Cryptocurrency

A Chain of blocks

Figure: A chain of block

Problem: How to organize them?Solution: Include hash of previous block

Cryptocurrency

A Chain of blocks

Problem: How to organize them?

Solution: Include hash of previous block

Cryptocurrency

A Chain of blocks

Cryptocurrency

A Chain of blocks

Lecture 2: Bitcoin and Cryptocurrency Ras DwivediIntroduction to Blockchain Lecture 2: Bitcoin and...

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