Asymmetric Key Signatures
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Introduction to Cryptocurrency University of Virginia cs4501 Fall 2015 http://bitcoin-class.org
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Introduction to Cryptocurrency
University of Virginia
cs4501 Fall 2015
http://bitcoin-class.org
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This document discusses cryptography and how it can be used to own digital goods like cryptocurrency. It begins by introducing key concepts in cryptography like cryptosystems, attacks, and asymmetry. It then discusses how early systems like Jefferson's wheel cipher provided security through obscurity of algorithms and keys. The document explores how brute force attacks become impractical as key sizes increase due to the vast amounts of energy required. It introduces public key cryptography and how RSA provides asymmetry through a trapdoor function. The document explains how asymmetric cryptography can be used for signatures and confidentiality. It concludes by noting how cryptography achieves the scarcity needed for digital ownership of coins.
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This document summarizes a class lecture on cryptocurrency mining. It discusses the mining process, which involves finding a nonce value that satisfies the mining difficulty target for a block. Miners include transactions and solve cryptographic puzzles to validate blocks and earn rewards. The document explains Merkle trees, which improve transaction verification scalability. It also discusses the high computational costs and energy requirements of mining, noting specialized mining hardware can solve puzzles thousands of times faster than CPUs. The goal of mining is to process and validate transactions in a decentralized manner to maintain blockchain integrity.
Class 1: What is Money?
This document provides an overview of a class on cryptocurrency and bitcoin. It discusses what makes a good currency, the history of currencies like salt and fiat currency, and challenges with decentralized digital currencies. It introduces bitcoin's approach of using a public ledger recorded through mining to record all transactions in a decentralized way without requiring trust in a central authority. The class will cover cryptography, computer science, economics and other topics through studying bitcoin as a concrete system. Students are assigned to set up a bitcoin wallet and complete readings before the next class.
Introduction to Cryptography
- The document provides an overview of the schedule and topics for a cryptography class, including an introduction to cryptography today, Elliptic Curve Cryptography and signatures on Wednesday, and a checkup on the first three classes next Monday.
- It also lists the assigned readings for chapters 1-4 of the textbook and provides information about the backgrounds of students in the class.
- The remainder of the document discusses setting up a Bitcoin wallet, downloading the blockchain, hierarchical deterministic wallets, and provides a recap of the concepts from the previous class around what makes something a currency and how ownership of digital goods can be established.
Hash functions
This document discusses hash functions and their uses in digital signatures and Bitcoin transactions. It explains that hash functions map arbitrary-length strings to fixed-length outputs and are used to sign transactions to prevent later modification. Common hash properties like collision resistance are described. The document also discusses the birthday problem as it applies to hash functions and estimates the number of trials needed to find collisions for different hash lengths. Examples of standardized hash functions and their security status over time are provided. Applications of hash functions like password storage, deduplication, and Merkle trees for partial verification in Bitcoin are also covered.
Merkle Trees
The document summarizes a class on Merkle trees. It recaps blockchain and exploring the Bitcoin core code. It discusses how transactions are recorded in blocks and introduces Merkle trees as a method to efficiently verify all transactions are included in a block. The class plan includes a quiz the following week to assess understanding of concepts covered so far, including mining. Students are notified that Project 2 will be assigned and they should begin work before the next class.
Recommended
Becoming More Paranoid
Introduction to Cryptocurrency
University of Virginia
cs4501 Fall 2015
http://bitcoin-class.org
Cryptography
This document discusses cryptography and how it can be used to own digital goods like cryptocurrency. It begins by introducing key concepts in cryptography like cryptosystems, attacks, and asymmetry. It then discusses how early systems like Jefferson's wheel cipher provided security through obscurity of algorithms and keys. The document explores how brute force attacks become impractical as key sizes increase due to the vast amounts of energy required. It introduces public key cryptography and how RSA provides asymmetry through a trapdoor function. The document explains how asymmetric cryptography can be used for signatures and confidentiality. It concludes by noting how cryptography achieves the scarcity needed for digital ownership of coins.
More mining
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Mining
This document summarizes a class lecture on cryptocurrency mining. It discusses the mining process, which involves finding a nonce value that satisfies the mining difficulty target for a block. Miners include transactions and solve cryptographic puzzles to validate blocks and earn rewards. The document explains Merkle trees, which improve transaction verification scalability. It also discusses the high computational costs and energy requirements of mining, noting specialized mining hardware can solve puzzles thousands of times faster than CPUs. The goal of mining is to process and validate transactions in a decentralized manner to maintain blockchain integrity.
Class 1: What is Money?
This document provides an overview of a class on cryptocurrency and bitcoin. It discusses what makes a good currency, the history of currencies like salt and fiat currency, and challenges with decentralized digital currencies. It introduces bitcoin's approach of using a public ledger recorded through mining to record all transactions in a decentralized way without requiring trust in a central authority. The class will cover cryptography, computer science, economics and other topics through studying bitcoin as a concrete system. Students are assigned to set up a bitcoin wallet and complete readings before the next class.
Introduction to Cryptography
- The document provides an overview of the schedule and topics for a cryptography class, including an introduction to cryptography today, Elliptic Curve Cryptography and signatures on Wednesday, and a checkup on the first three classes next Monday.
- It also lists the assigned readings for chapters 1-4 of the textbook and provides information about the backgrounds of students in the class.
- The remainder of the document discusses setting up a Bitcoin wallet, downloading the blockchain, hierarchical deterministic wallets, and provides a recap of the concepts from the previous class around what makes something a currency and how ownership of digital goods can be established.
Hash functions
This document discusses hash functions and their uses in digital signatures and Bitcoin transactions. It explains that hash functions map arbitrary-length strings to fixed-length outputs and are used to sign transactions to prevent later modification. Common hash properties like collision resistance are described. The document also discusses the birthday problem as it applies to hash functions and estimates the number of trials needed to find collisions for different hash lengths. Examples of standardized hash functions and their security status over time are provided. Applications of hash functions like password storage, deduplication, and Merkle trees for partial verification in Bitcoin are also covered.
Merkle Trees
The document summarizes a class on Merkle trees. It recaps blockchain and exploring the Bitcoin core code. It discusses how transactions are recorded in blocks and introduces Merkle trees as a method to efficiently verify all transactions are included in a block. The class plan includes a quiz the following week to assess understanding of concepts covered so far, including mining. Students are notified that Project 2 will be assigned and they should begin work before the next class.
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This document summarizes a class about hidden services using Tor and zero knowledge proofs. It discusses the rise of Bitcoin prices in August 2015, provides an overview of how Tor hidden services work through a network of nodes, and how the FBI was able to locate the Silk Road server. It also mentions that Problem Set 3 is due and lists upcoming office hours for students to attend.
Altcoins
This document discusses alternatives to Bitcoin cryptocurrency design. It summarizes Litecoin, which uses a different proof-of-work algorithm called Scrypt, allowing for faster transaction confirmations. Ripple is described as eliminating proof-of-work entirely, reaching consensus through a variation of Byzantine Paxos voting among servers. Ethereum allows for distributed applications through a scripting language and features a more complex mining reward system than Bitcoin. Common security issues with smart contracts are also outlined.
Scripting Transactions
The document summarizes a class on scripting and transactions in cryptocurrency. It discusses how Bitcoin core code has evolved over time to interpret scripts for locking and unlocking transactions. Examples are provided of common script patterns used prior to 2010, including pay-to-pubkey-hash and an important bug discovered that could allow stealing outputs. More advanced scripting options are also mentioned, such as checkmultisig.
Midterm Confirmations
1) The midterm discussion covered confirmations in cryptocurrency transactions and the average wait time for the first confirmation.
2) It was noted that the threshold for being considered a "bitcoin expert" based on answering questions well on the midterm was around 85% of questions answered correctly.
3) Students were given updates on assignment due dates and opportunities to improve their midterm score by identifying and correcting incorrect statements in a referenced blockchain report.
Bitcoin Script
The document summarizes a class on cryptocurrency and Bitcoin script. It discusses generating Bitcoin addresses through hashing public keys, describes the Bitcoin script language as a stack-based language similar to JVML used to write programs in transactions. It also notes that while Bitcoin script has limitations, altcoins are taking different approaches to scripting languages. Finally, it reminds students that project 2 is due Friday and the next class will feature a guest lecture from Tom Dukes on cyberlaw.
The Blockchain
http://bitcoin-class.org
Introduction to Cryptocurrency
University of Virginia
cs4501 Fall 2015
Anonymity in Bitcoin
This document summarizes anonymity and unlinkability in bitcoin transactions. It discusses how using different bitcoin addresses, or pseudonyms, makes it difficult to link transactions. Techniques like coinjoin and mixers are described that further confound tracing transactions by combining inputs from multiple users. The document mentions Silk Road, an illegal darknet market, and how its founder Ross Ulbricht now aims to create an economic simulation without coercion. It covers some threats to validity in analyzing anonymity and ends discussing communication privacy techniques like onion routing.
Cryptocurrency Jeopardy!
This document contains the notes from a class about cryptocurrency. It discusses the final exam, which will involve explaining bitcoin to different audiences and answering substantive questions. It then lists the names of students in the class divided into teams based on their answers to a registration question. The rest of the document outlines a jeopardy game about cryptocurrency topics played between the student teams, including questions about Satoshi Nakamoto, hashing, scripts, cryptography, randomness, and altcoins.
暗認本読書会11
The document summarizes key concepts in homomorphic encryption and secure multiparty computation including:
1) Homomorphic encryption allows computations to be performed directly on encrypted data without decrypting it first, such as adding or multiplying encrypted values.
2) Secure multiparty computation allows multiple parties to jointly compute a function over their private inputs while keeping those inputs private.
3) Secret sharing techniques like Shamir's secret sharing and verifiable secret sharing (VSS) allow a secret to be divided into shares and reconstructed from a subset of shares.
digital signatures.pptx
Digital signatures allow a document to be signed using a secret key so that the signature can be verified by anyone with the corresponding public key. A digital signature scheme (DSS) consists of key generation, signing, and verification algorithms. DSS provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. Message authentication codes (MACs) are similar but do not provide non-repudiation since anyone can generate valid MACs given the key. Common DSS include RSA signatures, which sign a hash of the message using the private key, and Schnorr signatures, which are based on discrete logarithm problems in groups.
module_14_digital_signatures (1).pptx
Digital signatures allow a document to be signed by a secret key holder and verified by anyone with the public verification key. A digital signature scheme (DSS) consists of key generation, signing, and verification algorithms. DSS provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. Message authentication codes (MACs) are similar but do not provide non-repudiation like signatures since anyone can generate MACs given the secret key. The RSA and Schnorr signature schemes are examples of DSS that are based on computational hardness assumptions like factoring or discrete logarithms.
digital signatures1.pptx
A digital signature allows a document to be signed using a secret key, and verified using a public key. It provides correctness, meaning the verification will succeed for a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not see signed. Digital signature schemes involve key generation, signing messages with the secret key, and verifying signatures with the public key. They differ from message authentication codes in that signatures can be verified by anyone with the public key, while MAC verification requires knowledge of the secret key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.
digital signatures10.pptx
A digital signature allows the holder of a secret key to sign a document, and anyone with the verification key can verify the signature is valid and correct. A digital signature scheme (DSS) includes key generation, signing, and verification algorithms. DSS provides correctness, meaning verification will accept a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not sign. While message authentication codes (MACs) are similar, they do not necessarily provide unforgeability without the key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.
module_14_digital_signatures.pptx
The document discusses digital signatures and digital signature schemes (DSS). It defines a digital signature as allowing the holder of a secret key to sign a document such that anyone with the public verification key can verify the signature is valid from the signer. A DSS includes key generation, signing, and verification algorithms. It also discusses how DSS provides correctness by verifying valid signatures and unforgeability by making signature forgery difficult. The document contrasts DSS with message authentication codes (MACs) and provides examples of RSA and Schnorr signature schemes.
Cs166 mynote
This document provides definitions and explanations of key concepts in information security and cryptography. It discusses symmetric and asymmetric cryptographic techniques such as stream ciphers, block ciphers, digital signatures, hash functions, and the use of random numbers for security applications. It also covers concepts like confidentiality, integrity, availability, cryptanalysis, plain text, cipher text, and the differences between symmetric and public key cryptography.
digital Information BD.pptx
- A digital signature allows the holder of a secret key to sign a document, and anyone with the public verification key can verify the signature is valid and correct. It is not possible to forge a signature even with the verification key.
- A digital signature scheme (DSS) involves key generation, signing messages with the secret key, and verifying signatures with the public key. It satisfies correctness, meaning signatures can be verified, and unforgeability, meaning signatures cannot be forged.
- While message authentication codes (MACs) also provide signature functionality by signing with a secret key, they are not considered true signatures because verification may not be possible without the secret key. Signatures use public/private key pairs to
digital10.pptx
The document discusses digital signatures and signature schemes. It defines a digital signature as allowing the holder of a secret key to sign a document so that anyone with the public verification key can verify the signature is valid. It describes the basic structure of a digital signature scheme including key generation, signing, and verification. It compares digital signature schemes to message authentication codes and discusses how signatures provide non-repudiation while MACs do not. It also covers the security properties of correctness and unforgeability for digital signature schemes.
Smart City Lecture 5 - Introduction to Encryption
This lecture gives an introduction to the field of cryptography for engineers. It provides an overview of hash algorithms, symmetric, asymmetric and hybrid ciphers, introduces Elliptic Curve Cryptography, and related algorithms (ECDH, ECDSA). It present Public Key Infrastructure (PKI), certificates (X.509), and how these can be automatically updated (ACME). It discusses Transport Encryption (TLS, DTLS), and End-to-End encryption, and when the latter is needed. Some common forms of attack are presented, to motivate the listener to implement the ubiquitous encryption policy (“Encrypt Everywhere”) in their solutions and organizations.
digital Information.pptx
A digital signature allows the holder of a secret key to sign a document, and anyone with the public verification key can verify the signature is valid and correct. No one can forge a signature even if they know the verification key. A digital signature scheme (DSS) involves key generation, signing messages, and verifying signatures. It provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. While message authentication codes (MACs) are similar, they do not necessarily provide non-repudiation like signatures since anyone can generate MACs without the secret key. Signatures require more computation than MACs due to public-key operations. To improve efficiency, signatures
暗認本読書会5
1. The document discusses public key cryptography concepts like Diffie-Hellman key exchange, finite fields, discrete logarithm problems, key encapsulation mechanisms, and the security properties of IND-CCA security.
2. It provides examples of finite field arithmetic and constructions of finite fields and explains how fields can be extended.
3. The document compares public key cryptography and common key cryptography, noting that public key cryptography allows each user to have a single private key regardless of the number of users.
Homomorphic Encryption
Homomorphic encryption allows computations to be performed on encrypted data without decrypting it first. This document discusses homomorphic encryption techniques including partially homomorphic encryptions that support either addition or multiplication operations, and fully homomorphic encryption introduced by Craig Gentry that supports both types of operations. It also covers the use of ideal lattices in lattice-based cryptosystems and the bootstrapping technique used to "refresh" ciphertexts and prevent noise from accumulating during homomorphic computations.
Lifted-ElGamal暗号を用いた任意関数演算の二者間秘密計算プロトコルのmaliciousモデルにおける効率化
This document summarizes an improved protocol for secure two-party computation using additive homomorphic encryption. The proposed protocol allows a server to compute an encrypted function f(m) on an encrypted input Enc(m), without learning the plaintext value m, with the help of a client who holds the decryption key. The improvement reduces the protocol to 1 round of communication, compared to 2 rounds previously, and reduces the communication size by a factor of 40-130x. It achieves this by having the client use zero-knowledge proofs to convince the server that it correctly generated the output encryption Enc'(f(m)) from the input encryption Enc(m), without revealing any plaintext values.
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This document summarizes a class about hidden services using Tor and zero knowledge proofs. It discusses the rise of Bitcoin prices in August 2015, provides an overview of how Tor hidden services work through a network of nodes, and how the FBI was able to locate the Silk Road server. It also mentions that Problem Set 3 is due and lists upcoming office hours for students to attend.
Altcoins
This document discusses alternatives to Bitcoin cryptocurrency design. It summarizes Litecoin, which uses a different proof-of-work algorithm called Scrypt, allowing for faster transaction confirmations. Ripple is described as eliminating proof-of-work entirely, reaching consensus through a variation of Byzantine Paxos voting among servers. Ethereum allows for distributed applications through a scripting language and features a more complex mining reward system than Bitcoin. Common security issues with smart contracts are also outlined.
Scripting Transactions
The document summarizes a class on scripting and transactions in cryptocurrency. It discusses how Bitcoin core code has evolved over time to interpret scripts for locking and unlocking transactions. Examples are provided of common script patterns used prior to 2010, including pay-to-pubkey-hash and an important bug discovered that could allow stealing outputs. More advanced scripting options are also mentioned, such as checkmultisig.
Midterm Confirmations
1) The midterm discussion covered confirmations in cryptocurrency transactions and the average wait time for the first confirmation.
2) It was noted that the threshold for being considered a "bitcoin expert" based on answering questions well on the midterm was around 85% of questions answered correctly.
3) Students were given updates on assignment due dates and opportunities to improve their midterm score by identifying and correcting incorrect statements in a referenced blockchain report.
Bitcoin Script
The document summarizes a class on cryptocurrency and Bitcoin script. It discusses generating Bitcoin addresses through hashing public keys, describes the Bitcoin script language as a stack-based language similar to JVML used to write programs in transactions. It also notes that while Bitcoin script has limitations, altcoins are taking different approaches to scripting languages. Finally, it reminds students that project 2 is due Friday and the next class will feature a guest lecture from Tom Dukes on cyberlaw.
The Blockchain
http://bitcoin-class.org
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University of Virginia
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This document summarizes anonymity and unlinkability in bitcoin transactions. It discusses how using different bitcoin addresses, or pseudonyms, makes it difficult to link transactions. Techniques like coinjoin and mixers are described that further confound tracing transactions by combining inputs from multiple users. The document mentions Silk Road, an illegal darknet market, and how its founder Ross Ulbricht now aims to create an economic simulation without coercion. It covers some threats to validity in analyzing anonymity and ends discussing communication privacy techniques like onion routing.
Cryptocurrency Jeopardy!
This document contains the notes from a class about cryptocurrency. It discusses the final exam, which will involve explaining bitcoin to different audiences and answering substantive questions. It then lists the names of students in the class divided into teams based on their answers to a registration question. The rest of the document outlines a jeopardy game about cryptocurrency topics played between the student teams, including questions about Satoshi Nakamoto, hashing, scripts, cryptography, randomness, and altcoins.
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The document summarizes key concepts in homomorphic encryption and secure multiparty computation including:
1) Homomorphic encryption allows computations to be performed directly on encrypted data without decrypting it first, such as adding or multiplying encrypted values.
2) Secure multiparty computation allows multiple parties to jointly compute a function over their private inputs while keeping those inputs private.
3) Secret sharing techniques like Shamir's secret sharing and verifiable secret sharing (VSS) allow a secret to be divided into shares and reconstructed from a subset of shares.
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Digital signatures allow a document to be signed using a secret key so that the signature can be verified by anyone with the corresponding public key. A digital signature scheme (DSS) consists of key generation, signing, and verification algorithms. DSS provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. Message authentication codes (MACs) are similar but do not provide non-repudiation since anyone can generate valid MACs given the key. Common DSS include RSA signatures, which sign a hash of the message using the private key, and Schnorr signatures, which are based on discrete logarithm problems in groups.
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A digital signature allows a document to be signed using a secret key, and verified using a public key. It provides correctness, meaning the verification will succeed for a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not see signed. Digital signature schemes involve key generation, signing messages with the secret key, and verifying signatures with the public key. They differ from message authentication codes in that signatures can be verified by anyone with the public key, while MAC verification requires knowledge of the secret key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.
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A digital signature allows the holder of a secret key to sign a document, and anyone with the verification key can verify the signature is valid and correct. A digital signature scheme (DSS) includes key generation, signing, and verification algorithms. DSS provides correctness, meaning verification will accept a valid signature, and unforgeability, meaning an adversary cannot generate a valid signature for a message they did not sign. While message authentication codes (MACs) are similar, they do not necessarily provide unforgeability without the key. Popular digital signature schemes include RSA signatures and the Schnorr signature scheme.
module_14_digital_signatures.pptx
The document discusses digital signatures and digital signature schemes (DSS). It defines a digital signature as allowing the holder of a secret key to sign a document such that anyone with the public verification key can verify the signature is valid from the signer. A DSS includes key generation, signing, and verification algorithms. It also discusses how DSS provides correctness by verifying valid signatures and unforgeability by making signature forgery difficult. The document contrasts DSS with message authentication codes (MACs) and provides examples of RSA and Schnorr signature schemes.
Cs166 mynote
This document provides definitions and explanations of key concepts in information security and cryptography. It discusses symmetric and asymmetric cryptographic techniques such as stream ciphers, block ciphers, digital signatures, hash functions, and the use of random numbers for security applications. It also covers concepts like confidentiality, integrity, availability, cryptanalysis, plain text, cipher text, and the differences between symmetric and public key cryptography.
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- A digital signature allows the holder of a secret key to sign a document, and anyone with the public verification key can verify the signature is valid and correct. It is not possible to forge a signature even with the verification key.
- A digital signature scheme (DSS) involves key generation, signing messages with the secret key, and verifying signatures with the public key. It satisfies correctness, meaning signatures can be verified, and unforgeability, meaning signatures cannot be forged.
- While message authentication codes (MACs) also provide signature functionality by signing with a secret key, they are not considered true signatures because verification may not be possible without the secret key. Signatures use public/private key pairs to
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The document discusses digital signatures and signature schemes. It defines a digital signature as allowing the holder of a secret key to sign a document so that anyone with the public verification key can verify the signature is valid. It describes the basic structure of a digital signature scheme including key generation, signing, and verification. It compares digital signature schemes to message authentication codes and discusses how signatures provide non-repudiation while MACs do not. It also covers the security properties of correctness and unforgeability for digital signature schemes.
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This lecture gives an introduction to the field of cryptography for engineers. It provides an overview of hash algorithms, symmetric, asymmetric and hybrid ciphers, introduces Elliptic Curve Cryptography, and related algorithms (ECDH, ECDSA). It present Public Key Infrastructure (PKI), certificates (X.509), and how these can be automatically updated (ACME). It discusses Transport Encryption (TLS, DTLS), and End-to-End encryption, and when the latter is needed. Some common forms of attack are presented, to motivate the listener to implement the ubiquitous encryption policy (“Encrypt Everywhere”) in their solutions and organizations.
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A digital signature allows the holder of a secret key to sign a document, and anyone with the public verification key can verify the signature is valid and correct. No one can forge a signature even if they know the verification key. A digital signature scheme (DSS) involves key generation, signing messages, and verifying signatures. It provides correctness, meaning signatures can be verified, and unforgeability, meaning an adversary cannot generate valid signatures for unsigned messages. While message authentication codes (MACs) are similar, they do not necessarily provide non-repudiation like signatures since anyone can generate MACs without the secret key. Signatures require more computation than MACs due to public-key operations. To improve efficiency, signatures
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2. It provides examples of finite field arithmetic and constructions of finite fields and explains how fields can be extended.
3. The document compares public key cryptography and common key cryptography, noting that public key cryptography allows each user to have a single private key regardless of the number of users.
Homomorphic Encryption
Homomorphic encryption allows computations to be performed on encrypted data without decrypting it first. This document discusses homomorphic encryption techniques including partially homomorphic encryptions that support either addition or multiplication operations, and fully homomorphic encryption introduced by Craig Gentry that supports both types of operations. It also covers the use of ideal lattices in lattice-based cryptosystems and the bootstrapping technique used to "refresh" ciphertexts and prevent noise from accumulating during homomorphic computations.
Lifted-ElGamal暗号を用いた任意関数演算の二者間秘密計算プロトコルのmaliciousモデルにおける効率化
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- Cryptocurrency mining requires a massive amount of energy. A single large bitcoin mining facility in China uses $60,000 worth of electricity per month.
- The total hashing power of the bitcoin network is estimated to be around 4.2 x 10^17 hashes per second, equivalent to around 212 megawatts of power continuously. This is around 9 times the power output of Dominion Power's Lake Anna Power Station.
- It is estimated that it takes around 35,395 kWh of electricity to mine a single bitcoin, costing $2,831 at a rate of $0.08 per kWh. However, the reward for mining a block is currently around 25 BTC, worth $5
Multi-Party Computation for the Masses
Talk at CROSSING 2015
https://www.crossing.tu-darmstadt.de/en/crossing/events/crossing-workshop-2015/agenda/
Proof of Reserve
This document contains the agenda for a cryptocurrency class. It lists several student presentations on topics related to cryptocurrency that will take place, including analyses of SHA hashing in Bitcoin, financial markets and game theory related to cryptocurrencies, and studying coinbase reserves to predict market price. It also references materials on the history of banking and reserve requirements. The document provides details on cryptocurrency student projects and presentations for an upcoming class.
Silk Road
This document summarizes a class on cryptocurrency and Silk Road. It discusses sidechains and how they allow bitcoin to evolve. It covers the legality of bitcoin in different jurisdictions, with some considering it legal, others contentious, and some viewing it as hostile. It then discusses Silk Road, the illegal online marketplace that was shut down, and how it used Tor and bitcoin. It summarizes how the FBI claims to have found the Silk Road server despite its use of Tor anonymity technology.
Blooming Sidechains!
This document discusses Bloom filters and their use in Bitcoin simplified payment verification (SPV) nodes. It also covers merged mining, which allows mining of multiple cryptocurrencies like Bitcoin and Namecoin using the same hashing power. Sidechains are also mentioned. The document provides details on Bloom filter design and analysis, including the probability of false matches. It notes examples of merged mining blocks and addresses potential issues like those found in the Namecoin code. Project presentation dates are provided at the end.
Useful Proofs of Work, Permacoin
This document summarizes a class about proofs-of-work for cryptocurrencies like Bitcoin. It discusses how Bitcoin and other cryptocurrencies use computationally intensive but useless proofs-of-work like SHA-256 to motivate investment in specialized hardware. It also explores the possibility of proofs-of-work that have useful outputs, like protein folding, and challenges in designing proofs-of-work that produce useful work while maintaining security properties. Finally, it announces an upcoming class about project proposals.
Alternate Cryptocurrencies
This document discusses cryptocurrencies and alternative proofs of work. It begins with announcing that project proposals for the final class project are due on Thursday. It then provides information on estimating the cost of mining Bitcoin and an alternative cryptocurrency called PointCoin. Several alternative cryptocurrencies besides Bitcoin like Ripple, Litecoin and Dogecoin are described. Different hash functions and memory-hard proofs of work are explored, with the goal of finding a proof of work that produces something useful in addition to securing the blockchain. The document concludes by reminding students that project proposals are due on Thursday.
Script
This document provides an overview of Bitcoin scripting and transactions. It discusses the Bitcoin scripting language, which is stack-based and includes around 80 opcodes. Transactions include programs written in this scripting language. The document explains how scripts are interpreted to unlock transaction outputs. It also discusses limitations in the scripting language and how alternative cryptocurrencies are exploring different approaches. Examples of common script patterns used in Bitcoin transactions are presented.
Selfish Mining
The document discusses cryptocurrency and blockchain technology. It begins with announcements about an upcoming class on "Selfish Mining" and project deadlines. It then covers the decreasing block subsidy over time in Bitcoin, explaining why the last block with a subsidy will occur around the year 2140. The document also discusses the concept of "selfish mining", where miners withhold found blocks to try to gain an advantage in the blockchain. It notes how network infrastructure like high-speed fiber links can provide an advantage in validating transactions faster.
Quiz 2: Bitcoin Protocol, Mining, Supsersizing
This document contains the notes from a cryptocurrency class. It outlines the plan for the day which includes a quiz on a video, discussion of the quiz answers, and a lesson on the concept of "selfish mining" in cryptocurrencies. It also announces an upcoming talk the next day on new payment infrastructures and their social impact. Finally, it reminds students that the second part of Project 2 is due the following Thursday.
Mostly About Superfish
This document summarizes a class about cryptocurrency and blockchain technology. It discusses the Superfish malware incident, updating estimates of mining profitability given increasing bitcoin difficulty, and opportunities for students to attack the blockchain network or create other projects for a class assignment on cryptocurrency. Students are encouraged to collude with each other or deceive others for advantages during the assignment, within legal bounds. The document provides context and guidelines for a project where students will undermine the blockchain network or create alternative cryptocurrency applications.
Mining Pools and Profits
This document summarizes a class on cryptocurrency mining. It discusses mining pools, where miners pool resources to receive a regular payout, and the risks of attacks. It also examines the expected revenues of a hypothetical $479 mining rig over 17 months, finding the most likely outcome is earning around $620 total during that period. The document concludes by noting the largest mining pool controls around 25% of network hash power, posing little risk of a 51% attack that could compromise the blockchain.
More Mining
The document summarizes a class on cryptocurrency mining. It discusses upcoming projects, including building a cryptocurrency miner for Project 2 and proposing an open-ended final project. It also covers the economics and energy costs of bitcoin mining, estimating that the total mining power currently requires around 212 megawatts of power, similar to a large power plant. A suggested open-ended project is analyzing and comparing the energy use and costs of cryptocurrency mining networks to traditional financial infrastructure.
Mining
This document summarizes a class about bitcoin mining. It discusses the cost of computing required for mining, analyzing the cost of a sample function, and announces that starting code and hints for student miners will be posted that night. It also outlines the plans for upcoming classes which will cover attacks on bitcoin and ways to create a cryptocurrency without wasting large amounts of energy through mining.
Proofs of Work
This document discusses proofs of work and blockchain technology. It begins by explaining the purpose of project 1 and opportunities for students to earn credit. It then covers how proofs of work can be used to establish distributed trust in a public ledger or blockchain without a centralized authority. Specifically, it discusses how Bitcoin uses the SHA-256 hash function and difficulty adjustment to implement a proof of work that requires computational resources to add a block to the blockchain and maintain consensus. Students are also given opportunities to earn credit for project 1 by posting additional comments.
DigiCash
The document discusses David Evan's class on cryptocurrency and DigiCash. It summarizes untraceable cash protocols developed by David Chaum in the 1980s using blind signatures to allow a bank to sign transactions without seeing their content, making them untraceable. It also discusses how unique identifiers, identity strings, and a challenge-response protocol allow catching double-spenders while preserving user anonymity.
More from David Evans (18)
Trick or Treat?: Bitcoin for Non-Believers, Cryptocurrencies for Cypherpunks
Trick or Treat?: Bitcoin for Non-Believers, Cryptocurrencies for Cypherpunks
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Embedded machine learning-based road conditions and driving behavior monitoring
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
22CYT12-Unit-V-E Waste and its Management.ppt
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant
Slides for the 4th Presentation on LLM Fine-Tuning with QLoRA Presented by Anant, featuring DataStax Astra
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
原版一模一样【微信：741003700 】【美国密歇根州立大学毕业证学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
AI assisted telemedicine KIOSK for Rural India.pptx
It gives the overall description of SIH problem statement " AI assisted telemedicine KIOSK for Rural India".
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Null Bangalore | Pentesters Approach to AWS IAM
#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
BRAIN TUMOR DETECTION for seminar ppt.pdf
BRAIN TUMOR DETECTION
AND CLASSIFICATION USING
ARTIFICIAL INTELLIGENCE
cnn.pptx Convolutional neural network used for image classication
Convolutional Neural Network used for image classification
学校原版美国波士顿大学毕业证学历学位证书原版一模一样
原版一模一样【微信：741003700 】【美国波士顿大学毕业证学历学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样
原件一模一样【微信：bwp0011】《(Humboldt毕业证书)柏林大学毕业证学位证》【微信：bwp0011】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问微bwp0011
【主营项目】
一.毕业证【微bwp0011】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微bwp0011】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Batteries -Introduction – Types of Batteries – discharging and charging of battery - characteristics of battery –battery rating- various tests on battery- – Primary battery: silver button cell- Secondary battery :Ni-Cd battery-modern battery: lithium ion battery-maintenance of batteries-choices of batteries for electric vehicle applications.
Fuel Cells: Introduction- importance and classification of fuel cells - description, principle, components, applications of fuel cells: H2-O2 fuel cell, alkaline fuel cell, molten carbonate fuel cell and direct methanol fuel cells.
Computational Engineering IITH Presentation
This Presentation will give you a brief idea about what Computational Engineering at IIT Hyderabad has to offer.
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Embedded machine learning-based road conditions and driving behavior monitoring
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Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
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Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
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AI assisted telemedicine KIOSK for Rural India.pptx
AI assisted telemedicine KIOSK for Rural India.pptx
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...
cnn.pptx Convolutional neural network used for image classication
cnn.pptx Convolutional neural network used for image classication
Asymmetric Key Signatures
- 1. Asymmetric Key Signatures David Evans and Samee Zahur CS4501, Fall 2015
- 2. Please pay $1000 to my employee --TheBoss You have money!
- 3. Real-life Signatures Easy to verify • Bank has your signature Forging unlikely • Legal consequences of forging • Checkbooks are well-guarded • Copying it requires physical access Hard to repudiate • Bank keeps a copy for few months
- 4. Digital Signatures Easy to verify • Everybody has your “verification key”, vk Hard to forge • Nobody but you has the “signing key”, sk Hard to repudiate • Everybody knows only you have signing key 𝑠 = sign 𝑠𝑘 𝑚 true, false = verify 𝑣𝑘(𝑚, 𝑠)
- 5. Topics • Asymmetric cryptography • Digital signatures • Elliptic curve cryptography • Implementation pitfalls
- 6. Ordinary (or symmetric) crypto Message key key
- 7. Whitfield Diffie Martin Hellman New Directions in Cryptography, 1976
- 8. Diffie-Hellman Key Exchange 𝑔 𝑎 mod 𝑝 𝑔 𝑏 mod 𝑝 Picks secret a Computes 𝑔 𝑏 𝑎 = 𝑔 𝑎𝑏 Picks secret b Computes 𝑔 𝑎 𝑏 = 𝑔 𝑎𝑏 Public values: 𝑔, 𝑝, 𝑔 𝑎 , 𝑔 𝑏 Shared secret: 𝑔 𝑎𝑏
- 9. Discrete Logarithm Problem Given 𝑔, 𝑦, 𝑝 find 𝑥 such that: 𝑔 𝑥 mod 𝑝 = 𝑦
- 11. Random element out of …? 𝑔 𝑎 mod 𝑝 𝑔 𝑏 mod 𝑝 Picks random a Computes 𝑔 𝑏 𝑎 = 𝑔 𝑎𝑏 Picks random b Computes 𝑔 𝑎 𝑏 = 𝑔 𝑎𝑏
- 12. Mod 5 Exponentiation 0 1 2 3 4 5 6 … 0 - 0 0 0 0 0 0 … 1 1 1 1 1 1 1 1 … 2 1 2 4 3 1 2 4 … 3 1 3 4 2 1 3 4 … 4 1 4 1 4 1 4 1 … Order 1 Order 2 In mod 𝑝 multiplication, multiplicative order is always a factor of (𝑝 − 1)
- 13. Exponent Modulus • Multiplicative order 𝑛 is at most 𝑝 − 1 • Pick random 𝑥 such that 0 ≤ 𝑥 < 𝑝 − 1 • 𝑔 𝑎 𝑔 𝑏 mod 𝑝 = 𝑔 𝑎+𝑏 mod 𝑝 = 𝑔 𝑎+𝑏 mod 𝑛 mod 𝑝
- 16. Public-key Cryptography Publicly announces 𝑔 𝑎 𝑔 𝑏 , 𝑔 𝑎𝑏 𝑚 Picks secret a Computes 𝑔 𝑏 𝑎 = 𝑔 𝑎𝑏 Picks random secret b. Computes 𝑔 𝑎 𝑏 = 𝑔 𝑎𝑏 Encrypts message 𝑚: 𝑔 𝑎𝑏 𝑚 Public values: 𝑔, 𝑝, 𝑔 𝑎 , 𝑔 𝑏 Shared secret: 𝑔 𝑎𝑏
- 17. Man-in-the-Middle (MITM) 𝑔 𝑎 𝑔 𝑏′, 𝑔 𝑎𝑏′ 𝑚 Picks secret a Computes 𝑔 𝑏 𝑎 = 𝑔 𝑎𝑏 Picks secret b. Computes 𝑔 𝑎′ 𝑏 = 𝑔 𝑎′𝑏 Encrypts message 𝑚: 𝑔 𝑎′𝑏 𝑚 𝑔 𝑎′ 𝑔 𝑏, 𝑔 𝑎′𝑏 𝑚 Picks random 𝑎’, 𝑏’, Reads everything
- 19. Recall Easy to verify • Everybody has your “verification key”, vk Hard to forge • Nobody but you has the “signing key”, sk Hard to repudiate • Everybody knows only you have signing key 𝑠 = sign 𝑠𝑘 𝑚 true, false = verify 𝑣𝑘(𝑚, 𝑠)
- 21. ElGamal Signature Scheme Signing Input: message 𝑚 1. Pick random 𝑘 2. Compute 𝑟 = 𝑔 𝑘 mod 𝑝 ; 𝑠 = 𝑚 − 𝑎𝑟 𝑘−1 mod(𝑝 − 1) 3. Send (𝑟, 𝑠) with message 𝑚 Verification Input: message 𝑚, 𝑟, 𝑠 Check if 𝑟 𝑠 𝑔 𝑎 𝑟 = 𝑔 𝑚(mod 𝑝) Fixed global parameters: 𝑔, 𝑝 Private key: 𝑎 Public key: 𝑔 𝑎 mod 𝑝
- 22. Bitcoin Payment Sign it like a check!
- 23. Recap 1. We want to sign transactions digitally on the bitcoin network, such that they are: a) Easy to verify b) Hard to forge c) Hard to repudiate 2. Discrete exponentiation is easy, logarithm is hard 3. We used it to make asymmetric (aka. public) key crypto 4. Same principle used for digital signatures
- 26. Informal Requirements Given 𝑔 and 𝑦, 𝑔 𝑥 = 𝑦 should be hard to solve for 𝑥
- 27. Group A group is a set of elements (denoted 𝐺) and an associated binary operation (denoted ∗) that satisfies the following: • Closure: 𝑎 ∗ 𝑏 is also a group element, or ∀𝑎, 𝑏: 𝑎 ∗ 𝑏 ∈ 𝐺 • Associativity: ∀𝑎, 𝑏, 𝑐: 𝑎 ∗ 𝑏 ∗ 𝑐 = 𝑎 ∗ (𝑏 ∗ 𝑐) • Identity element: ∃𝑒∀𝑎: 𝑎 ∗ 𝑒 = 𝑎 = 𝑒 ∗ 𝑎 • Inverse: ∀𝑎∃𝑏: 𝑎 ∗ 𝑏 = 𝑒 = 𝑏 ∗ 𝑎 Not necessary, but okay to have: • Commutativity: ∀𝑎, 𝑏: 𝑎 ∗ 𝑏 = 𝑏 ∗ 𝑎
- 28. Additional Cryptographic Properties • Discrete logarithm should be hard • Group operation should be efficient • Implies small key sizes
- 29. Elliptic Curve Cryptography (ECC) • Group elements: points on the curve, P, Q, and R • Point “addition”: using “geometry”. P+Q=R 𝑦2 = 𝑥3 + 7 P Q R
- 30. Elliptic “Curve” Image from: http://www.coindesk.com/math-behind-bitcoin/
- 31. Elliptic Curve Digital Signature Algorithm (ECDSA) ElGamal Signature Inputs: message 𝑚, private key 𝑎 1. Pick random 𝑘 2. Compute a) 𝑟 = 𝑔 𝑘 mod 𝑝 b) 𝑠 = 𝑚 − 𝑎𝑟 𝑘−1 mod 𝑛 3. Send 𝑟, 𝑠 with message 𝑚 Verification Check if 𝑟 𝑠 𝑔 𝑎 𝑟 = 𝑔 𝑚 ECDSA Inputs: message , private key 1. Pick random k 2. Compute a) , let 3. Send with message Verification If , check
- 34. Please pay $1000 to my employee --TheBoss You have money! Jason Benjamin
- 35. Logistics • Next class: hash functions and Bitcoin consensus • Checkup 1 on Monday. Includes everything till today