More on Web3 & Crypto
Ajay Shrestha
2 years ago
Bitcoin's technical innovation: addressing the issue of the Byzantine generals
The 2008 Bitcoin white paper solves the classic computer science consensus problem.
Issue Statement
The Byzantine Generals Problem (BGP) is called after an allegory in which several generals must collaborate and attack a city at the same time to win (figure 1-left). Any general who retreats at the last minute loses the fight (figure 1-right). Thus, precise messengers and no rogue generals are essential. This is difficult without a trusted central authority.
In their 1982 publication, Leslie Lamport, Robert Shostak, and Marshall Please termed this topic the Byzantine Generals Problem to simplify distributed computer systems.
Consensus in a distributed computer network is the issue. Reaching a consensus on which systems work (and stay in the network) and which don't makes maintaining a network tough (i.e., needs to be removed from network). Challenges include unreliable communication routes between systems and mis-reporting systems.
Solving BGP can let us construct machine learning solutions without single points of failure or trusted central entities. One server hosts model parameters while numerous workers train the model. This study describes fault-tolerant Distributed Byzantine Machine Learning.
Bitcoin invented a mechanism for a distributed network of nodes to agree on which transactions should go into the distributed ledger (blockchain) without a trusted central body. It solved BGP implementation. Satoshi Nakamoto, the pseudonymous bitcoin creator, solved the challenge by cleverly combining cryptography and consensus mechanisms.
Disclaimer
This is not financial advice. It discusses a unique computer science solution.
Bitcoin
Bitcoin's white paper begins:
“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Source: https://www.ussc.gov/sites/default/files/pdf/training/annual-national-training-seminar/2018/Emerging_Tech_Bitcoin_Crypto.pdf
Bitcoin's main parts:
The open-source and versioned bitcoin software that governs how nodes, miners, and the bitcoin token operate.
The native kind of token, known as a bitcoin token, may be created by mining (up to 21 million can be created), and it can be transferred between wallet addresses in the bitcoin network.
Distributed Ledger, which contains exact copies of the database (or "blockchain") containing each transaction since the first one in January 2009.
distributed network of nodes (computers) running the distributed ledger replica together with the bitcoin software. They broadcast the transactions to other peer nodes after validating and accepting them.
Proof of work (PoW) is a cryptographic requirement that must be met in order for a miner to be granted permission to add a new block of transactions to the blockchain of the cryptocurrency bitcoin. It takes the form of a valid hash digest. In order to produce new blocks on average every 10 minutes, Bitcoin features a built-in difficulty adjustment function that modifies the valid hash requirement (length of nonce). PoW requires a lot of energy since it must continually generate new hashes at random until it satisfies the criteria.
The competing parties known as miners carry out continuous computing processing to address recurrent cryptography issues. Transaction fees and some freshly minted (mined) bitcoin are the rewards they receive. The amount of hashes produced each second—or hash rate—is a measure of mining capacity.
Cryptography, decentralization, and the proof-of-work consensus method are Bitcoin's most unique features.
Bitcoin uses encryption
Bitcoin employs this established cryptography.
Hashing
digital signatures based on asymmetric encryption
Hashing (SHA-256) (SHA-256)
Hashing converts unique plaintext data into a digest. Creating the plaintext from the digest is impossible. Bitcoin miners generate new hashes using SHA-256 to win block rewards.
A new hash is created from the current block header and a variable value called nonce. To achieve the required hash, mining involves altering the nonce and re-hashing.
The block header contains the previous block hash and a Merkle root, which contains hashes of all transactions in the block. Thus, a chain of blocks with increasing hashes links back to the first block. Hashing protects new transactions and makes the bitcoin blockchain immutable. After a transaction block is mined, it becomes hard to fabricate even a little entry.
Asymmetric Cryptography Digital Signatures
Asymmetric cryptography (public-key encryption) requires each side to have a secret and public key. Public keys (wallet addresses) can be shared with the transaction party, but private keys should not. A message (e.g., bitcoin payment record) can only be signed by the owner (sender) with the private key, but any node or anybody with access to the public key (visible in the blockchain) can verify it. Alex will submit a digitally signed transaction with a desired amount of bitcoin addressed to Bob's wallet to a node to send bitcoin to Bob. Alex alone has the secret keys to authorize that amount. Alex's blockchain public key allows anyone to verify the transaction.
Solution
Now, apply bitcoin to BGP. BGP generals resemble bitcoin nodes. The generals' consensus is like bitcoin nodes' blockchain block selection. Bitcoin software on all nodes can:
Check transactions (i.e., validate digital signatures)
2. Accept and propagate just the first miner to receive the valid hash and verify it accomplished the task. The only way to guess the proper hash is to brute force it by repeatedly producing one with the fixed/current block header and a fresh nonce value.
Thus, PoW and a dispersed network of nodes that accept blocks from miners that solve the unfalsifiable cryptographic challenge solve consensus.
Suppose:
Unreliable nodes
Unreliable miners
Bitcoin accepts the longest chain if rogue nodes cause divergence in accepted blocks. Thus, rogue nodes must outnumber honest nodes in accepting/forming the longer chain for invalid transactions to reach the blockchain. As of November 2022, 7000 coordinated rogue nodes are needed to takeover the bitcoin network.
Dishonest miners could also try to insert blocks with falsified transactions (double spend, reverse, censor, etc.) into the chain. This requires over 50% (51% attack) of miners (total computational power) to outguess the hash and attack the network. Mining hash rate exceeds 200 million (source). Rewards and transaction fees encourage miners to cooperate rather than attack. Quantum computers may become a threat.
Visit my Quantum Computing post.
Quantum computers—what are they? Quantum computers will have a big influence. towardsdatascience.com
Nodes have more power than miners since they can validate transactions and reject fake blocks. Thus, the network is secure if honest nodes are the majority.
Summary
Table 1 compares three Byzantine Generals Problem implementations.
Bitcoin white paper and implementation solved the consensus challenge of distributed systems without central governance. It solved the illusive Byzantine Generals Problem.
Resources
Resources
Source-code for Bitcoin Core Software — https://github.com/bitcoin/bitcoin
Bitcoin white paper — https://bitcoin.org/bitcoin.pdf
https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/
https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf
Genuinely Distributed Byzantine Machine Learning, El-Mahdi El-Mhamdi et al., 2020. ACM, New York, NY, https://doi.org/10.1145/3382734.3405695
Vitalik
4 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
JEFF JOHN ROBERTS
3 years ago
What just happened in cryptocurrency? A plain-English Q&A about Binance's FTX takedown.
Crypto people have witnessed things. They've seen big hacks, mind-boggling swindles, and amazing successes. They've never seen a day like Tuesday, when the world's largest crypto exchange murdered its closest competition.
Here's a primer on Binance and FTX's lunacy and why it matters if you're new to crypto.
What happened?
CZ, a shrewd Chinese-Canadian billionaire, runs Binance. FTX, a newcomer, has challenged Binance in recent years. SBF (Sam Bankman-Fried)—a young American with wild hair—founded FTX (initials are a thing in crypto).
Last weekend, CZ complained about SBF's lobbying and then exploited Binance's market power to attack his competition.
How did CZ do that?
CZ invested in SBF's new cryptocurrency exchange when they were friends. CZ sold his investment in FTX for FTT when he no longer wanted it. FTX clients utilize those tokens to get trade discounts, although they are less liquid than Bitcoin.
SBF made a mistake by providing CZ just too many FTT tokens, giving him control over FTX. It's like Pepsi handing Coca-Cola a lot of stock it could sell at any time. CZ got upset with SBF and flooded the market with FTT tokens.
SBF owns a trading fund with many FTT tokens, therefore this was catastrophic. SBF sought to defend FTT's worth by selling other assets to buy up the FTT tokens flooding the market, but it didn't succeed, and as FTT's value plummeted, his liabilities exceeded his assets. By Tuesday, his companies were insolvent, so he sold them to his competition.
Crazy. How could CZ do that?
CZ likely did this to crush a rising competition. It was also personal. In recent months, regulators have been tough toward the crypto business, and Binance and FTX have been trying to stay on their good side. CZ believed SBF was poisoning U.S. authorities by saying CZ was linked to China, so CZ took retribution.
“We supported previously, but we won't pretend to make love after divorce. We're neutral. But we won't assist people that push against other industry players behind their backs," CZ stated in a tragic tweet on Sunday. He crushed his rival's company two days later.
So does Binance now own FTX?
No. Not yet. CZ has only stated that Binance signed a "letter of intent" to acquire FTX. CZ and SBF say Binance will protect FTX consumers' funds.
Who’s to blame?
You could blame CZ for using his control over FTX to destroy it. SBF is also being criticized for not disclosing the full overlap between FTX and his trading company, which controlled plenty of FTT. If he had been upfront, someone might have warned FTX about this vulnerability earlier, preventing this mess.
Others have alleged that SBF utilized customer monies to patch flaws in his enterprises' balance accounts. That happened to multiple crypto startups that collapsed this spring, which is unfortunate. These are allegations, not proof.
Why does this matter? Isn't this common in crypto?
Crypto is notorious for shady executives and pranks. FTX is the second-largest crypto business, and SBF was largely considered as the industry's golden boy who would help it get on authorities' good side. Thus far.
Does this affect cryptocurrency prices?
Short-term, it's bad. Prices fell on suspicions that FTX was in peril, then rallied when Binance rescued it, only to fall again later on Tuesday.
These occurrences have hurt FTT and SBF's Solana token. It appears like a huge token selloff is affecting the rest of the market. Bitcoin fell 10% and Ethereum 15%, which is bad but not catastrophic for the two largest coins by market cap.
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The Secret Developer
3 years ago
What Elon Musk's Take on Bitcoin Teaches Us
Tesla Q2 earnings revealed unethical dealings.
As of end of Q2, we have converted approximately 75% of our Bitcoin purchases into fiat currency
That’s OK then, isn’t it?
Elon Musk, Tesla's CEO, is now untrustworthy.
It’s not about infidelity, it’s about doing the right thing
And what can we learn?
The Opening Remark
Musk tweets on his (and Tesla's) future goals.
Don’t worry, I’m not expecting you to read it.
What's crucial?
Tesla will not be selling any Bitcoin
The Situation as It Develops
2021 Tesla spent $1.5 billion on Bitcoin. In 2022, they sold 75% of the ownership for $946 million.
That’s a little bit of a waste of money, right?
Musk predicted the reverse would happen.
What gives? Why would someone say one thing, then do the polar opposite?
The Justification For Change
Tesla's public. They must follow regulations. When a corporation trades, they must record what happens.
At least this keeps Musk some way in line.
We now understand Musk and Tesla's actions.
Musk claimed that Tesla sold bitcoins to maximize cash given the unpredictability of COVID lockdowns in China.
Tesla may buy Bitcoin in the future, he said.
That’s fine then. He’s not knocking the NFT at least.
Tesla has moved investments into cash due to China lockdowns.
That doesn’t explain the 180° though
Musk's Tweet isn't company policy. Therefore, the CEO's change of heart reflects the organization. Look.
That's okay, since
Leaders alter their positions when circumstances change.
Leaders must adapt to their surroundings. This isn't embarrassing; it's a leadership prerequisite.
Yet
The Man
Someone stated if you're not in the office full-time, you need to explain yourself. He doesn't treat his employees like adults.
This is the individual mentioned in the quote.
If Elon was not happy, you knew it. Things could get nasty
also, He fired his helper for requesting a raise.
This public persona isn't good. Without mentioning his disastrous performances on Twitter (pedo dude) or Joe Rogan. This image sums up the odd Podcast appearance:
Which describes the man.
I wouldn’t trust this guy to feed a cat
What we can discover
When Musk's company bet on Bitcoin, what happened?
Exactly what we would expect
The company's position altered without the CEO's awareness. He seems uncaring.
This article is about how something happened, not what happened. Change of thinking requires contrition.
This situation is about a lack of respect- although you might argue that followers on Twitter don’t deserve any
Tesla fans call the sale a great move.
It's absurd.
As you were, then.
Conclusion
Good luck if you gamble.
When they pay off, congrats!
When wrong, admit it.
You must take chances if you want to succeed.
Risks don't always pay off.
Mr. Musk lacks insight and charisma to combine these two attributes.
I don’t like him, if you hadn’t figured.
It’s probably all of the cheating.
Sad NoCoiner
3 years ago
Two Key Money Principles You Should Understand But Were Never Taught
Prudence is advised. Be debt-free. Be frugal. Spend less.
This advice sounds nice, but it rarely works.
Most people never learn these two money rules. Both approaches will impact how you see personal finance.
It may safeguard you from inflation or the inability to preserve money.
Let’s dive in.
#1: Making long-term debt your ally
High-interest debt hurts consumers. Many credit cards carry 25% yearly interest (or more), so always pay on time. Otherwise, you’re losing money.
Some low-interest debt is good. Especially when buying an appreciating asset with borrowed money.
Inflation helps you.
If you borrow $800,000 at 3% interest and invest it at 7%, you'll make $32,000 (4%).
As money loses value, fixed payments get cheaper. Your assets' value and cash flow rise.
The never-in-debt crowd doesn't know this. They lose money paying off mortgages and low-interest loans early when they could have bought assets instead.
#2: How To Buy Or Build Assets To Make Inflation Irrelevant
Dozens of studies demonstrate actual wage growth is static; $2.50 in 1964 was equivalent to $22.65 now.
These reports never give solutions unless they're selling gold.
But there is one.
Assets beat inflation.
$100 invested into the S&P 500 would have an inflation-adjusted return of 17,739.30%.
Likewise, you can build assets from nothing. Doing is easy and quick. The returns can boost your income by 10% or more.
The people who obsess over inflation inadvertently make the problem worse for themselves. They wait for The Big Crash to buy assets. Or they moan about debt clocks and spending bills instead of seeking a solution.
Conclusion
Being ultra-prudent is like playing golf with a putter to avoid hitting the ball into the water. Sure, you might not slice a drive into the pond. But, you aren’t going to play well either. Or have very much fun.
Money has rules.
Avoiding debt or investment risks will limit your rewards. Long-term, being too cautious hurts your finances.
Disclaimer: This article is for entertainment purposes only. It is not financial advice, always do your own research.
Tim Denning
3 years ago
Read These Books on Personal Finance to Boost Your Net Worth
And retire sooner.
Books can make you filthy rich.
If you apply what you learn. In 2011, I was broke and had broken dreams.
Someone suggested I read finance books. One Up On Wall Street was his first recommendation.
Finance books were my crack.
I've read every money book since then. Some are good, but most stink.
These books will make you rich.
The Almanack of Naval Ravikant by Eric Jorgenson
This isn't a cliche book.
This book was inspired by a How to Get Rich tweet thread.
It’s one of the best tweets I’ve ever read.
Naval thinks differently. He nukes ordinary ideas. I've never heard better money advice.
Eric Jorgenson wrote a book about this tweet thread with Navals permission. A must-read, easy-to-digest book.
Best quote
Seek wealth, not money or status. Wealth is having assets that earn while you sleep. Money is how we transfer time and wealth. Status is your place in the social hierarchy — Naval
Morgan Housel's The Psychology of Money
Many finance books advise investing like a dunce.
They almost all peddle the buy an index fund BS. Different book.
It's about money-making psychology. Because any fool can get rich and drunk on their ego. Few can consistently make money.
Each chapter is short. A single-page chapter breaks all book publishing rules.
Best quote
Spending money to show people how much money you have is the fastest way to have less money — Morgan Housel
J.L. Collins' The Simple Path to Wealth
Most of the best money books were written by bloggers.
JL Collins blogs. This easy-to-read book was written for his daughter.
This book popularized the phrase F You Money. With enough money in your bank account and investment portfolio, you can say F You more.
A bad boss is an example. You can leave instead of enduring his wrath.
You can then sit at home and look for another job while financially secure. JL says its mind-freedom is powerful.
Best phrasing
You own the things you own and they in turn own you — J.L. Collins
Tony Robbins' Unshakeable
I like Tony. This book makes me sweaty.
Tony interviews the world's top financiers. He interviews people who rarely do so.
This book taught me all-weather portfolio. It's a way to invest in different asset classes in good, bad, recession, or depression times.
Look at it:
Investing isn’t about buying one big winner — that’s gambling. It’s about investing in a diversified portfolio of assets.
Best phrasing
The best opportunities come in times of maximum pessimism — Tony Robbins
Ben Graham's The Intelligent Investor
This book helped me distinguish between a spectator and an investor.
Spectators are those who shout that crypto, NFTs, or XYZ platform will die.
Tourists. They want attention and to say "I told you so." They make short-term and long-term predictions like fortunetellers. LOL. Idiots.
Benjamin Graham teaches smart investing. You'll buy a long-term asset. To be confident in recessions, use dollar-cost averaging.
Best phrasing
Those who do not remember the past are condemned to repeat it. — Benjamin Graham
The Napoleon Hill book Think and Grow Rich
This classic book introduced positive thinking to modern self-help.
Lazy pessimists can't become rich. No way.
Napoleon said, "Thoughts create reality."
No surprise that he discusses obsession and focus in this book. They are the fastest ways to make more money to invest in time and wealth-protecting assets.
Best phrasing
The starting point of all achievement is DESIRE. Keep this constantly in mind. Weak desire brings weak results, just as a small fire makes a small amount of heat — Napoleon Hill
Ramit Sethi's book I Will Teach You To Be Rich
This book is mostly good. The part about credit cards is trash.
Avoid credit card temptations. I don't care about their airline points.
This book teaches you to master money basics (that many people mess up) then automate it so your monkey brain doesn't ruin your financial future.
The book includes great negotiation tactics to help you make more money in less time.
Best quote
The 85 Percent Solution: Getting started is more important than becoming an expert — Ramit Sethi
David Bach's The Automatic Millionaire
You've probably met a six- or seven-figure earner who's broke. All their money goes to useless things like cars.
Money isn't as essential as what you do with it. David teaches how to automate your earnings for more money.
Compounding works once investing is automated. So you get rich.
His strategy eliminates luck and (almost) guarantees millionaire status.
Best phrasing
Every time you earn one dollar, make sure to pay yourself first — David Bach
Thomas J. Stanley's The Millionaire Next Door
Thomas defies the definition of rich.
He spends much of the book highlighting millionaire traits he's studied.
Rich people are quiet, so you wouldn't know they're wealthy. They don't earn much money or drive a BMW.
Thomas will give you the math to get started.
Best phrasing
I am not impressed with what people own. But I’m impressed with what they achieve. I’m proud to be a physician. Always strive to be the best in your field…. Don’t chase money. If you are the best in your field, money will find you. — Thomas J. Stanley
by Bill Perkins "Die With Zero"
Let’s end with one last book.
Bill's book angered many people. He says we spend too much time saving for retirement and die rich. That bank money is lost time.
Your grandkids could use the money. When children inherit money, they become lazy, entitled a-holes.
Bill wants us to spend our money on life-enhancing experiences. Stop saving money like monopoly monkeys.
Best phrasing
You should be focusing on maximizing your life enjoyment rather than on maximizing your wealth. Those are two very different goals. Money is just a means to an end: Having money helps you to achieve the more important goal of enjoying your life. But trying to maximize money actually gets in the way of achieving the more important goal — Bill Perkins