Blockchain and Bitcoin

CBDC

Central Bank Digital Currency is a digital form of a country's fiat currency issued and regulated by the central bank. It aims to provide a secure and efficient way for governments to offer a digital payment option to the public.

Pros of Blockchain

decentralization, verifiability, trustlessness

Cons of Blockchain

high computing power, and privacy concerns 

In the News Brazil

Brazil opted for a centralized system for its CBDC because it is faster and more private 

Chaos

a process that is deterministic but unpredictable

Hash Functions

they have the same input, but every output is different (deterministic to unpredictable)

One-Way Function of Hash Functions

you can calculate the hash from an input, but you can’t go backwards making it one directional

Collision in Hash Functions 

many possible outcomes exist so it is basically impossible for two different inputs to have the same output 

Chaos in Hash Functions

hash functions repeatedly scramble bits through deterministic steps until the data is unrecognizable (every step follows strict deterministic math, the final result appears random)

Cryptographic hash function

a set of all possible messages is mapped to a set of fixed-length outputs

properties include collision resistance, one-way property, and extremely sensitive

hash functions in blockchains

Blockchains use hash functions because of the one-way property, since you can never find x from H(x), and for proof-of-work, because you need to mine and brute-force a new hash function to mine a new coin, showing that work has been done

How does one prove that they signed something

you first set up a public key and a private key. the person then uses the private key to produce a signature, and anyone with the public key can verify if the person has actually signed it

Digital Signature Scheme

1. Generate keys (public and private key)

2. sign a message

3. verify the signature

every bitcoin transfer is authenticated through a digital structure scheme using one-way, chaotic functions

Stablecoins

cryptocurrencies that are pegged to the value of traditional assets. the goal is to offer the speed and decentralization of crypto wihtout price volatility

how issuing stable coins work

1. people deposit dollars with you in exchange for crypto tokens

2. you invest those dollars in short-term, low risk assets

3. promise redemption

4. pay no interest to users, so you keep the yield from the investments

Problem with stablecoins

the business model draws attention because of it resemblance to banking but without regulation

GENIUS Act

the genius act prohibits paying interest on stable coins, so technically they can’t share their 4% yields with users

Workaround for GENIUS Acts

users pay fees to crypto exchanges to promote their stable coin as the default one on that platform. then the exchange rebates some of that money back to end users - effectively mimicking interest payments. Banks are wary of this as a full implementation of stablecoins could see banks be obsolete

what is a Merkle tree

a structure that uses hash functions to efficiently verify the integrity of a large set of data. its purpose is to ensure that none of the data has been tampered with or corrupted, without needing to recheck every single file

building a merkle tree 

1. hash each file 

2. combine hashes pairwise 

3. keep combining laters upward 

top hash is called the merkle root 

Advantages of Merkle Trees

1. efficiency (instead of storing 1 hash per file, you store just the merkle root and that accounts for all hashes)

2. storage (thanks to non-invertibility of hash functions, it’s practically impossible to fake a valid Merkle Proof)

3. verification speed

Blockchain and Merkle Root

every block in bitcoin or eth contains a merkle root summarizing all its transactions allowing anyone to verify that a specific transaction is part of the block without downloading the entire blockchain

What is a blockchain?

a list of records that cryptographically linked together using hash functionsw

what does each block contain in a blockchain

1. a list of records 

2. a digital signature 

3. a unique cryptographic hash 

4. a reference to the previous block’s hash 

Centralized Blockchains

• cannot create false messages since it still needs the private key

• can choose to stop adding blocks or roll back to an older version

• can’t selectively delete one record

(coinbase, binance)

Decentralized Blockchain

instead of one admin, multiple participants can add transactions like a democratic system. proof of work was introduced to make participation costly but fair

Proof of Work 

it uses hash puzzles to decide who gets to add the next block. this way you must brute-force in finding a valid number and it is easy to verify 

Double Spending

you cannot double spend a bitcoin because each block depends on the all previous ones and removing one transaction invalidates all later hashes

51%

you need to control 51% of the network’s computational power and then you can outpace honest miners and make a fake chain and become the longest one - rewriting history

Google’s AP2

the blockchain principles are being applied in AI, payments, and digital identity 

What determines if Bitcoin mining is profitable?

Mining is profitable when the BTC reward is worth more than the electricity cost. If BTC price > cost, miners join; if BTC price < cost, they stop

why can’t bitcoin rely on price alone to control mining? 

because when price changes, the mining rate changes - too many miners make blocks too fast, too few slow the network down 

how does bitcoin keep blocks coming at a steady rate?

through difficulty adjustment - every 2016 blocks (14 days), it makes mining harder or easier to keep block time near 10 minutes

what happens when btc price goes up

more miners join - network hash rate rises - difficulty increases - mining costs rise - profit per dollar of electricity returns to normal

what is bitcoin’s equilibrium condition 

At equilibrium, profit from mining equals the cost of electricity — no extra profit remains, keeping the system stable.

How is Bitcoin mining like the “Money Pot Game”?

Both balance themselves: when rewards attract too many players, competition lowers profit until everyone earns just enough to keep playing.

bitcoin’s price and mining difficulty related

they move together - higher btc price attracts miners, raising difficulty; lower price drives miners away, lowering difficulty 

Why do energy prices matter for Bitcoin mining?

Electricity cost sets the floor for profitability — when energy prices rise, mining becomes less profitable until difficulty readjusts.

How powerful and energy-intensive is Bitcoin mining today?

The network performs 842 exahashes/s — using roughly 1% of global electricity — showing huge efficiency gains but high energy demand.

Why do Bitcoin mining costs stay close to rewards?

Because as tech improves, difficulty increases — keeping total costs roughly equal to the total BTC mined each year (~$8–15B).

What’s Bitcoin halving and its effect?

Every 4 years, block rewards halve (now 3.125 BTC/block). This enforces scarcity but doesn’t slow block creation thanks to difficulty adjustment.

Why did Satoshi cap Bitcoin’s supply at 21 million?

To mimic scarcity and prevent inflation while keeping divisibility (8 decimal places) for everyday use.

Why do miners charge transaction fees in Bitcoin?

To earn additional income for processing transactions and to decide which ones to include based on priority (higher fee = faster confirmation)

How are Bitcoin transaction fees measured?

In Satoshis per virtual byte (sat/vB) — the fee per unit of transaction size, based on data storage cost.

What is the Bitcoin mempool?

A waiting area where unconfirmed transactions sit until a miner includes them in a block.

How significant are transaction fees in miners’ income?

Usually under 10% of total block revenue but can spike when the network is congested.

How does decentralization prevent transaction censorship?

Many independent miners compete — if one ignores a transaction, another will include it, ensuring fair access.

Why is Bitcoin’s incentive system stable?

Because miners earn both predictable block rewards and smaller but dynamic transaction fees, balancing long-term motivation and fairness.

Why are transaction fees expected to become more important over time?

As block rewards halve every 4 years, fees will make up a larger share of miner income.

What is a Satoshi?

The smallest Bitcoin unit: 1 Satoshi = 0.00000001 BTC (1/10⁸ BTC).

What is a Bitcoin block reward?

The total compensation miners receive for adding a block — includes new BTC created + all transaction fees in that block.

What was the first Bitcoin purchase?

In 2010, Laszlo Hanyecz bought two pizzas for 10,000 BTC — now worth hundreds of millions.

What is a Merkle tree in Bitcoin?

A hierarchical hash structure that summarizes all transactions in a block, ensuring integrity and efficient verification.

What does it mean that block headers start with many zeros?

It’s the proof-of-work requirement — miners must find a hash that meets difficulty, ensuring block validity.

Why do transactions take about an hour to finalize?

Each block takes ~10 minutes, and waiting several blocks ensures irreversible confirmation, preventing double-spends.

What is the Bitcoin white paper?

The original 2008 document outlining Bitcoin’s concept: decentralized digital cash using blockchain and proof-of-work.

What is the Genesis Block?

The very first Bitcoin block, mined by Satoshi, containing a reference to the 2008 financial crisis.

What’s the main difference between software and hardware wallets?

Software wallets (Exodus, MetaMask) store private keys online; hardware wallets (Ledger, Trezor) keep them offline for higher security.

What’s the difference between self-custody and custodial ownership?

Self-custody = user controls keys; custodial = exchange or institution controls keys on your behalf.

What does “Buy the Market” mean in relation to Bitcoin?

Under CAPM, Bitcoin’s rising market cap (~2% of S&P 500) makes it a small but legitimate part of diversified portfolios.

Why is Bitcoin’s market cap considered misleading?

It assumes all coins could sell at the current price, ignoring liquidity and lack of yield (no dividends or coupons).

What is a custodial wallet?

A wallet managed by a third party (e.g., exchange), where users don’t directly control private keys.

What is market capitalization in crypto?

The total value of all coins in circulation (price × supply), but it doesn’t represent realizable liquidity.