🌐 Ethereum (ETH) – Explained

OverView 

• Launch Year - 2015 

• Founder - Vitalik Buterin 

• Symbol - ETH

• Purpose - To enable smart contracts and decentralized applications(DApps) that run without middlemen.

• Native Currency - Ether - Used to pay gas fees for running apps and sending transactions.

Technology

Blockchain Type - Public and open source  - Anyone can join, use or build on Ethereum.

Consensus Mechanism - Proof of Stake(since 2022)- Users stake ETH instead of mining to validate transactions.

Smart Contracts - Self Executing digital agreements - Code runs automatically when conditions are met.

Scalability - Being improved with upgrades like sharding and Layer 2 rollups to make transactions faster and cheaper.

Key Use  Cases 

• Decentralized Finance - Borrow, Lend and trade crypto without banks or intermediaries.

• NFTs(Non Fungible Tokens)- Unique digital assets like art, music and in game collectibles.

• DAOs (Decentralized Autonomous Organization)- Communities that make decisions collectively using tokens.

• Gaming and Metaverse - Powering play-to-earn games and digital worlds with virtual assets.
  
  

Advantages

• Strong Ecosystem - Ethereum ha sthe largest community of developers and application in crypto.

• Innovation Hub - Most DeFi, NFT and Web3 projects started here before spreading to other chains.

• Upgrades in Progress - The network is constantly evolving to solve issues like speed and costs.

• Trust and Adoption- Considered the most reliabel blockchain after Bitcoin.

Limitations

• High Gas Fees - Transactions often become very expensive when the network is busy

• Scalability Issues - Ethereum can handle fewer transactions per second compared to newer blockchains.

• Rising Competiton- Blockchains like Solan, Cardano and Avalanche are faster and cheaer alternatives.

🧮 Ethereum – Mathematical Foundations

1. State Transition Function

Ethereum is modeled as a state machine:

σt+1=Υ(σt,T)\sigma_{t+1} = Υ(\sigma_t, T)

• σt\sigma_t = state at time tt
  
  

• TT = transaction
  
  

• ΥΥ = state transition function
  
  

2. Block-Level Transition

Blocks contain transactions, so the state evolves as:

σt+1=Π(σt,B)\sigma_{t+1} = Π(\sigma_t, B)

• BB = block (list of transactions)
  
  

• ΠΠ = block transition function
  
  

3. Currency Units (Ether Denominations)

1 ETH=1018 Wei1 \, ETH = 10^{18} \, Wei 1 Finney=1015 Wei1 \, Finney = 10^{15} \, Wei 1 Szabo=1012 Wei1 \, Szabo = 10^{12} \, Wei

4. Transaction Fee (Gas Model)

Fee=Gas Used×Gas Price\text{Fee} = \text{Gas Used} \times \text{Gas Price}

• Gas Limit = maximum allowed
  
  

• Unused Gas → refunded to sender
  
  

5. Upfront Transaction Cost

v0=Tg⋅Tp+Tvv_0 = T_g \cdot T_p + T_v

• TgT_g = gas limit
  
  

• TpT_p = gas price
  
  

• TvT_v = value transferred
  
  

6. Intrinsic Gas of a Transaction

g0=∑i∈Ti,Td{Gtxdatazero,i=0Gtxdatanonzero,i≠0+  Gtransactiong_0 = \sum_{i \in T_i, T_d} \begin{cases} G_{txdatazero}, & i = 0 \\ G_{txdatanonzero}, & i \neq 0 \end{cases} + \; G_{transaction}

7. Refundable Gas

g∗=g′+min⁡(⌊Tg−g′2⌋,Ar)g^* = g' + \min\left(\left\lfloor \frac{T_g - g'}{2} \right\rfloor, A_r \right)

• g′g' = remaining gas after execution
  
  

• ArA_r = refund counter
  
  

8. Block Difficulty Adjustment (Proof of Work Era)

D(H)={D0if Hi=0max⁡(D0,P(H)d+x⋅ς+ε)otherwiseD(H) = \begin{cases} D_0 & \text{if } H_i = 0 \\ \max \left(D_0, P(H)_d + x \cdot \varsigma + \varepsilon \right) & \text{otherwise} \end{cases}

• P(H)dP(H)_d = parent block difficulty
  
  

• xx = adjustment factor
  
  

• ς,ε\varsigma, \varepsilon = difficulty adjustment constants
  
  

9. Transaction Receipt

R=(Rσ,Ru,Rb,Rl)R = (R_\sigma, R_u, R_b, R_l)

• RσR_\sigma = post-transaction state
  
  

• RuR_u = cumulative gas used
  
  

• RbR_b = Bloom filter
  
  

• RlR_l = logs
  
  

10. Contract Address Creation

a=B96..255(KEC(RLP(s,σ[s]n−1)))a = B_{96..255}\Big( KEC(RLP(s, \sigma[s]_n - 1)) \Big)

• ss = sender
  
  

• σ[s]n\sigma[s]_n = sender’s nonce
  
  

• KECKEC = Keccak-256 hash
  
  

• RLPRLP = recursive length prefix encoding
  
  

🌐 Ethereum Whitepaper – Simplified Explanation

Why Ethereum was created?

BITCOIN LIMITATIONS

• Bitcoin showed the world that decntralized money is possible.

• Bitcoin is limited to peer to peer payments.

• Developers tried to add more features (colored coins, meta-protocols, sidechains) but they were too complex and limited.

NEED FOR PROGRAMMABILITY

• People wanted a blockchain that could handle more than payments - Agreements, Applications, Tokens, Organizations

• Instead of building a new blockchain for every new use case - a blockchain that can run any program is built.

AIM OF ETHEREUM

• To be a world computer that runs decentralizzed applications.

• To provide a Turing-complete programming language.

• To make it easy for developers to write smart contracts without needing to design a new blockchain from scratch.

• To move beyond money  only blockchain and enable - DeFi, DAOs, NFTs

CORE IDEAS IN WHITEPAPER

STATE MACHINE

• Ethereum is a transaction-based state machine.

• Every transaction changes the global "state". (balances, contracts, storage)

ETHEREUM VIRTUAL MACHINE (EVM)

• The "engine" that executes smart contracts.

• Runs on thousan of computers worldwide, making Ethereum decentralized .

SMART CONTRACTS

• Pieces of code that run automatically on the blockchain .

• Example - If Alice sends ETH, release a digital certificate to Bob .

GAS

• To avoid spam and misuse, every operation costs gas.

• Gas fees ensure people pay for using network resources.

Goals Of Ethereum

• Simplicity- Easy for developers to build.

• Universality - Can run any logic, not just payments.

• Modularity - Designed to adapt and upgrade over time . 

• Agility - Quick response to new needs and ideas 

• Non Discrimination - The system doesn't judge what apps people build