Cryptography in Ethereum
Ethereum (ETH), like other blockchain technologies, uses cryptography extensively for several purposes:
Public Key Cryptography (Asymmetric Cryptography): In Ethereum, each account is associated with a pair of cryptographic keys - a public key and a private key. The public key is used to derive the Ethereum address, which is publicly known and acts like a username. The private key is kept secret and acts like a password. This cryptographic scheme allows only the person in possession of the private key to sign transactions for the associated address.
Digital Signatures (ECDSA and EdDSA): Ethereum initially used Elliptic Curve Digital Signature Algorithm (ECDSA) for the signature scheme, which involves the private key to sign transactions and the public key to verify them. This way, everyone can confirm that a transaction has indeed been signed by the holder of the private key (i.e., the sender of a transaction) without needing to know the private key itself. As of Ethereum's Berlin Upgrade in 2021, Ethereum also started supporting Ethereum Improvement Proposal 2935 (EIP-2935) which introduces the Edwards-curve Digital Signature Algorithm (EdDSA) as an alternative to ECDSA.
Hashing Functions: Ethereum uses Keccak-256, a variant of the SHA-3 hash function, to generate a deterministic output (a hash) from an input of any size. This is used in multiple places, including generating addresses from public keys and creating transaction identifiers.
Merkle Trees and Patricia Tries: Ethereum uses cryptographic data structures like Merkle Trees and Patricia Tries for efficient data storage and verification. These structures are built from hashes of data and provide a way to verify that a piece of data is part of the set with just a small piece of proof (called a Merkle Proof).
Secure Randomness: For some smart contracts, such as those for decentralized lotteries or games, secure randomness is needed. Generating random numbers in a transparent and deterministic system like Ethereum is a challenge and it's an active area of research. Various techniques have been proposed, many of them relying on cryptographic principles.
Zero-Knowledge Proofs: These are advanced cryptographic techniques that allow one party to prove to another that they know a value (such as a secret key), without conveying any information apart from the fact they know the value. Although not a part of the base Ethereum protocol, they are used in some Ethereum applications, such as ZK-Rollups for scalability and privacy.
These are some of the main ways in which Ethereum uses cryptography, but the full details are complex and involve more specifics depending on the exact part of Ethereum you're looking at (like the core protocol, smart contract development, or second-layer solutions).
Conclusion/Summary
In summary, cryptography plays a vital role in Ethereum's infrastructure, enabling secure transactions, digital signatures, unique identifiers, efficient data storage, secure randomness, and privacy-enhancing techniques. These cryptographic mechanisms ensure the integrity, security, and privacy of transactions and smart contracts within the Ethereum ecosystem, making it a trusted platform for decentralized applications and financial interactions.