source: Mastering Ethereum, Chapter 3 by Andreas Antonopoulos

cryptography is one of Ethereum’s foundational technologies, however, the Ethereum protocol does not involve encryption. Communication between nodes is unencrypted

  • This means that anyone can verify state updates

We use Public Key Cryptography (PKC) to control ownership of funds

Keys and Addresses

private keys are used to derive:

  • public keys, which generate account addresses
  • digital signatures give you access to funds and enable transactions on the blockchain

contracts have account addresses that are not generated by a private key

Public Key Cryptography

aka asymmetric cryptography - it’s easy to calculate a public key from a private key, but the opposite is difficult

  • used to create public-private key pairs in Ethereum

digital signatures - can only be produced with a transaction and a private key. Proves that the person with the private key sent the transaction

  • it’s trivial to verify that the transaction is valid with the public key

prime factorization - finding prime factors is difficult with very large numbers

trapdoor functions you can invert some math functions easily if you know some secret information (for example, if you have one of the prime factors)

elliptic curve arithmetic adding points on a curve together

  • discrete logarithm problem multiplication modulo of a prime is simple, division is practically impossible - no known trapdoors

elliptic curve cryptography forms the basis of Ethereum’s private keys and digital signatures

Private Keys

a number, picked at random. Used to create signatures (signatures are required to spend ether)

Public Keys

represents a point (x, y) on an elliptic curve

  • in Ethereum, the public key is those two numbers joined together
  • derived from a private key in a one way function

$K = k*G$, where:

  • $k$ is the private key
  • $G$ is a generator point (a constant)
  • $K$ is the public key
  • $*$ is the elliptic curve “multiplication” operator

note: elliptic curve multiplication is not like normal multiplication

  • it’s a one-way function
  • multiplication is easy, division is currently impossible

Elliptic Curve Cryptography

it’s a type of asymmetric cryptography

  • based on the discrete logarithm problem
  • expressed by addition and multiplication on the points of an elliptic curve

Cryptographic Hash Functions

Hash function used to map data of arbitrary size to data of a fixed size

  • input is called pre-image, message or input data
  • output is called the has

Cryptographic hash functions are a one-way hash functions. Used throughout cryptographic systems

  • many-to-one many inputs could create the output

hash collision two sets of input data that could create the same output

  • effectively impossible in Ethereum

Ethereum uses cryptographic hash functions to:

  • transform ethereum public keys into addresses
  • create digital finger prints (aid in verification of data)

properties of a hash function

  • determinism
  • verifiability computing hash is linearly complex
  • noncorrelation a small change to the message creates a large change in the output
  • irreversibility
  • collision protection this is important for Ethereum because it prevents people from forging digital signatures

Keccak-256

Ethereum’s cryptographic has function is called Keccak-256

Ethereum Addresses

unique identifiers - derived from public keys (or contracts)

  • we use keccak-256 to caculate the hash
  • then we keep the last 20 bytes

address formats

raw hex, no checksum. This can lead to problems if you mistype an address

Inter exchange Client Address Protocol

ICAP - Ethereum address encoding

  • partly compatible with the International Bank Account Number (IBAN) encoding
  • can encode addresses registered with an ethereum name registry