Fields

• Define a field just for two operations
• A field is a set of integers with two operations
• Division is tricky because if we divide two integers we get may get a float

zk Ecosystem

• stark system came out in 1976
• ZKSNARKS have small proofs but require an initial setup and are not quantum resistant
• STARKS are quantum resistant and don't require a trusted setup

Rollups

• transaction execution is done outside layer 1
• data or proof of transaction is on layer 1 (incl. state transitions)
• Verifier is a contract on layer 1 and can secure the latest state
• zero knowledge proofs can be done recursively
  • a proof to prove 100 proofs are valid
  • layer 3 and layer 4 -> can create specific applications on each layer

Starknet Specifics

• Account abstraction: your account is a contract
• Cairo language: prove the correctness of the computation
• Hints: pass the value that we want to prove into the programme as a hint (using python)
• range_check_ptr: to make sure things haven’t overflowed
• No loops in cairo, use recursion
• Validium mode: data is stored off chain
• Volition mode: hybrid mode, data is stored off chain and on chain