Hash

• Money / A token can be valuable because we think it is valuable

• A cryptocurrency is a digital or virtual currency that is secured by cryptography, which makes it nearly impossible to counterfeit or double-spend.

• A defining feature of cryptocurrencies is that they are generally not issued by any central authority, rendering them theoretically immune to government interference or manipulation.

Money

• pros of banks: digital payments, maintain the balance

• cons of banks: 1. bank must be online 2. bank can fail 3. bank can delay 4. privacy

E-cash

• should make sure that people can’t copy the coins

• the bank keeps a serial number, make sure that it’s the same coin after transaction

• pros of simple e-cash : digital payments, peer-to-peer

• cons: 1. bank needs to be online 2. bank can fail 3. privacy 4. bank can delay or censor transactions

Chaumian e-cash

• Alice can choose serial number (SN)

• Alice adds some random noise to the SN to the bank so bank can’t see SN

• when Bob redeems, bank doesn’t know payment came from Alice

• if Alice give the same coin to two people (double spent), bank would know it was Alice, then she would be punished.

• Alice gives a coin to Bob, the coin holds both SN and sig(SN), the bank makes sure that each SN is seen once

• pros：digital, peer-to-peer, privacy, offline double-spend detection

• cons: bank can censor withdraw transactions

Hash functions:

1. data can be any size, output is fixed size & “random” looking
Hash function with n bit output is referred to as an n-bit hash function
“Avalenche effect” : change 1 bit of the input, about half the output should change

1. properties:

• preimage resistance
• given y, you can’t find any x such that hash(x) == y

• 2nd preimage resistance
• given x, y, such that hash(x) == y, can’t find x’ ≠ x, where hash(x’)==y

• collision resistance （ harder ）
• nobody can find any x, z such that x ≠ z, where hash(x) == hash(z)

1. usages:

1. Commit reveal

1. signature ( a message signed by someone ):

• GenerateKeys()
• returns a privateKey, publicKey pair
• takes in only randomness
• public key : your identity
• secrete key : only you control, prove your identity

• Sign( secreteKey, message )
• signs a message given a secreteKey

• Verify( publicKey, message, signature )
• verify a signature on a message from a public key. returns a boolean

• Generate Key

• Sign

• verify