# How to store and use Bitcoin
- The primary challenge is how to store secret keys
- Goals:
- Availability
- security
- convenience
## Simplest approach: store key in a file, on your device
- Very convenient
- As available as your device
- device lost/wiped => key lost => coins lost
- As secure as your device
- device compromised => key leaked => coins stolen
## Wallet software
- nice trick: use a seperate address/key for each coin
- let wallet do the bookkeeping
### Encoding addresses
- Encode as test string: base58 notation
- QR code

## Hot storage / Cold storage
- Hot storage: online
- convenient but risky
- Cold storage: offline
- archival but safer

### Problem:
- We want to use a new address (and key) for each coin sent to cold storage. But how can hot wallet learn new addresses if cold wallet is offline?
- Hierarchical wallet

## Hierarchical key generation

## How to store cold info
1. Info stored in device, device locked in a safe
2. encrptt info under passphrase that user remembers
3. Paper wallet: print info on paper, lock up the paper
4. In "tamperproof" device: device will sign things for youm but won;t divulge keys

## Secret sharing
- Idea: split secret into N pieces, such that fiven any K pieces, can reconstruct the secret given fewer than K pieces, don't learn anything
- Example: N=2, K=2
- P = a large prime
- S = secret in [0, P)
- R = random in [0, P)
- split:
- $X_1=(S+R)mod\ P$
- $X_2=(S+2R)mod\ P$
- reconstruct:
- $(2X_1-X_2)mod\ P=S$
- Good: store shares separately, adversary must compromise several shares to get the key
- Bad: to sign, need to bring shares together, an d reconstruct the key

## Proof of Reserve
- Prove that the bank have at least X amount of reserve currency
- By creating a transaction of X amount to itself
- Prove that customers have at most Y amount deposited
- By exploring the merkel tree
- So reserve fraction $\ge$ X / Y

## Making a payment with Bitcoin

## Transaction fees
- transaction fee = value of inputs - value of outputs
- fee goes to miner who create the block
- 

## Supply & Demand