Cryptography

Cryptography is the practice of secure communication in an adversarial environment, with some encoding and decoding. Encryption is the process of transforming information in a way that (ideally) only authorised parties can decode, such that an intercepted message can’t be decoded.

We define:

• $P(M)$: encryption of a message $M$ to $C$.
• $S(C)$: decryption of an encrypted message $C$.

Basics

There are two main types of encryption. Symmetric encryption proposes that both parties agree on a single key. The sender has a plaintext message $M$ and uses the key to encrypt, then transmits it. The receiver then uses the same key to decrypt the message.

Obvious problem: what if the sender/receiver don’t meet physically? How do you securely exchange the key?

In asymmetric encryption, we use two keys: a public and private key. Hence, we also call this public-key cryptography. Here, the sender and receiver both have a set of public and private keys. A private key is possessed only by a single person. Here, the communication workflow is different:

• The sender signs the message with the public key of the receiver, then encrypts and sends the message.
• The receiver decrypts the message with their private key.

Unsorted notes

from special lecture by Prof Veneris

how to generate key pairs?

• relies on cryptography, essentially number theory. relies on idea that Prime factorisation is very difficult

RSA:

• select two very large primes $p,q$ (over 1000 bits; RSA with ~700 bits has been cracked already)
• compute $n=pq$
• compute $\phi (n)=(p-1)(q-1)$
• select small odd integer $e$, relative prime to $\phi (n)$
• compute $d$ such that $de\mathrm{mod}\phi (n)=1$, i.e., modulo fn == 1
• keys
  • public key $P=(e,n)$
  • secret key $S=(d,n)$
• basically: $n$ too large. so very hard to invert operation
• but RSA no longer really used, use elliptic curve cryptography

Ethereum

• vs Bitcoin
  • bitcoin has no programmability, based on a simple stack language
  • Ethereum written in Solidity, based on JavaScript
• Smart contract
  • Ethereum guarantees execution of the contract
  • as a Finite state machine
  • idea: charge per computation
  • trustless computer, all miners have to agree on state transitions

criticisms

• power: Bitcoin consumes a shit ton of power, more than the country of Austria consumes. Ethereum also has same problem
• proof of stake — stake down your own ether, verify transactions? idk
• scalability
  • per network
    • bitcoin: 3-7 trans/sec
    • eth: ~20
    • visa: 2000, can hit 20k at peak
    • paypal: 200
  • L1 network: Ethereum, bitcoin
  • L2 network: slightly separate, aggregate transactions, register back to L1 network
    • but not necessarily secure or decentralised

decentralised finance v centralised finance

• DeFi vs CeFi
• centralised: what we have now. idea: allows middlemen fees (ex with foreign currency exchanges), has delays (foreign transfers)
• decentralised: transparent, on chain. assets can be traded with absolute transparency

central bank digital currencies

• or just digital currencies
• like in China
• most govts studying them