sarcasticnastik / blockchain-experimentation

Code and notes for the course `Distributing Trust and Blockchain`

Blockchain Experimentation

Introductory Stuff

Cryptography

• RSA: Asymmetric Key Cryptosystems

  Check the implementation for more info. (check the notebook)

  ​ Problems:

• Birthday Paradox : In a room of $n$ people, alteast two people have birthday in a year of $d$ days on the same day? Ans: around $O(n)$.

Digital Signatures: Much like the signature on a currency.

A mathematical technique used to validate the authenticity and integrity of a message, software or digital document.

Digital signature scheme. A digital signature scheme consists of the following three algorithms: • (sk, pk) := generateKeys(keysize) The generateKeys method takes a key size and generates a key pair. The secret key sk is kept privately and used to sign messages. pk is the public verification key that you give to everybody. Anyone with this key can verify your signature. • sig := sign(sk, message) The sign method takes a message and a secret key, sk, as input and outputs a signature for message under sk. • isValid := verify(pk, message, sig) The verify method takes a message, a signature, and a public key as input. It returns a boolean value, isValid, that will be true if sig is a valid signature for message under public key pk, and false otherwise.
We require that the following two properties hold: • Valid signatures must verify: verify(pk, message, sign(sk, message)) == true. • Signatures are existentially unforgeable.

Discrete Log Problem

El' Gamal problem reduces to Discrete log problem. (So as computationally hard as the other one)

El' Gamal

$g$ -> Generator, large prime

• $h = g^x\ mod\ p$

Public Key: $$(h, g, p)$$

Secret Key: $(x, g, p)$

• Encryption: If a message $m$ ought to be sent,

  1. Choose random $y$ from (1, p)
  2. $S = h^y\ mod\ p$
  3. $c_2 = m \times s\ mod\ p$
  4. $c_1 = g^y\ mod\ p$

• Send $(c_1, c_2)$

• Decryption: $(c_1^x)^{-1}c_2$ is the decrypted message.

• Signature: $(r, s)$

  1. $$h = g^x\ mod\ p$$

  2. Select random $k$ from $(1, p - 1)$

  3. $r = g^k\ mod\ p$; $s = k^{-1} (m\ - xr)\ mod\ p$ (;;m is message here)

• Verification:

  $$\begin{align*} h^r r^s\ mod\ p &= g^{xr}(g^{k})^{k^{-1}(m - xr)}\ mod\ p\ &= g^{xr} \times g^{m - xr}\ mod\ p\end{align*}$$

Elliptical Curve Discrete Log Problem

$$x^2 / a^2 + y^2 / b^2 = 1\ mod\ p$$ given $(a, b)$

• Security provided by 168 bits ECDLP := by 1024bits El' Gamal

Cryptographic Hash Functions

The hash funtions work on inputs of arbitrary length. Luckily, as long as we can build a hash function that works on fixed-length inputs, there’s a generic method to convert it into a hash function that works on arbitrary-length inputs

• Merkle-Damgård transform: (Will consider SHA-256 while writing the following)
  • Compression Function : underlying hash function (working on a fixed-length input).
  • Divide the messages into blocks of fixed size, and consecutively compute the hash functions.
  • SHA-256 takes 768 bit input and gives 256 bit output.

Desirable Properties

• Deterministic, Efficient
• Difficult to find a message from its hash (pre-image resistance)
• Infeasible to find out two messages having same has (collision resistance)

Properties

$hash\ =\ H()$

1. Pre-image resistance :: Given $h$, difficult to compute $m = H^{-1}(h)$
2. Second pre-image resistance:: Given message $x$, difficult to compute $y$ s.t. $H(x) = H(y), x \ne y$.
3. Collision resistance:: Difficult to find $x$, $y$ s.t $H(x) = H(y)$.

Usage

• Distributing trust 😛
• Message Digest

Ex: SHA, SHA1, SHA2, RIPEMD.

Desirable properties of Cryptocurrency

• Decentralized
• Anonymous
• Mining not associated with any currency/ commodity (in real world)
• Should avoid double spending

Distributed Consensus

• Fischer-Lynch-Paterson Impossibility: Under some conditions, distributed consensus is impossible even with one single faulty node.

• Byzantine Generals Problem.

• Paxos: Never produces inconsistent results.(but assumptions are many)

• RAFT used now-a-days.

Bitcoin Consensus

• Broadcast transactions to all the nodes
• Each node collects new transactions into a block.
• A random node gets chance to write the ledger. It broadcasts this block.
• Nodes accept the blog, if they include it's hash in the next block they create.
• Longest chain is considered valid.

Selecting a random node

• Not using IP, cuz of Sybil attacks.
• Solving a crypto puzzle and select whoever solves it first.

Malicious Node

• Stealing
• DoS (Denial of Service)
• Double spending

Puzzles

Ex:- $$Find\ out \ a\ nonce\ s.t.: \ H(nonce || prev_hash || tx_1 || tx_2 || \ldots)\ \lt target$$

• Miner: Node which writes the next block.
• Block reward: Miner plays himself (using game theory just google :p)

Applications of BitCoin Scripts

1. Escrow Transactions:

   An escrow is a financial arrangement where a third party holds and regulates payment of the funds required for two parties involved in a given transaction.

2. Green Addresses:

3. Micro-payments:

Role of BitCoin Node

• Check the transaction inputs are in UTXO.
• Ensure transaction is not a double spending.
• Execute the o/p script of input transaction along with scriptSig.
• Broadcast the transaction.

TODO

• How Paxos work?

• Ethereum Reading List

• Libbitcoin (C++ library for bitcoin)

Checkout the wiki for the same. Found Cryptoeconomics part pretty sweet (ofc, for a noobda like me :p)