Show notes
So, here's my Top 100 snippets of knowledge for blockchain: Blockchains use public key methods to integrate digital trust. Bob signs for a transaction with his private key, and Alice proves this with Bob's public key. The first usable public key method was RSA — and created by Rivest, Shamir and Adleman. It was first published in 1979 and defined in the RSA patent entitled "Cryptographic Communications System and Method". Blockchains can either be permissioned (requiring rights to access the blockchain) or permissionless (open to anyone to use). Bitcoin and Ethereum are the two most popular permissionless blockchains, and Hyperledger is the most popular permissioned ledger. Ralph Merkle — the boy genius — submitted a patent on 5 Sept 1979 and which outlined the Merkle hash. This is used to create a block hash. Ralph Merkle's PhD supervisor was Martin Hellman (famous as the co-creator of the Diffie-Hellman method). David Chaum is considered as founders of electronic payments, and, in 1983, created ECASH, along with publishing a paper on "Blind signatures for untraceable payments". Miners gather transactions on a regular basis, and these are added to a block and where each block has a Merkle hash. The first block on a blockchain does not have any previous blocks — and is named the genesis block. Blocks are bound in a chain, and where the previous, current and next block hashes are bound into the block. This makes the transactions in the block immutable. Satoshi Nakamoto worked with Hal Finney on the first versions of Bitcoin, and which were created for a Microsoft Windows environment. Craig Steven Wright has claimed that he is Satoshi Nakamoto, but this claim has never been verified. Most blockchains use elliptic curve cryptography — a method which was created independently by Neal Koblitz and Victor S. Miller in 1985. Elliptic curve cryptography algorithms did not take off until 2004. Satoshi selected the secp256k1 curve for Bitcoin, and which gives the equivalent of 128-bit security. The secp256k1 curve uses the mapping of y²=x³ + 7 (mod p), and is known as a Short Weierstrass ("Vier-strass") curve. The prime number used with secp256k1 is ²²⁵⁶−²³²−²⁹−²⁸−²⁷−²⁶−²⁴−1. Satoshi published a 9-page paper entitled "Bitcoin: A Peer-to-Peer Electronic Cash System" White Paper on 31 Oct 31, 2008. In 1997, Adam Black introduce the concept of Proof of Work of Hashcash in a paper entitled, "Hashcash — a denial of service countermeasure." This work was used by Satoshi in his whitepaper. Satoshi focused on: a decentralized system, and a consensus model and addressed areas of double-spend, Sybil attacks and Eve-in-the-middle. The Sybil attack is where an adversary can take over the general consensus of a network — and leads to a 51% attack, and where the adversary manages to control 51% or more of the consensus infrastructure. Satoshi used UK spelling in his correspondence, such as using the spelling of "honour". The first Bitcoin block was minted on 3 Jan 2009 and contained a message of "Chancellor on brink of second bailout for banks" (the headline from The Times, as published in London on that day). On 12 Jan 2009, Satoshi sent the first Bitcoin transaction of 50 BTC to Hal Finney [here]. A new block is created every 7–10 minutes on Bitcoin. In Aug 2023, the total Bitcoin blockchain size is 502 GB. As of Aug 2023, the top three cryptocurrencies are Bitcoin, Ether, and Tether. Bitcoin has a capitalization of $512 billion, Ether with $222 billion, and Tether at $83 billion. The total cryptocurrency capitalisation is $1.17 trillion. The original block size was 1MB for Bitcoin, but recently upgraded to support a 1.5MB block — and has around 3,000 transactions. Currently the block sizes are more than 1.7MB. Bitcoin uses a gossip protocol — named the Lightning Protocol — to propagate transactions. A Bitcoin wallet is created from a random seed value. This seed value is then used to create the 256-bit secp256k1 private key. A wallet seed can be converted into a mnemonic format using BIP39, and which uses 12 common words. This is a deterministic key, and which allows the regeneration of the original key in the correct form. BIP39 allows for the conversion of the key to a number of languages, including English, French and Italian. A private key in a wallet is stored in a Wif format, and which is a Base58 version of the 256-bit private key. The main source code for the Bitcoin blockchain is held at https://github.com/bitcoin, and is known as Bitcoin core. This is used to create nodes, store coins, and transactions with other nodes on the Bitcoin network. A 256-bit private key has 115,792 billion billion billion billion billion billion billion billion different keys. A public Bitcoin ID uses Base58 and has a limited character set of '123456789ABCDEFGHJKLMN PQRSTUVWXYZabcdefghijkmno pqrstuvwxyz', where we delete '0' (zero), 'l' (lowercase 'l'), and 'I' (capital I) — as this can be interpreted as another character. In Bitcoin and Ethereum, a private key (x) is converted to a public key with x.G, and where G is the base point on the secp256k1 curve. An uncompressed secp256k1 public key has 512 bits and is an (x,y) point on the curve. The point starts with a "04". A compressed secp256k1 public key only stores the x-co-ordinate value and whether the y coordinate is odd or even. It starts with a "02" if the y-co-ordinate is even, otherwise it starts with a "03". In 1992, Eric Hughes, Timothy May, and John Gilmore set up the cypherpunk movement and defined, "We the Cypherpunks are dedicated to building anonymous systems. We are defending our privacy with cryptography, with anonymous mail forwarding systems, with digital signatures, and with electronic money." In Ethereum, the public key is used as the identity of a user (a.G), and is defined as a hexademical value. In Bitcoin, the public ID is created from a SHA256 hash of the public key, and then a RIPEMD160 of this, and then covered to Base58. In computing the public key in ECC of a.G, we use the Montgomery multiplication method and which was created by Peter Montgomery in 1985, in a paper entitled, "Modular Multiplication without Trial Division." Elliptic Curve methods use two basic operations: point address (P+G) and point doubling (2.P). These can be combined to provide the scalar operation of a.G. In 1999, Don Johnson Alfred Menezes published a classic paper on "The Elliptic Curve Digital Signature Algorithm (ECDSA)". It was based on the DSA (Digital Signature Algorithm) — created by David W. Kravitz in a patent which was assigned to the US. The core signature used in Bitcoin and Ethereum is ECDSA (Elliptic Curve Digital Signature Algorithm), and which uses a random nonce for each signature. The nonce value should never repeat or be revealed. Ethereum was first conceived in 2013 by Vitalik Buterin, Gavin Wood, Charles Hoskinson, Anthony Di Iorio and Joseph Lubin. It introduced smaller blocks, an improved proof of work, and smart contracts. Bitcoin is seen as a first-generation blockchain, and Ethereum as a second-generation. These have been followed by third-generation blockchains, such as IOTA, Cardano and Polkadot — and which have improved consensus mechanisms. Bitcoin uses a consensus mechanism which is based on Proof-of-Work, and where miners focus on finding a block hash that has a number of leading "0"s. The difficulty of the mining is defined by the hashing rate. At the current time, this is around 424 million TH/s. There are around 733,000 unique Bitcoin addresses being used. Satoshi defined a reward to miners for finding the required hash. This was initially set at 50 BTC, but was set to half at regular intervals. On 11 January 2021, it dropped from 12.5 BTC to 6.2 BTC. Bitcoin currently consumes around 16.27 GWatts of power each year to produce a consensus — equivalent to the power consumed by a small country. In creating bitcoins, Satoshi created a P2PKH (Pay to Public Key Hash) address. These addresses are used to identify the wallet to be paid and links to the public key of the owner. These addresses start with a '1'. In order to support the sending of bitcoins to and from multiple addresses, Bitcoin was upgraded with SegWit (defined in BIP141). The wallet address then integrates the pay-to-witness public key hash (Pay to script hash — P2SH). These addresses start with a '3'. Ethereum uses miners to undertake work for changing a state and running a smart contract. They are paid in "gas" or Ether and which relates to the amount of computation conducted. This limits denial of service attacks on the network and focuses developers on creating efficient code. Ethereum supports the creation of cryptocurrency assets with ERC20 tokens — and which are FT (Fungible Tokens). For normal crypto tokens (ERC-20) we use, there is a finite number of these, and each of these is the same. Ethereum creates NFTs (Non-Fungible Tokens) with ERC721 tokens. We mint these each time and each is unique. Solidity is the programming language used in Ethereum, while Hyperledger can use Golang, Node.js and Java. For Ethereum, we compile Solidity code into EVM (Ethereum Virtual Machine) code. This is executed on the blockchain. Blockchain uses the SHA-256 hash for transaction integrity. Ethereum uses the Keccak hash is used to define the integrity of a transaction. This is based on SHA-3, and differs slightly from Keccak. The Keccak hash family uses a sponge function and was created by Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche, and standardized by NIST in August 2015 as SHA-3. The DAO is a decentralized autonomous organization (DAO) for the Ethereum blockchain and was launched in 2016. In 2016, DAO raised $150 million through a token sale but was hacked and funds were stolen. This resulted in a forking of the blockchain: Ethereum and Ethereum Classic. Non-interactive Zero Knowledge Proofs (NI-ZKP) allow an entity to prove that they have knowledge of something — without revealing it. A typical secret is the ownership of a private key. NI-ZKPs involve a prover (Peggy), a verifier (Victor) and a witness (Wendy) and were first defined by Manuel Blum, Paul Feldman, and Silvio Micali in their paper entitled, "Non-interactive zero-knowledge and its applications". Popular ZKP methods include ZK-SNARKs (Zero-Knowledge Succinct Non-Interactive Argument of Knowledge) and ZK-STARKs (Zero-Knowledge Scalable Transparent Argument of Knowledge). Bitcoin and Ethereum are pseudo-anonymised, and where the sender and recipient of a transaction, and its value, can be traced. Privacy coins enable anonymous transactions. These include Zcash and Monero. In 1992, David Chaum and Torben Pryds Pedersen published "Wallet databases with observers," and outlined a method of shielding the details of a monetary transaction. In 1992, Adi Shamir (the "S" in RSA) published a paper on "How to share a secret" in the Communications of the ACM. This supported the splitting of a secret into a number of shares (n) and where a threshold value (t) could be defined for the minimum number of shares that need to be brought back together to reveal the secret. These are known as Shamir Secret Shares (SSS). In 1991, Torbin P Pedersen published a paper entitled "Non-interactive and information-theoretic secure verifiable secret sharing" — and which is now known as Pedersen Commitment. This is where we produce our commitment and then show the message that matches the commitment. Distributed Key Generation (DKG) methods allow a private key to be shared by a number of trusted nodes. These nodes can then sign for a part of the ECDSA signature by producing a partial signature with these shares of the key. Not all blockchains use ECDSA. The IOTA blockchain uses the EdDSA signature, and which uses Curve 25519. This is a more lightweight signature version, and has better support for signature aggregation. It uses Twisted Edwards Curves. The core signing method used in EdDSA is based on the Schnorr signature scheme and which was created by Claus Schnorr in 1989. This was patented as, a "Method for identifying subscribers and for generating and verifying electronic signatures in a data exchange system". The patent ran out in 2008. Curve 25519 uses the prime number of ²²⁵⁵-19 and was created by Daniel J. Bernstein. Peter Shor defined that elliptic curve methods can be broken with quantum computers. To overcome the cracking of the ECDSA signature from quantum computers, NIST are standardising a number of methods. At present, this focuses on CRYSTALS-Dilithium, and which is a lattice cryptography method. Bulletproofs were created in 2017 by Stanford's Applied Cryptography Group (ACG). They define a zero-knowledge proof as where a value can be checked to see it lies within a given range. The name of "bulletproofs" is defined as they are short, like a bullet, and with bulletproof security assumptions. While Bitcoin can take up to 7–10 minutes to mine a new block and create a consensus, newer blockchains, such as IOTA, can give an almost instantaneous consensus. Banks around the world are investigating CBDC (Central Bank Digital Currency) and which is not a cryptocurrency but a way to quickly define a consensus on a transaction. Homomorphic encryption methods allow for the processing of encrypted values using arithmetic operations. A public key is used to encrypt the data, and which can then be processed using an arithmetic circuit on the encrypted data. The owner of the associated private key can then decrypt the result. Some traditional public key methods enable partial homomorphic encryption. RSA and ElGamal allow for multiplication and division, whilst Pailier allows for homomorphic addition and subtraction. Full homomorphic encryption (FHE) supports all of the arithmetic operations and includes Fan-Vercauteren (FV) and BFV (Brakerski/Fan-Vercauteren) for integer operations and HEAAN (Homomorphic Encryption for Arithmetic of Approximate Numbers) for floating point operations. Most of the Full Homomorphic encryption methods use lattice cryptography. Some blockchain applications use Barreto-Lynn-Scott (BLS) curves which are pairing friendly. They can be used to implement Bilinear groups and which are a triplet of groups (G1, G2 and GT), so that we can implement a function e() such that e(g1^x,g2^y)=gT^{xy}. Pairing-based cryptography is used in ZKPs. The main BLS curves used are BLS12–381, BLS12–446, BLS12–455, BLS12–638 and BLS24–477. An accumulator can be used for zero-knowledge proof of knowledge, such as using a BLS curve to create to add and remove proof of knowledge. Open Zeppelin is an open-source Solidity library that supports a wide range of functions that integrate into smart contracts in Ethereum. This includes AES encryption, Base64 integration and Elliptic Curve operations. Metamask is one of the most widely used blockchain wallets and can integrate into many blockchains. Most wallets generate the seed from the operating system and where the browser can use the Crypto.getRandomValues function, and compatible with most browsers. Solidity programs can be compiled with Remix at remix.ethereum.org. The main Ethereum network is Ethereum Mainnet. We can test smart contracts on Ethereum test networks. Current networks include sepolia.etherscan.io and goerli.net. Ether can be mined for test applications from a faucet, such as faucet.metamask.io. This normally requires some proof of work to gain the Ether — in order to protect against a Denial of Service against the Faucet. The private key can be revealed from two ECDSA signatures which use the same random nonce value. Polkadot is a blockchain which allows blockchains to exchange messages and perform transactions. The proof of work method of creating is now not preference because of the energy that it typically uses. Many systems now focus on proof of stack (PoS). A time-lock puzzle/Proof of Work involves performing a computing task which has a given cost and which cannot be cheated again. This typically involves continual hashing or continual squaring. The Chia blockchain network uses both Proof of Space (PoS) and Proof of Time (PoT). The PoS method makes use of the under-allocation of hard-disk space. With a Verifiable Delay Function (VDF), we can prove that a given amount of work has been done by a prover (Peggy). A verifier (Victor) can then send the prover a proof value and compute a result which verifies the work has been done, with the verifier not needing to do the work but can still prove the work has been done. A Physical Unclonable Functions (PUFs) is a one-way function which creates a unique signature pattern based on the inherent delays within the wireless and transistors. This can be used to link a device to an NFT. In Blockchain applications, we can use Non-interactive zero-knowledge (NIZK) proofs for the equality (EQ) of discrete logarithms (DL) — DLEQ. With this — in discrete logarithms — we have 𝑎=𝑔^x and 𝑏=ℎ^x and can prove the knowledge of x by showing that log_𝑔(𝑎)=log_ℎ(b).